arXane › Physics
Wednesday, 4 November 2026: 29 new papers, 18 cross-lists and 27 replacements in General Relativity and Quantum Cosmology (gr-qc), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
In this paper, we establish the nonlinear stability of the Schwarzschild exterior for the spherically symmetric Einstein-massless Dirac system. More precisely, we consider sufficiently small perturbations of Schwarzschild characteristic initial data and prove that the corresponding maximal development remains globally controlled in the exterior region (orbital stability), and converges, in a suitable teleological double-null gauge, to a Schwarzschild spacetime with a final mass (asymptotic stability). In particular, the maximal future development contains a complete future null infinity and a regular event horizon, with a nonempty black hole region in its interior. The main difficulties in the proof arise from the delicate coupling between the Dirac operator and the geometry, compared with the scalar wave counterpart, as well as from the failure of the Dirac stress-energy tensor to satisfy a positive energy condition. To overcome these difficulties, we rely on a bootstrap argument coupling the geometry and the Dirac field. Working in suitable teleological double-null gauges adapted to the asymptotic null boundaries, we establish weighted energy estimates combining integrated local energy decay, red-shift estimates near the event horizon, and an rp-estimates towards null infinity. A core ingredient is the use of suitable reweightings of the spinor components, which allow us to close these estimates despite the nonlinear coupling to the geometry.
We develop a gauge-invariant teleparallel framework in which the universality of the gravitational coupling is relaxed for a scalar field, while the gravitational sector retains the form of the teleparallel equivalent of General Relativity. The non-universal interaction is encoded in a scalar-sector tetrad whose coupling to the universal translational gauge potential is controlled by a field-dependent gravitational charge. A St\"uckelberg completion preserves local translational gauge invariance, and we derive the gravitational, scalar-field, and St\"uckelberg equations, together with the antisymmetric constraint and their consistency relations. As a first application, we investigate homogeneous and isotropic cosmology, where the St\"uckelberg constraint provides a first integral governing the evolution of the non-universal coupling. In the kination-dominated regime, the standard stiff-fluid behavior is recovered asymptotically, whereas in the potential-dominated regime, accelerated expansion requires additional conditions beyond potential domination. We identify compatible expanding solutions in which departures from universality are dynamically suppressed, including examples approaching power-law inflation or asymptotically de Sitter expansion. Including a universally coupled perfect fluid and a constant scalar potential, we obtain a late-time solution exhibiting a subdominant matter-like contribution to the background Friedmann equation and an asymptotic de Sitter limit. These results provide a gauge-theoretic realization of non-universal scalar couplings and highlight their potential implications for early- and late-time cosmology.
We develop a reference-renormalized Jacobi-primitive Gauss-Bonnet formalism for finite-distance weak deflection of massive particles in static, spherically symmetric spacetimes. The construction uses the fixed-energy Jacobi metric associated with timelike geodesics and treats the radial curvature primitive as a quantity defined only up to an additive constant. Instead of fixing this constant by requiring the primitive to vanish at a circular timelike orbit, we subtract a reference Jacobi geometry at the same conserved particle energy and impose endpoint normalization on the curvature-density discrepancy. This gives a circular-orbit-free primitive representation of the Gauss-Bonnet curvature contribution while preserving the operational finite-distance definition of the bending angle through local source and receiver directions. We prove that the reference-normalized and circular-orbit-normalized prescriptions agree whenever both are admissible, since their primitives differ only by a constant that cancels from the exact curvature strip integral. The method remains applicable when no admissible circular timelike orbit exists, when the orbit lies outside the Riemannian Jacobi domain, or when the natural no-lens comparison geometry is non-Euclidean. We demonstrate the formalism in three representative settings: Schwarzschild-like bumblebee, Kottler, and Janis-Newman-Winicour (JNW) spacetimes. The formalism therefore identifies circular-orbit anchoring as an auxiliary primitive gauge choice rather than a prerequisite for finite-distance Jacobi Gauss-Bonnet deflection.
We study circular null orbits, thermodynamic topology, and the holographic thermodynamic description of a four-dimensional magnetically charged AdS black hole in nonlinear electrodynamics. The background orbit structure is classified using Duan s phi-mapping construction and compared with the extraordinary electromagnetic characteristics. The latter defines an effective optical metric with an additional radial factor that modifies the orbit condition and introduces explicit dependence on the AdS radius. For four representative configurations, the local indices of the five isolated orbits are unchanged while their radii shift by up to 5.187 %. The background mass thresholds vary smoothly across sigma = 1/4 when the total mass is used, whereas the fixed-m0 parametrization is singular there. Regularity at the center requires sigma > 1 and m0 = 0. The thermodynamic analysis separates local stability indices from equilibrium coexistence: stable Gibbs-free-energy branches cross only in model-dependent parameter intervals. The boundary canonical ensemble exhibits critical behavior consistent with mean-field exponents, and the examined grand-canonical ensemble has a Hawking-Page crossing. In the mixed ensemble, the free-energy branches have a finite endpoint discontinuity, but the sampled competing states do not satisfy the full local-stability criterion
We prove the nonexistence of non-rotating and degenerate horizon components in the stationary, asymptotically flat, $I^+$-regular, analytic vacuum spacetime. This result rules out the final case in the classification of stationary analytic black-hole spacetimes. Consequently, the stationary, asymptotically flat, $I^+$-regular, analytic vacuum black hole uniqueness conjecture is settled affirmatively in full.
We show that the convergence region of the QNM representation of the retarded Green's function of the Kerr spacetime is set by complex-time bouncing singularities, as in our previous work for the Schwarzschild case. The main difference between Kerr and Schwarzschild is that there are two distinct QNM families, prolate and oblate, which have different convergence regions. We provide explicit analytical formulae for the bounce radii and corresponding convergence regions in Boyer-Lindquist coordinates. We also provide an analysis of convergence in the Reissner-Nordstr\"om spacetime.
