Papers

The Teukolsky and SpinWeightedSpheroidalHarmonics packages of the black hole perturbation toolkit (BHPT) are one of the main public libraries to compute numerical solutions to the Teukolsky equation and related quantities. This work is a companion paper presenting their new and improved weak-field analytic functionality focusing on post-Newtonian expansions. The Teukolsky package now allows users to independently extract multiple useful quantities, such as the so called MST coefficients, renormalized angular momentum, amplitudes of the radial functions or the phase shift as a low frequency/PM expansion. It also provides PN expansions of the homogeneous radial functions or - for circular orbits in Kerr - inhomogeneous amplitudes, as well as energy and angular momentum fluxes at infinity and the horizon. All quantities can be computed to state of the art precision on regular laptops. It also provides a suite of tools for post-Newtonian self force computations and updates the analytic functionality of the SpinWeightedSpheroidalHarmonics package. Computations are possible both for specific and generic spin weight $s$ and harmonic mode numbers $\ell$ and $m$. This package paves the way for intensive high-order post-Newtonian self-force calculations at the forefront of waveform modelling of small mass ratio black hole binaries, as well as giving widely useful low-frequency expansions for black hole perturbation theory. All functions described in this paper are available in BHPT versions Teukolsky v.1.2 and SpinWeightedSpheroidalHarmonics v.1.1.

The Unruh effect predicts that a uniformly linearly accelerated observer with proper acceleration $a$ reacts to the Minkowski vacuum through excitations and de-excitations with the characteristics of a thermal state at temperature $T_U=a/(2\pi)$. An observer in uniform circular motion will experience similar excitations and de-excitations that we may use to operationally define an effective temperature, which however depends not only on the acceleration but also on the orbital speed and excitation energy. Motivated by the experimental interest in the circular motion Unruh effect, we investigate how spatial confinement modifies the response of an Unruh-DeWitt detector in $2+1$ Minkowski spacetime. We consider a massless scalar field confined within a circular boundary prepared in either the vacuum or a thermal state, probed by an Unruh-DeWitt detector on a circular orbit, a setting that describes proposed analogue spacetime systems for testing the effect, and in which both a boundary and an ambient temperature will necessarily be present. We establish analytic results for the detector response in the large-boundary regime and identify resonance peaks, which are more prominent when the field has an ambient temperature.

We study and compare rotating Hayward-like and Bardeen-like geometries within a common Kerr-like axisymmetric ansatz, with the models distinguished by their areal-radius functions $R_i(\rho)$. On the adopted radial branches, the positive minimum areal radius excludes the Kerr ring locus, and the curvature invariants examined here remain finite. We identify the parameter domains containing two, one, or no horizons. The two geometries have the same asymptotic Komar charges but different finite-radius values. If we treat the Einstein tensor as an effective stress tensor, then for every nonzero regularity length $\ell$, this ansatz violates the null and weak energy conditions, as demonstrated by the equatorial radial-null contraction. For the complete photon family on a black-hole branch, the shadow boundary is identical to that of Kerr at the same mass, spin, and observer inclination, and is also identical for the two regular geometries. The corresponding area-equivalent shadow diameters for M87* and Sgr~A* are consistent with the approximate Event Horizon Telescope (EHT)-based intervals adopted here, and we do not obtain further constraints on $\ell$. By contrast, the prograde equatorial strong-deflection limit (SDL) calculations are only partly degenerate. At fixed spin, $u_m^+$ and $\theta_\infty^+$ are common to Kerr and the two regular geometries, whereas $\bar a_+$, $\bar b_+$, the image separation, the relative magnitude, and the subleading time-delay correction depend on $\ell$ and on the areal-radius profile. Within the stated strong-deflection approximation, future measurements of $\Delta T_{2,1}$, $s^+$, and $r_{\rm mag}^+$ may help test these rotating geometries and distinguish the Hayward-like and Bardeen-like predictions from Kerr, including in the one-horizon parameter domain where the adopted branch contains no Kerr-like inner horizon.

In a tetrad formulation of general relativity, an ideal Ohm-type condition for the gravitational field implies the conservation of gravitational fluxes and the preservation of the connectivity of gravitational field sheets. We investigate the consequences of departures from ideal gravitational evolution by developing a theory of gravitational reconnection, defined as a change in the connectivity of gravitational field sheets arising from the breakdown of the ideal frozen-in evolution of the gravitational field. We derive quantitative measures of the gravitational reconnection rate, show that gravitational reconnection alters the energy-momentum exchange between the gravitational and matter sectors, and determine how it modifies the evolution of gravitational helicity. Our results provide a quantitative framework for describing changes in gravitational connectivity and their consequences in dynamical spacetimes.

Spacetime can undergo complex nonlinear evolution, as governed by the Einstein field equations, and a central challenge is to understand the geometric structures that arise, persist, and interact throughout its evolution. Using a formulation of Einstein equations that parallels nonlinear electrodynamics of continuous media, we show that general relativity admits gravitational field connections—two-surfaces and associated field lines whose connectivity is maintained by the spacetime dynamics. This gravitational frozen-in behavior is enabled by an ideal Ohm-type condition for the gravitational field. We further show that the same framework naturally leads to a conserved “gravitational magnetic” flux. A conserved gravitational helicity also emerges, with a clear topological interpretation in terms of gravitational field-line structures. These results identify well-defined topological constraints on admissible spacetime evolution and provide an organizing principle underlying the nonlinear dynamics of spacetime.

We investigate an isotropic Hořava-Lifshitz fermion theory supplemented by a dimension-six spatial derivative operator, preserving first order time evolution while modifying the ultraviolet dispersion relation. Within the regime of validity of the derivative expansion, we develop three complementary consequences of the $z=2$ sector. First, a Bardeen-Cooper-Schrieffer/Nambu-Jona-Lasinio (BCS/NJL) mean field treatment of fermion pairing yields the particle and antiparticle quasiparticle spectra, the finite temperature gap equation, and the gauge invariant criterion for a stable superconducting phase. The modified dispersion alters both the density of states governing the pairing scale and the electromagnetic vertices entering the Meissner response. Second, using the scalar pole denominator as a minimal spin independent exchange kernel, we derive an exponentially damped and oscillatory massive potential and obtain the corresponding Born scattering amplitudes. The quartic momentum dependence renders both the forward and total cross sections finite and produces a large transfer behavior distinct from Rutherford scattering. Finally, we evaluate the induced shifts of the hydrogenic $1S$, $2S$, and $2P$ levels in closed form, retaining the full dependence on the interaction range. In other words, these latter results gives direct spectroscopic constraints on the product of nuclear and leptonic couplings, with muonic atoms, showing the respective sensitivity to the short distance Hořava-Lifshitz sector.

We study cosmological stasis in coupled dark matter and dark energy models in which a scalar field drives the dark energy and sets the dark matter mass, with the Dark Dimension as the motivating realization. Treating dark matter, dark energy, baryons, and radiation as an autonomous dynamical system, we show that exact stasis requires exponential slopes along the trajectory, and that running slopes give exact stasis or a drifting quasi-stasis depending on whether the running is integrable. The constant abundance solutions are the stationary solutions of coupled quintessence, which we read as stasis epochs with computable lifetimes and exits. Anchoring the cosmology to the measured abundances at matter-radiation equality and today, we show that the stasis region for this model cannot accelerate for any initial conditions, and that the total equation of state is never phantom although the effective dark energy of a $\Lambda$CDM fit can appear so. For the Dark Dimension, capture into stasis in the future is excluded for geometric sources of the potential once dark fifth-force bounds are imposed, and dark matter production from the Standard Model brane supports a further stasis which the standard scenario does not reach. The stasis solutions provide analytic exclusions of the parameter space which do not depend on initial conditions.

The characteristic oscillations of a black hole can be understood in terms of null rays trapped near its unstable light ring, with this correspondence becoming exact in the high-frequency limit. In this regime, we uncover a hidden ladder symmetry in the perturbation equations, which maps the calculation of quasinormal modes, Regge poles, and greybody factors for a spherically symmetric black hole onto the quantum-mechanical problem of an anharmonic oscillator. This provides a systematic, efficient framework for computing the black hole response, with improved convergence properties compared with existing approximation schemes. As an explicit application, we analytically compute all three quantities for a Schwarzschild black hole through eighteenth order in inverse angular momentum, obtaining highly accurate results. We explore different resummation schemes and find that they can further improve the accuracy of the Regge poles and, particularly, the greybody factors. Our framework can be readily extended to rotating black holes and to modified theories of gravity.