We construct electrically charged black holes in Einstein's gravity coupled to the bosonic sector of the electroweak theory, focusing on static, spherically symmetric and asymptotically flat solutions, with the weak mixing angle fixed to its Standard Model value. Horizon regularity imposes a resonance condition relating the charged-vector frequency to the electromagnetic potential at the horizon, corresponding to the threshold of charged superradiance. A perturbative analysis further shows that nonextremal Reissner-Nordstr\"om black holes do not support regular, exponentially localized, spherically symmetric electroweak clouds satisfying such condition. Thus, the hairy solutions cannot emerge via a bifurcation from this electrovacuum family. Moreover, our numerical investigation reveals two apparently disconnected families of bosonic stars. Within the explored parameter space, the hairy black holes are connected to the strongly gravitating one.
We solve the frequency-domain, $m$-mode Teukolsky equation for the spin-weight $s=-2$ Weyl scalar $\psi_4$ sourced by a point mass on a circular, equatorial orbit around a Kerr black hole. The equation is posed on hyperboloidal slices that reach the event horizon and future null infinity, so that the physical (retarded) solution is selected by regularity alone, without imposing radiation conditions. The particle is treated with the $m$-mode puncture/effective-source scheme, and the resulting two-dimensional elliptic problem is solved with a four-domain pseudo-spectral method in which the equatorial symmetry is broken and handled by an even/odd decomposition of the field. We test the method for orbital radius $r_0=10M$ and spins up to $|a|/M=0.9$, covering prograde and retrograde orbits. The energy fluxes to infinity agree with independent Black Hole Perturbation Toolkit results to $\sim10^{-7}$ for the dominant modes and to better than $2\times10^{-5}$ for all modes up to $m=20$ at moderate resolutions. The static $m=0$ mode requires no special treatment.
We present a calculation of the first-order metric perturbation arising from a point mass moving on a circular, equatorial orbit in Kerr spacetime. The metric perturbation is specifically aimed at meeting the requirements of second-order self-force theory: it is highly accurate; incorporates all contributions, including those associated with perturbations to the black hole's mass and angular momentum; is in Lorenz gauge near the worldline and in (near) Bondi--Sachs gauge at large radius; and can be efficiently evaluated across the entire exterior spacetime. The Lorenz gauge gives a well-understood singular structure at the particle, while the (near) Bondi--Sachs gauge ensures the asymptotic fall-off needed for an asymptotically flat second-order source. Our formalism reconstructs the metric from separable Teukolsky-type equations, decomposed into spin-weighted spheroidal harmonic modes and solved spectrally on hyperboloidal slices. The resulting $(\ell,m)$-mode sums converge rapidly across most of the domain, but slowly near the point mass; we overcome this with a novel use of a puncture to extract accurate $m$-mode data, yielding output accurate to $\sim 10^{-10}$ per $m$-mode and suitable for use at second order. Our metric-perturbation results cover a range of Kerr spins $-0.9 \le a/M \le 0.9$ and orbital radii out to $50M$. In addition to its immediate application in second-order self-force calculations, our results can also be used as input to other calculations involving Kerr metric perturbations, including studies of environmental effects and quasinormal modes.
We investigate the quasinormal modes (QNMs) and time-domain response of a massless, minimally coupled test scalar field on static, spherically symmetric covariant loop quantum black hole (cLQBH) backgrounds. Focusing on a phenomenological, Gaussian-localized holonomy profile, we obtain a localized deformation of the scalar effective potential containing both positive and negative parts. This provides a geometric realization of the bump effect, with the potential deformation and tortoise-coordinate mapping determined consistently by the same background. We characterize the deformation by its location, amplitude, and width, and study its effects using frequency-domain shooting and time-domain evolution, supplemented by matrix-pencil mode extraction and waveform reconstruction. The QNM spectrum exhibits spiral trajectories as the bump location varies, enhanced sensitivity of the overtones, and mode overtaking, whereby the branch continued from the first Schwarzschild overtone becomes longer-lived than the continued fundamental branch. Despite substantial spectral changes, the early response can remain close to its Schwarzschild counterpart, with more pronounced differences emerging later. To quantify this behavior, we introduce a local waveform-deviation time and compare it with a relative-amplitude faintness time, thereby defining an operational observation window. The deviation time depends nonmonotonically on the bump location, and suitable parameter choices allow appreciable departures to emerge before the adopted faintness threshold is reached. These results connect localized holonomy corrections with spectral sensitivity and waveform evolution, providing a basis for future gravitational-perturbation studies and assessments of gravitational-wave detectability.
The Laser Interferometer Space Antenna (LISA) is expected to observe gravitational-wave signals from massive black hole binaries, extreme mass ratio inspirals, and more. Despite the significant scientific potential, accurately extracting these signals from the data will only be possible if LISA's instrumental noise is understood: poor noise modelling will result in lost signals, biased parameter estimates, and incorrect astrophysical insights. Modelling LISA's instrumental noise is more challenging than its ground-based counterpart since the data is highly correlated, meaning that the noise covariance matrix can no longer be assumed diagonal in frequency and in the different data streams. In this work, we present an initial approach to perform non-parametric noise inference for LISA that requires no prior knowledge of the LISA observatory. By fitting the full noise covariance matrix with a combination of splines and inverse Lorentzians, we show that our model can estimate the power and cross spectral densities for LISA from 7 days of simulated noise-only data. We find that the median estimate from our non-parametric model whitens the data according to the expected unit normal distribution. We envision that our non-parametric model can be used as part of the global fit, as well as in combination with modelled approaches to identify, quantify, and constrain the frequency dependence of unknown noise artifacts.
We study fully non-linear binary black hole mergers in massive Einstein-scalar-Gauss-Bonnet (EsGB) gravity with a linear Gauss-Bonnet coupling function. In the absence of a well-developed initial data solver for EsGB gravity, we demonstrate that the conventional workaround solution for massless scalar fields results in confined junk radiation that contaminates late-time dynamics in the massive theory. We propose a solution to this problem by suitably modifying the equations of motion at the early stages of the simulation to tame such junk radiation, thereby allowing us to study the dynamics of the scalar field during the process of a black hole merger. This is followed by a preliminary analysis of the frequency content in the ringdown of the scalar and tensor modes. In particular, the quadrupole scalar mode exhibits a rich ringdown structure: while it is dominated by the spin-2 ``contamination'' frequency in the early stages, its late time morphology becomes primarily determined by the scalar mass frequency.
The next generation of an international network of gravitational-wave observatories is now in the advanced planning stages. With Australia's substantial history of contributions in this field, its history of scientific mega-projects like the Square Kilometer Array, and its unique geographic location and conditions, it is ideally placed to host an observatory in the global network. It has already been demonstrated that a gravitational wave detector in Australia plays an important role in minimizing the sky localization uncertainty of gravitational wave events. We study a particular science case for an Australian observatory, focusing on its potential contributions to multimessenger astronomy. We demonstrate that an observatory in Australia can enable the detection of up to eight multimessenger gravitational-wave plus kilonova events per year, with localisations better than $1-10\deg^2$ in both second- and third-generation networks. We show that, in a global network of XG observatories, an Australian observatory with 2G sensitivity would still enable significant advances in multimessenger science. The full case for an Australian observatory must be considered in a much broader context; however, this work indicates it could make substantial contributions to multimessenger astrophysics.
We develop a systematic complex representation of Lorentzian relativity based on the imaginary temporal coordinate $X^0=ict$. Rather than treating this substitution as a Wick rotation to Euclidean spacetime, we formulate it as an invertible change of representation in which physical spacetime is identified with a real subspace of a complex vector space. This construction introduces two related metric structures: a complex-bilinear form and a Hermitian form, both of which reproduce the original Lorentzian interval when restricted to physical spacetime. We extend the representation to relativistic dynamics, including proper time, four-momentum, and the Hamilton-Jacobi formulation, and show that the metric, connection, curvature tensors, Einstein equations, and conservation laws retain their conventional content in curved spacetime. Explicit applications to the Kerr and Friedmann-Lema\^itre-Robertson-Walker geometries demonstrate consistency for rotating and time-dependent spacetimes. We further examine relativistic wave equations and their nonrelativistic limit, showing how the Schr\"odinger equation and its relation to Euclidean-time evolution emerge within the same complex temporal framework. The resulting formulation introduces no new physical predictions, but clarifies the geometric role of imaginary temporal coordinates and reveals structural connections among relativistic geometry, action, wave propagation, and analytic continuation.
Regular black holes (RBHs) are often constructed with a regular point-like center and two horizons, including an inner Cauchy horizon susceptible to mass inflation. We show that a two-horizon structure is not a necessary consequence of regularity. For static, spherically symmetric geometries with an asymptotically static exterior, we establish a horizon-parity theorem: a regular point-like center requires an even number of sign-changing zeros of $f$. We then construct two classes of single-horizon RBHs with a finite-area core, distinguished by whether the horizon lies outside the core or coincides with it, and analyze their matter content, energy conditions, and thermodynamic properties. The absence of an inner Cauchy horizon eliminates the classical mass-inflation mechanism on the single-horizon patch. We further establish mode stability against scalar perturbations for these finite-area-core configurations by showing that the effective potential is non-negative. Our results establish how the central geometry and asymptotic structure constrain horizon multiplicity and identify single-horizon configurations that avoid the classical inner-horizon instability.
We simulate the propagation and scattering of an incident plane scalar wave in the spacetime of an ultracompact, horizonless constant-density star using a time-domain multipole mode-sum method. By reconstructing the coherently superposed time-domain waveforms, we compare the star's dynamical response with that of a Schwarzschild black hole. We find that the early-time response closely mimics a black-hole ringdown due to wave scattering near the exterior unstable photon sphere. Conversely, the late-time signal develops a sequence of delayed echoes originating from wave trapping near the interior stable light ring and subsequent leakage through the exterior potential barrier. While individual multipoles exhibit regular echoes, their coherent superposition induces interference, producing complex waveforms with irregular profiles that nonetheless retain an underlying temporal organization with alternating peak separations. Finally, as a proof of concept, we perform a signal-to-noise ratio analysis using an assumed strain normalization, demonstrating that these weak, late-time signatures can be resolved by third-generation gravitational-wave detectors.
Mass inflation in non-extremal regular black holes with a non-linear dependence of the Misner-Sharp mass $M$ on the asymptotic mass $m>0$ may be a transient phenomenon followed by a model-dependent non-exponential late-time divergence. We analyse these regimes based on the generalised Ori model for a class of static spherically symmetric and asymptotically flat regular black holes with a de Sitter core and an $m$-independent upper bound on the Misner-Sharp mass density and Kretschmann scalar inspired by quasi-topological gravity. We discuss the geometric mechanism behind divergences of physical quantities at the inner horizon of the perturbed spacetime, and show that these require the unphysical mass parameter inside the shell to evolve outside the positive-real domain, or in some cases force a distinct type of dynamical continuation of the static metric. Imposing an asymptotic late-time divergence in form of a fractional power-law scaling, tunable to be arbitrarily mild within the considered approximation and effectively taming mass inflation, allows us to single out a family of generalised Fan-Wang regular black holes.
In the recent paper arXiv:2504.02253 we generalized classical Isaacson's procedure for describing back-reaction of the averaged energy-momentum for high frequency gravitational waves to $f(R)$ gravity case with a choice of the de Sitter background. To describe this second order effect we used standard first order decomposition of metric tensor. In this paper, we take into account possible contribution to this process from second order term in metric tensor decomposition. We find that on the de Sitter background all possible contributions from this term are strongly suppressed and therefore results obtained in the paper arXiv:2504.02253 are left unchanged.
This article examines the instability of charged black holes, using Einstein-Maxwell-dilaton theory and a massless charged scalar field. Our study demonstrates that these black holes become unstable in a certain range of frequencies, which causes scalar "hair" to form outside the event horizon. By using numerical integration on the coupled field equations, we show that there is a phase transition between a purely charged black hole and a hairy black hole configuration. The results show that the hairy phase appears when the temperature is less than $T_C$, the critical temperature, whereas for $T>T_C$, the system stays purely charged. Also, our findings show that the critical temperature increases with the size of the black hole, implying that the onset of the phase transition becomes progressively more difficult for larger horizons. Lastly, we see that the system enters a stable equilibrium at the critical temperature, which is the final state of the superradiant instability. These results provide us with useful information on how nonlinear superradiant events change and how scalarized black holes arise in more comprehensive theories of gravity.