Standard models for stellar core collapse predict the birth of neutron stars with masses exceeding a solar mass. In the collapsar model, a rapidly rotating massive star collapses to a black hole surrounded by a dense, neutrino-cooled accretion disk, whose outer regions may in some cases fragment into neutron-rich clumps that collapse to form subsolar-mass neutron stars. These disk-formed objects can then merge either with one another or, following possibly hierarchical evolution, with the central black hole. In this work, we characterize the gravitational-wave signatures of these binaries, focusing on distinctive features of the collapsar environment: Doppler and other phase modulations from orbital motion about the central black hole, gas-driven migration in the disk, and tidal interactions during inspiral. We show that the combination of anomalously low component masses with these environmental imprints produces unique waveform signatures that can distinguish the collapsar channel from other subsolar merger scenarios. Current and next-generation detectors have good prospects for identifying the intrinsic properties of such objects and, if subsolar mergers are discovered, for testing and constraining the collapsar formation pathway.

We introduce a gravity-informed neural-network (GravINNs) framework for learning post-Newtonian binary orbital dynamics. The method incorporates the equations of motion directly into the training phase and is developed at three complementary levels. First, we construct single-orbit surrogates for conservative post-Newtonian dynamics and assess their accuracy across different orbital configurations. We then extend the approach to a parametric model spanning a four-dimensional parameter space defined by the initial separation, radial and tangential momenta, and symmetric mass ratio, allowing a single trained network to represent entire families of orbits and replace repeated numerical integrations. Finally, we consider dissipative dynamics by including the leading radiation-reaction contribution at $2.5$PN order. In this regime, the network accurately reproduces both the orbital evolution and the associated secular energy loss without using dissipative reference trajectories in the training. These results show that physics-informed neural-networks (PINNs) can provide accurate and flexible representations of both conservative and dissipative post-Newtonian dynamics. The complete implementation and the models used in this work are publicly available through the GravINNs repository.

We prove that a Third Law of black hole mechanics holds for the BTZ black hole in 3d gravity coupled to matter obeying the dominant energy condition. This law states that initial data containing a trapped surface cannot evolve in finite time to a black hole that coincides with extremal BTZ on the event horizon, for any choice of boundary conditions at infinity. The result is proved by defining a quasilocal energy and angular momentum and using spinorial methods to establish a BPS inequality that is saturated by the extremal BTZ solution. Nevertheless, we show that gravitational collapse of a massless scalar field can result in the formation of an extremal BTZ black hole in finite time. The difference between these results arises because gravitational collapse occurs in the Neveu-Schwarz sector, whereas extremal BTZ is supersymmetric in the Ramond sector. Solutions that settle down to extremal BTZ in infinite time along the event horizon are also discussed.

We construct an exact Weyl double copy of the singly spinning five-dimensional Emparan–Reall black ring. Its complete nonlinear Weyl curvature is the sum of two scalar-weighted Maxwell squares. One field is generated by the stationary Killing vector; the other carries topological magnetic flux through a sphere linking the ring. Both are source-free Maxwell fields on the black-ring spacetime, with corresponding scalar partners obeying a common sourced wave equation. This extends exact five-dimensional Weyl doubling beyond the type-$\mathrm D$ and type-$\mathrm N$ examples to a black hole whose exterior contains both type-$\mathrm G$ and type-$\mathrm{I}_i$ regions. The Weyl polynomial factorizes into two distinct irreducible quadratics, establishing genuine De Smet type $22$, thereby ruling out a reduction to a single Maxwell square.