The astrophysical discovery potential of future gravitational wave detectors will hinge on accurate and rapid waveform generation. Third generation detectors are expected to observe many long duration compact binary coalescence signals that can probe binary formation and evolution as well as the nature of matter under extreme conditions. We develop a unified framework that combines physical modeling with deep learning. The framework uses an analytic residual spectral representation, shared learning, and decoders for each binary type. It generates waveforms for binary black holes, binary neutron stars, and neutron star black hole binaries, providing a single unified generator for all compact binary coalescences. The generated waveforms include the physical effects described by each reference model, such as spin precession, higher order modes, matter effects, and postmerger radiation for binary neutron stars. The waveforms span hundreds to thousands of cycles, with mean mismatches ranging from $5.89\times10^{-4}$ to $5.34\times10^{-2}$ relative to the reference waveforms. Batch generation achieves a maximum speedup of about 1800 over reference waveform generation.
In this paper, we establish an analytical correspondence between the equatorial dynamics of spinless and spinning test particles in a slowly rotating charged Einstein--Bumblebee black hole spacetime and those in an effective Kerr--Newman spacetime. For spinning particles, the correspondence is established within the Mathisson--Papapetrou--Dixon framework under appropriate parameter matching. We show that corresponding circular orbits have identical radii and coordinate angular velocities, while their radial dynamics and local instability rates exhibit a Lorentz-violation-dependent scaling. Nevertheless, the correspondence does not imply complete dynamical equivalence, as orbital trajectories and radial perturbation growth over an azimuthal period generally differ. These results delineate the scope and limitations of the effective Kerr--Newman correspondence by distinguishing the dynamical properties preserved under parameter matching from those modified by the Lorentz-violating radial deformation.
We study the $SU(2)$ Einstein-Yang-Mills system with non-minimal $RF^2$-type couplings of Yang-Mills fields to curvature, formulated with exterior differential forms and a Lagrange-multiplier constraint for the Levi-Civita connection. We show that the conformally flat Bertotti-Robinson geometry $AdS_2\times S^2$ carries the Wu-Yang magnetic pole as an exact solution for arbitrary non-minimal couplings; the couplings only renormalise the radius of the $S^2$. The non-conformally-flat branch of solutions known for this system is recalled. The Hopf fibration $S^3/S^2\cong S^1$ of the gauge group manifold projects the Wu-Yang field on a uniform Dirac-type magnetic field, and the motion of a point electric charge in it is solved in closed form: the charge moves on a cone and oscillates between the horizon and a maximal radius.
We construct the leading mixed-order $\mathcal{O}(\zeta_{\rm GB}\zeta_{\rm CS})$ deformation of rotating black holes in a combined scalar Gauss-Bonnet and dynamical Chern-Simons effective theory, the sector in which the parity-even and parity-odd corrections act simultaneously. Using a pseudospectral solution of the coupled mixed scalar and metric equations, we compute horizon and equatorial-geodesic observables--the horizon angular velocity, surface gravity, area, and Wald entropy; the innermost stable circular orbit and photon-ring radii; and photon-ring eikonal estimates of the ringdown--at fixed mass and angular momentum over the spin range $0.1\le a\le0.9$, where the solution is numerically convergent and the perturbative expansion is controlled for sufficiently small dimensionless couplings. We verify the exact Kerr and Schwarzschild limits, reproduce available pure-sector benchmarks, and quantify spectral, residual, and extraction uncertainties. The mixed solution satisfies every component of the field equations, including the one that is not imposed in its construction, and its Wald entropy satisfies the first law to about one part in $10^{5}$. The mixed coefficients exhibit spin dependence qualitatively distinct from the individual sectors within this EFT truncation. All four horizon quantities, and several orbital and eikonal ones, change sign as functions of spin. The ringdown results are leading photon-ring eikonal estimates; a full coupled finite-$\ell$ perturbation calculation is left to future work.
In this work, the weak-field dynamics of a gravitational-wave compatible subclass of Horndeski gravity is investigated on galactic and intergalactic scales. The analysis is performed within the weak-field approximation for stationary and approximately spherically symmetric configurations, retaining the nonlinear scalar derivative interactions responsible for scale-dependent modifications of the gravitational field. On galactic scales, the transition regime is investigated through the effective potential, the stability of circular orbits, galaxy rotation curves, and the relation between dynamical and lensing masses. The analysis shows that the scalar field modifies the orbital dynamics and the radial dependence of the rotational velocity, while generating a nonvanishing gravitational slip between the dynamical and lensing mass estimates. On intergalactic scales, the asymptotic weak-field dynamics is investigated and a turnaround scale is derived from the balance between the effective gravitational attraction and the large-scale curvature contribution. At large distances, the asymptotic gravitational field is governed by the background curvature contribution.
Gravitational waves (GWs) can have wavelengths comparable to the Schwarzschild radius of their lenses, and detectors record their phase, so lensing requires wave optics. Its standard tool, the diffraction integral, follows from the particle path integral of a scalar wave on a static weak field, under the eikonal (one-way) and paraxial approximations, plus the thin-lens limit. We give a self-contained account of how the proper-time (worldline) representation overcomes these steps. An auxiliary proper time makes the wave equation exactly first order, with frequency as $1/\hbar$, so geometric optics and, for paraxial thin-lens paths, the diffraction integral follow from stationarity of an exact integral. For a point mass, the Duru-Kleinert (DK) gauge and Kustaanheimo-Stiefel map give the exact propagator; for a distant observer the DK time and fibre angle become the radius and azimuth of a lens plane, the result is the point-lens amplification factor with the offset set by the excess path, and geometric optics requires $w\gg1$ and $wy\gg1$. This agreement reflects the Coulomb potential, not the approximations: the exact eikonal condition, $\varepsilon_E\simeq\bar\lambda/d+GM/c^2d+\mathcal O(\sin^2\theta/2)$, fails near the lens and at large angles, and the one-way step is a non-relativistic limit. We then treat the bound lens, a GW source orbiting its lens, which emits a backscattered echo and moves during the lensing delays. Its exact time-domain signal gives each worldline its own retarded time and Doppler factor, so no single amplification factor describes it. In the diffraction regime the Shapiro phase alone misses all lensing beyond it, geometric optics misses 46-100% of it near conjunction at $w=0.3$, the paraxial geometry fails on the far side, and the static amplification factor along the orbit errs by $\approx(1-2)\,wM/R$ near conjunction and by the echo amplitude elsewhere.
We study excitation factors and investigate exceptional points (EPs) of Kerr--Newman quasinormal modes using the exact separated gravitoelectromagnetic equations. At fixed charge, the magnitudes of the excitation factors for the gravitational-led modes studied here decrease with increasing spin, whereas those for electromagnetic-led modes exhibit both monotonic and nonmonotonic behavior. The magnitude of the excitation factor for the first overtone can be comparable to or larger than that for the fundamental mode. We identify 42 EPs at which pairs of modes coalesce in the gravitational-led and electromagnetic-led sectors. Some EPs form sequences involving successive overtone pairs, with higher-overtone pairs coalescing progressively closer to the extremal limit. The additional EPs identified outside these sequences all share the same mode-pair labels as sequence members, but occur at different values of the black hole spin and charge. These findings clarify how rotation and charge shape the relative excitation strengths of different modes and the pattern of mode coalescence in the non-Hermitian spectrum of Kerr--Newman black holes.
We derive fully analytic overlap reduction functions for the full-Stokes response of a pulsar timing array to an anisotropic tensor gravitational-wave background in general relativity. The response retains both pulsar distances and their complete propagation phases. At each fixed finite sky multipole, the intensity and circular polarization responses reduce to finite combinations involving exponential integrals and logarithms, while the electric and magnetic linear polarization responses require only elementary functions. We evaluate all components through $\ell=8$. Symmetry separates exact nulls from additional Earth-term nulls that propagation can lift. Even an unpolarized background can produce an imaginary cross-spectrum. For a pair with three-dimensional separation $d$, the pulsar terms can remain coherent when $2\pi fd/c\lesssim1$, even if both pulsars are many wavelengths from Earth. A uniform approximation retaining all four Earth and pulsar terms connects this regime to the short-wavelength limit, and a rotationally invariant relation fixes the leading transverse magnetic response. Common-distance errors cancel from the aligned pair phase, while relative-depth errors directly affect coherence. Under Gaussian differential averaging, fixed low-multipole norms and the squared norm summed over all multipoles decay at different rates as the response shifts to higher multipoles. Published pulsar configurations illustrate the roles of distance accuracy, bandwidth, and timing fits. At fixed pointwise intensity, a polarization covariance bound and a relative-depth noise budget quantify when differencing suppresses the background. Independent sky integration and matched-accuracy benchmarks test the analytic expressions over the parameter ranges studied.
We study self-gravitating configurations of a charged classical spinor field coupled to gravity and to Euler-Heisenberg (EH) nonlinear electrodynamics, truncated at quartic order. The spinor is gauged under a U(1) field and may carry a quartic self-interaction. For static and spherically symmetric configurations we derive the field equations, reduce them to a dimensionless eigenvalue problem for the spinor frequency and solve it numerically. In the uncharged limit our solutions coincide with the known Dirac stars of general relativity. The electric charge increases the frequency, the mass and the size of the stars, and the maximal mass grows from $0.709$ to $1.027$ (in units of $M_{\rm Pl}^2/\mu$) when the charge coupling rises from zero to $0.75$. The quartic term changes the relation between the electric field and the enclosed charge, so that the field inside the star is weaker than in the Maxwell case. Our central result concerns stars with the same number of fermions, and therefore the same total charge. For them the quartic term changes the mass by less than $0.2\%$, but it makes the stars more compact and more strongly bound and shifts the turning point of the family to a smaller particle number. This shift is what lowers the maximal mass, by $9\%$ (from $0.924$ to $0.840$) at charge coupling $0.6$ as the dimensionless EH coupling goes from zero to $200$. In the weak-field regime of quantum electrodynamics (QED) the relative mass correction is $-1.5\times10^{-5}(E_{\max}/E_c)^2$, so the larger couplings describe the quartic model as an effective nonlinear electrodynamics rather than a controlled QED correction. All solutions satisfy the null, weak, strong and dominant energy conditions, show a positive pressure anisotropy, and remain free of horizons. Their stability is discussed through the binding energy and the turning point of the mass curve.
Gravitational self-force calculations are needed to accurately describe the motion of a small body in a spinning (Kerr) black hole spacetime, which is vital to predict gravitational wave signals from asymmetric-mass compact binaries. Accurate calculations for the upcoming LISA mission require a minimum of second perturbative order in the mass ratio, which has thus far only been achieved for nonspinning (Schwarzschild) black holes due to nonlinear complexities of the Einstein equations. In this work, we calculate Kerr metric perturbations with a new computational approach based on numerical relativity methods, extending recent scalar self-force results to full general relativity. We formulate the perturbative Lorenz-gauge Einstein equations in terms of azimuthal $m$-modes in the frequency domain and solve the resulting elliptic partial differential equations using a spectral discontinuous Galerkin discretization, adaptive mesh refinement, and preconditioned iterative solvers. With our new method, we achieve exponentially convergent first-order gravitational self-force calculations for circular equatorial orbits in Kerr spacetime up to spin $|a|/M=0.998$ (the Thorne limit). Our framework is designed to carry over to second order by delivering accurate and well-behaved first-order data for nonlinear source construction, and as a solver for the second-order metric perturbations themselves.