We establish a direct quantum Clausius relation for conformal fields inside the apparent horizon of a quasi-de Sitter spacetime. We compute the net heat flow across the horizon from the renormalized stress-energy tensor, and independently determine the time evolution of the renormalized von Neumann entropy using the replica method. At leading order in the Hubble-flow expansion, the two calculations agree exactly, without using the gravitational equations of motion. Beyond leading order, we find a scheme-independent entropy balance that includes the corresponding Wald entropy. Our results provide a quantum field theoretic realization of dynamical horizon thermodynamics beyond exact de Sitter equilibrium.

Gravity (g) modes are the only neutron-star oscillations that report on the composition of dense matter rather than on its stiffness, and work on hybrid stars has established that a first-order quark transition raises their frequency. Quarkyonic matter does the opposite. Quark-nucleon chemical equilibrium is maintained by the strong interaction, so the quarks acquire no thermodynamic freedom on an oscillation period and $c_s^2-c_e^2$ reduces to a positive-definite quadratic form in the lepton gradients alone. The nucleon momentum shell stiffens both sound speeds together instead of separating them, so the buoyancy factor collapses by a factor of 9.5 to 19 at an early transition and the core is left only weakly stratified. Solving the $l=2$ relativistic Cowling problem for ten equations of state that share one isoscalar sector, seven quarkyonic and three nucleonic controls at matched symmetry-energy slope, we found the g-mode confined to the nucleonic shell outside the core, with the horizontal flow that it lives on excluded from the core while the core is displaced almost rigidly. Its frequency falls from 158-522 Hz across the controls to $81-254$~Hz across the quarkyonic models, and by 14% at 1.4$M_\odot$ for the matched pair at $L=50\mev$; more important than the shift, it decreases with mass where the controls rise. Writing each frequency as the dynamical frequency $(GM/R^3)^{1/2}$ times a dimensionless remainder separates structure from composition. The $f$ and $p_1$ trends prove to be inherited from the mass–radius relation; the $g_1$ remainder, constant to $2-9\%$ along a nucleonic sequence, falls by a quarter to a third along a quarkyonic one and departs by a factor of two from the nucleonic $g$-mode relation at fixed compactness and $L/K_0$. These are Cowling values, lower bounds at the ten-per-cent level, and the sign of the trend survives a correction of that size.

Numerical classification of black-hole orbits can depend on how prescribed inner capture or absorbing boundaries are implemented. This study investigated how discrete evaluation of such a boundary affects orbit classification. Massless particles were integrated about an isolated Newtonian point mass and initialized at periapsis with an absorbing boundary at rsink = 104RS. Because the Keplerian periapsis q is constant, the expected classification can be analytically determined. A classifier omitting evaluation at initialization can miss particles that already satisfy the removal criterion, but evaluation at t = 0 reproduced the analytic classification on every sampled grid. As the grid resolution increased, the inferred critical periapsis approached the imposed sink radius. These results demonstrate that an apparent critical periapsis can depend on both the imposed boundary and its numerical evaluation, emphasizing the need to distinguish numerical effects from genuine dynamical thresholds.

We present an analytical framework to translate detector sensitivity into stray light requirements for the core optics region of ground based gravitational wave interferometers. We derive analytical estimates for several relevant scattering regimes, extend the treatment to collections of planar baffles, and obtain an analogous requirement for deterministic ghost beams intercepted by beam dumps. The framework is intended to provide conservative design requirements before a complete optical layout is available. We apply it to Cosmic Explorer to show how these estimates can be used to derive requirements for next generation detectors. The resulting expressions provide a compact set of tools for stray light budgeting and early design studies in current and future gravitational wave detectors.