We study the gravitational wave (GW) spectrum generated by supercooled first-order phase transitions in two-field conformal models. We construct three representative toy models that capture the essential features of these models, derive analytical criteria for the existence of two-step transitions, and show how the two-field dynamics generate a genuine two-peak GW spectrum. We identify regions of parameter space in which two-peak GW spectra are observable at LISA and the Einstein Telescope. By way of illustration, we apply our analysis to a realistic conformal dark SU(3) model.
We show that the Belinski-Zakharov soliton construction factorizes into signed Pfaffian tau-functions, revealing a pure-spinor description of the metric and its regularity conditions. We derive analytic restrictions on the integral rod data, prove uniqueness for the asymptotically flat balance problem at fixed rod structure and periods, and give a conditional criterion for global existence. Combining these results with exhaustive enumeration of the admissible data and rigorous existence certificates, we construct a catalogue of regular asymptotically flat solutions representing 356 rod-word classes through twelve turning points, and 52 isolated regular asymptotically locally flat solutions through eight turning points. Analytic positivity and smooth-completion results establish regularity beyond the finite numerical solve. Based on this catalogue, we investigate two organizations of the solution space: generalized rank-two root systems and compositions of simpler endpoint geometries. The endpoint composition rules reproduce exactly all retained asymptotically flat words through twelve turning points.
Bit threads express holographic entropy as the maximal flux of a divergenceless vector field subject to a local capacity bound, but do not identify a physical carrier of that flux. In our previous work, we identified the projected string charge density with a bit-thread flow, reproduced the entropies of BTZ and ten-dimensional three-charge black holes, and showed that the maximal entropy flux is preserved under S- and T-dualities. However, the norm bound was imported from the bit-thread prescription, while the string-current configurations were prescribed along known bit-thread lines. In this paper, we give a stringy foundation for the local capacity and construct dynamical probe-string representatives of maximal flow. At genus zero and two-derivative order, the conical variation of the target-space action derived from the off-shell sphere fixes the string-frame entropy density. The gravitational replica construction and weighted flow-cut duality then yield the string-frame norm bound. We next find regular stationary F1 solutions in an NS-NS supported BTZ black hole whose spatial parts are logarithmic spirals. A uniform ensemble produces a conserved, constant-norm projected string charge density and realizes a maximal flow whose flux equals the BTZ entropy. We finally extend the construction to BTZ backgrounds with mixed NS-NS and RR flux. Varying the flux fraction changes the stationary F1 configurations at fixed metric and dilaton, while the corresponding conserved flows reproduce the same leading BTZ entropy. Thus, both the norm bound and its physical maximal-flow representative arise from string theory, with stationary strings providing physical channels for the entropic flux represented geometrically by bit threads.
Reversing the sign of the scalar potential exchanges de Sitter and anti-de Sitter vacua and, through the domain-wall/cosmology correspondence, maps flat domain walls onto flat FLRW cosmologies, but its supersymmetric version has ghosts on the cosmological side. We show that this pointwise correspondence is realized between two ordinary, ghost-free four-dimensional $\mathcal{N}=1$ supergravities with spontaneously broken supersymmetry. Within a single superconformal K\"ahler cone, a $\mathbb{Z}_2$ reflection of the nilpotent goldstino K\"ahler metric through the flat limit $V=0$ reverses $V\leftrightarrow-V$ pointwise while preserving the visible K\"ahler metric, the superpotential, and the unitary-gauge fermion Lagrangian. The paired vacua obey a sharp dictionary with $H=1/L$, $m^2_{\rm dS}=-m^2_{\rm AdS}$, equal conformal weights, and $m_{3/2}>H$, and are simultaneously stable precisely within the window $0\le m^2_{\rm dS}\le\frac94H^2$ set by the Breitenlohner--Freedman bound. Applied to string compactifications and cosmology, this correspondence pairs over-uplifted with under-uplifted anti-D3-brane vacua, confines the de Sitter swampland conjecture to the goldstino (anti-brane) sector, and maps slow-roll inflation onto a healthy AdS domain wall obeying the holographic $c$-theorem.
We derive the basic equations suitable for the coupled fluid--spacetime eigenvalue problem from the second-order action in full general relativity and accurately determine quasi-normal modes of a variety of rapidly rotating stars with outgoing-wave boundary conditions. For MIT-bag strange stars, the spectrum realizes Chandrasekhar's instability picture, with distinct Chandrasekhar--Friedman--Schutz and Jacobi-like neutral conditions and the transition to dynamical bar-mode growth. For neutron stars, we determine the $f$-, $r$-, and other inertial-mode spectra and their radiative damping or growth times. Interactions between $f$- and inertial modes reveal avoided crossings and exchanges for radiative damping or growth rates. We locate quasiradial collapse thresholds through a static stability analysis and independently verify them by tracking the fundamental $F$-mode frequency to zero, clarifying that the central density at the onset of the dynamical instability is always larger than that of the secular instability for uniform rotation. Our formalism and numerical implementation can also resolve highly damped $w$-modes.
In applied statistics, likelihoods involving high-dimensional integrals are often approximated via Monte Carlo summation. Controlling the resulting numerical variance is crucial for reliable inference. We provide a practical introduction to Latin hypercube sampling (LHS) and its extension based on orthogonal arrays (OA-LHS) as strategies to reduce this variance by stratifying the sampling distribution. LHS asymptotically removes variance contributions from individual coordinates, while strength-2 OA-LHS also removes those from pairwise interactions, yielding orders-of-magnitude improvements over plain Monte Carlo estimators for suitable integrands. As a case study, we investigate their application to the selection function entering hierarchical inference of gravitational-wave populations. At approximately one million injections, we find only a marginal reduction in variance, with low statistical significance. Nevertheless, the computational cost of constructing these designs is negligible relative to evaluating gravitational-wave injections, making even marginal gains worth considering for future applications. This practical introduction to LHS and OA-LHS offers a starting point for other applications in physics and astronomy involving computationally expensive Monte Carlo calculations.
We present a systematic study of the spin evolution of accreting black holes. Using the BHAC code for general relativistic magnetohydrodynamic simulations, we conduct a total of 500 high resolution simulations of magnetized accretion disks around Kerr BHs with spin parameters ranging from $\chi=0$ to $\chi = 0.99$. The baseline configuration follows the default Fishbone--Moncrief torus setup in BHAC. We further explore the effects of: I) introducing multiple poloidal magnetic loops, II) the initial position of the torus, III) magnetic field strength and IV) radial loop modulation. From each simulation we extract the mass flux and angular momentum flux through the horizon to compute the time-averaged spin evolution rate after the system becomes quasi-stationary. The equilibrium spin ranges from $\chi_{\rm eq}\simeq0.88$ in the fiducial model to $\chi_{\rm eq}\simeq0.98$ for weak-flux model. Applied to Sgr A$^*$, even an optimistic estimate for rapid spin evolution gives a timescale longer than $10^{13}$ yr, indicating an earlier growth or merger history. These trends are consistent with the picture that larger net magnetic flux threading the horizon enhances jet-torques and reduces the equilibrium spins, whereas weak net flux yields near-maximal spins. Our results provide a pathway to interpret the high spins reported for X-ray binaries and active galactic nuclei and they sharpen the astrophysical viability of near-horizon high-energy processes that rely on near-extremal black holes.
We develop a gauge-invariant formulation of the thermodynamics of rotating black strings in five-dimensional minimal supergravity through Kaluza-Klein reduction. At the two-derivative level, we consistently reduce the bulk action and the Gibbons-Hawking-York boundary term, carefully accounting for the surface contributions induced by the Chern-Simons coupling. The resulting four-dimensional theory is $\mathcal{N}=2$ supergravity coupled to a single vector multiplet, with prepotential $P=\frac{1}{3\sqrt{3}}\frac{X_1^3}{X_0}$. Employing the Hamiltonian formalism, we establish the quantum statistical relation between the Euclidean on-shell action and the Gibbs free energy. We further compute the leading four-derivative corrections to the thermodynamics of a rotating magnetic black string using the Reall-Santos method. The resulting corrections are in precise agreement with previous results obtained directly for the Kerr-Newman black hole in four-dimensional $\mathcal{N}=2$ supergravity.
We investigate the circuit complexity of primordial scalar and tensor perturbations in the luminal branch of Einstein--Gauss--Bonnet inflation. Starting from the quadratic perturbation actions, we construct the two-mode Hamiltonians and derive the evolution equations for the squeezing amplitudes and angles. Although the tensor speed is fixed to unity, the Gauss--Bonnet (GB) coupling remains dynamical through the scalar and tensor pump fields. We track the squeezing dynamics from the subhorizon to the superhorizon regime and evaluate the Nielsen wave-function complexity of the resulting two-mode squeezed states. The GB correction produces a clear separation in the squeezing amplitudes, while the unwrapped squeezing angles remain nearly phase locked. Consequently, the circuit complexity is controlled mainly by the amplitude evolution. A positive coupling enhances the scalar complexity but slightly suppresses the tensor complexity for the benchmarks considered. These opposite trends show that scalar and tensor Gaussian states retain distinct information about the same modified inflationary background even when tensor propagation is luminal.
We consider a massive object, such as a neutral atom or an Unruh-DeWitt detector, moving at constant speed in a quantum field and investigate how motion affects the quantum coherence of its internal degrees of freedom, manifesting as quantum dispersion in the absence of a quantum field, and decoherence in its presence. Our investigation aims to serve two purposes: One is to obtain the correct results for these effects, which are essential for the design of quantum information processing schemes where the quantum coherence of an atom's internal degrees of freedom is of major concern. The other is to expose the fallacies in commonplace approaches, which start with a non-relativistic calculation and then add on relativistic ``corrections". We first show a fully relativistic calculation of the internal dynamics based on covariance principles, and then one which ignores these principles, often justified by the atom's slow motion. By a direct comparison of results from these two approaches, we identify {significant discrepancies} in a non-relativistic treatment, even at low atomic speeds. The proper procedure, and a much safer one in terms of accuracy, is recommended here: first derive the dynamics and the necessary regularizations within a fully covariant relativistic framework. Only after the exact, internally consistent equations of motion are established should low-velocity limits be extracted from them. Only in this way can all the relativistic effects which matter: time dilation, aberration, non-inertial mass shifts, be systematically preserved, and accurate results obtained.
We study scalar perturbations in a ten-dimensional D3 brane spacetime, developing a (higher-dimensional) Mano-Suzuki-Takasugi-like formalism adapted to the present case leading to a sourced modification of a Mathieu equation. As an application, we compute the energy loss both at infinity and at the horizon in terms of scalar waves due to a scalar charge moving along a circular "equatorial" geodesic.
Near-extremal black holes are controlled by a small set of soft modes, and counting these modes fixes the coefficient of $\log T$ in the entropy. We ask whether genuine six-derivative interactions change that count, working in seven-dimensional third-order Lovelock gravity, the simplest setting where the cubic Lovelock term is dynamical. The multiplicities stay the same, but the naive count fails. At fixed charge the Maxwell mode is frozen out, and the fifteen rotational modes of the $S^5$ act as a quantum rotor that only switches on above the scale $K_J^{-1}$. As a result, the coefficient of $\log T$ runs from $3/2$ at the lowest temperatures to $9$ above that scale, and never reaches the naive Gaussian value $19/2$. We compute the moment of inertia $K_J$ from the charged slow-rotation solution and find that the Lovelock couplings move the crossover without changing the multiplicities. Only large AdS black holes have a wide window in which the full rotational contribution competes with the classical entropy. Adding a probe charged scalar, we derive an analytic near-horizon Schwinger threshold in the cubic coupling. Its large-AdS limit tells us when the broad rotational crossover window can coexist with the absence of a charged-scalar Breitenlohner--Freedman (BF) bound violation.
Weyl transformations, --local rescalings in which the metric transforms as $g_{\mu\nu}(x)\longrightarrow \Omega^2(x)\, g_{\mu \nu}(x)$--, are expected to be a symmetry of nature at extremely high energy, that should be (spontaneously) broken at low energy. In Cartan's first order formulation of gravity this translates into the condition that the local frames (vielbein) scale as $e^a(x) \longrightarrow \Omega(x) e^a(x)$. In this construction, the Lorentz connection one-form fields $\omega^a{}_b$ are independent from $e^a$, and since Lorentz transformations and dilatations commute, $\omega$ and $R(\omega)$ must be Weyl invariant, while in the second order metric formalism the Ricci tensor undergoes a non-homogeneous transformation. This generates a tension between the two formulations, which should be equivalent in the vanishing torsion limit. Here we show how the puzzle can be resolved taking into account the role of torsion. This also sheds some light on the conformal coupling of matter fields to gravity.
The radial Teukolsky equation is invariant under exchange of the outer and inner horizons, although the physical boundary condition is not. We derive an exact monodromy relation between the corresponding Mano--Suzuki--Takasugi (MST) near-zone responses. At leading order in frequency and to all orders in spin, this relation yields, for every multipole, an expression for the leading horizon-exchange-odd response. For gravitational perturbations, it determines the exchange-odd contribution to quadrupolar absorption and organizes the exchange-even dynamical response into a digamma function whose expansion accounts for the odd- and even-zeta structures found in Kerr-Compton calculations. The exact relation, rather than the individual previously known small-spin coefficients, is the central result.
We study the formation and evolution of the cosmic large-scale structure (LSS) in a scalar-tensor Horndeski theory of gravity without dark matter. We impose that this theory reduces to Refracted Gravity (RG) in the weak-field limit. RG is a non-relativistic theory where the gravitational permittivity $\epsilon(\rho)$, with $\rho$ the baryonic matter density, provides the gravitational boost required to describe both the dynamics of galaxies and galaxy clusters without dark matter. We show that $\epsilon(\rho)$ equals the function $G_4(\varphi)$ of the scalar field $\varphi$ of our Horndeski model. The background evolution of a flat, matter-dominated, homogeneous and isotropic universe shows that $\varphi$ is also responsible for the accelerated expansion of the universe and that the model is capable of reproducing the observed redshift evolution of the Hubble-Lema\^itre parameter. We finally develop the linear perturbation theory and study the growth factor equation. The model fails to correctly describe the LSS by predicting a late onset of the formation of cosmic structure at redshift $z\lesssim 1$.
We investigate the cosmological dynamics of axion-monopole interacting dark energy, examining whether a microscopically motivated dark-sector interaction can sustain stable late-time acceleration. In particular, magnetic monopoles constitute dark matter and an ultralight axion contributes to dark energy, with their interaction arising from the Witten effect through field-dependent dyon masses. We formulate the autonomous system, classify its critical points and stability, and investigate the evolution analytically and numerically. We find that stable de Sitter attractors at finite positive Hubble parameter require a positive cosmological constant and correspond to axion-potential minima, whereas those at maxima are unstable. Nevertheless, transient axion-driven acceleration remains possible without an explicit cosmological constant. Furthermore, the interaction induces matter-era tracking, namely an attracting slow-drift regime rather than an exact critical point. The interaction-effective dark-energy equation of state can cross the phantom divide, although the physical equation of state remains non-phantom. Extending the analysis to the full Bogomol'nyi-Prasad-Sommerfield dyon mass, we find that the main dynamical features persist, while the field evolution and interaction strength depend on the microscopic dyon properties. Our results demonstrate how a microscopically motivated dark-sector interaction can give rise to distinctive cosmological evolution and effective dark-energy behavior.
We classify the simply connected toric gravitational instantons whose torus action has four fixed points. They are the hyperk\"ahler multi-Eguchi--Hanson and multi-Taub--NUT metrics with four collinear centres, the asymptotically flat instantons on Li and Sun's manifold $X_3$, up to scale one for each twist at infinity in $(0,1)$ for a fixed orientation of the torus, and, up to scale, a single further instanton with an ALF end, which is not hyperk\"ahler. The last two are Hermitian for neither orientation. In particular, the toric asymptotically flat instanton on $X_3$ with a given twist is unique up to scale, as conjectured by Li and Sun. The proof combines the solitonic form of Geroch's conjecture, which turns smoothness into polynomial equations for the soliton data, with a convexity principle adapted from Aksteiner. At a fixed asymptotic parameter, the cone errors of the conical metrics with a given rod structure are the gradient of a strictly convex function of the rod lengths, and the strict convexity gives uniqueness. Existence follows from an explicit solution for the ALF end and, for the AF ends, from Li and Sun's existence theorem. We also outline how a chart of Aksteiner identifies these AF instantons with those found by Teo.
In this work we assess non-Gaussian extensions of Fisher forecasting based on the Derivative Approximation for Likelihoods (DALI). We simulate ensembles of bright siren catalogs for third-generation observatories, adopting a Cosmic Explorer (CE) and a triangular Einstein Telescope (ET) network, frequency-domain inspiral waveforms, and selection-motivated priors for counterpart detection. We reconstruct approximate likelihoods using Fisher and the first DALI correction (Doublet), and propagate the inferred distance information to cosmological inference in a w0waCDM model. We find that the Doublet approximation provides tighter cosmological constraints than the Fisher approximation, reducing the inferred uncertainties by approximately a factor of two in agreement with non-approximate likelihood (called Exact) results. For our GW network onfiguration, 300 bright-siren detections up to z=1 yield an H0 precision of ~2.7% with the Doublet approximation, compared with ~2.5% for the exact likelihood. The adopted non-Gaussian GW priors induce a systematic displacement of the inferred luminosity distances from the fiducial values, which is also present in the exact GW reconstruction and propagates into the cosmological parameters. Compared with the exact cosmological likelihood, the Doublet results differ by only ~10% on average in the parameter uncertainties, compared with ~195% for the traditional Fisher approximation. The Doublet approximation also substantially reduces the computational cost, by a factor of ~55 for the GW analysis and by ~12 for cosmological likelihood evaluations, yielding an estimated reduction of ~55 in the total computational cost of the combined analysis. Our results show the potential of DALI-based approximations to provide accurate and computationally efficient tools for forecasting in bright siren cosmology.