Can primordial cosmological correlations originate from statistical fluctuations of an early-universe thermal system? We connect grand-canonical thermodynamics, stochastic transport, and gauge-invariant cosmological perturbations for a charged fluid at finite chemical potential. Energy-charge susceptibilities determine curvature, charge-isocurvature, and cross-correlation amplitudes, while transport sets when each mode leaves equilibrium. For an isolated, adiabatic conformal plasma with conserved charge-to-entropy ratio and power-law diffusion, diffusive freeze-out yields the universal spectrum $\mathcal P_S(k)\propto k^3$, with $n_{\rm iso}=4$, while equal-time local-equilibrium curvature-isocurvature covariance vanishes in the conformal source basis. Thus neither finite chemical potential nor replacing Hubble crossing by diffusion crossing alone yields approximate scale invariance. We evade this obstruction with an open subsystem of massless Dirac fermions during a sourced quasi-de Sitter phase. There, grand-canonical energy cumulants generate a nearly scale-invariant red curvature spectrum. A benchmark gives $\mathcal P_{\zeta_X}(k_\star)=2.10\times10^{-9}$ and $n_s(k_\star)=0.9649$, stays within $0.30%$ of the fitted power law over $0.002\leq k/k_\star\leq4$, and predicts weak negative running and small positive intrinsic non-Gaussianity from higher-order cumulants, $f_{\rm NL}(k_\star)\simeq0.106$ and $g_{\rm NL}(k_\star)\simeq0.0158$. With a two-helicity vacuum tensor spectrum, the tensor-to-scalar ratio is $r_{t/s}(k_\star)=1.82\times10^{-4}$. This isolates the limitation of isolated conformal thermal seeding and the open-system ingredient needed to overcome it. Thermal energy-charge fluctuations thus provide a calculable source of realistic scalar correlations, while reservoir dynamics, equilibration, and later curvature-isocurvature transfer must come from a microscopic model.

The collective coordinate dynamics of antiferromagnetic and ferrimagnetic textures emerges as a geodesic equation governed by the quantum geometry of the CP$^1$ state associated with the Néel vector, rendering an effective Riemannian gravity and a Lorentz force in the texture motion. This unveils a physical scenario fundamentally distinct from the Thiele equation widely used for ferromagnetic textures, which is inertialess without any gravity analogy. Applying our framework to an optically driven ultrafast antiferromagnetic domain wall, we can explain the helicity-dependent asymmetric motion observed experimentally and predict a vibrantly breathing wall width.

Recent DESI baryon acoustic oscillation measurements, combined with cosmic microwave background and type-Ia supernova data, suggest that dark energy may evolve with cosmic time. Along a cosmological background, an evolving dark-energy density can be expressed locally as a function of a monotonic curvature invariant, motivating an effective curvature-dependent cosmological term. Moreover, quantum field theory in curved spacetime and approaches to quantum gravity with running gravitational couplings provide complementary motivations for exploring such a term. Here we study how the phenomenology of nonsingular rotating black holes embedded in a Universe dominated by dark energy can differ substantially from that of the Kerr and Kerr–de Sitter geometries. The problem is directly formulated in phase space using a null geodesic super-Hamiltonian and a Mino-type parameter. The shadows of the black holes are calculated by backward ray tracing from a zero-angular-momentum observer. We define and analyze a comprehensive set of standard shadow observables, characterizing the size, shape, and displacement of the shadow. We show that the area of the shadow and its vertical diameter provide particularly clear signatures of a running cosmological term. In this way, joint analyses of multiple strong-field observables and of several black holes with different masses and spins could provide a realistic route to tightly constraining, or potentially measuring, the effective regularization scale behind the running of the cosmological term and statistically distinguishing the non-singular black hole geometry from Kerr/Kerr-dS solutions.

Microscopic black holes may form at the centers of neutron stars through the accumulation and collapse of dark matter. While Standard Model particles produced by Hawking evaporation are efficiently absorbed by the dense stellar medium, sufficiently weakly interacting and long-lived particles can escape and subsequently decay into high-energy neutrinos, photons, or charged particles, providing an indirect probe of Hawking radiation. We examine the joint energy–angular distribution of these secondary particles, incorporating mediator propagation, energy-dependent decay, and relativistic decay kinematics. For relativistic mediators, the normalized energy-integrated angular profile becomes approximately independent of the black hole temperature, with its characteristic extent controlled primarily by the combination $c\tau_S/D$ of the mediator lifetime and source distance, as the boost enhancement of the decay length is compensated by relativistic beaming. We demonstrate the viability of this mechanism and illustrate its phenomenology with gravitationally coupled scalars, dark photons, dark-$Z$ bosons, and heavy neutral leptons. Comparing with monochromatic mediator production from dark matter annihilation, we find that the energy-integrated angular profiles can be nearly degenerate, while the energy spectra and energy-resolved angular distributions remain distinct. These complementary spectral and angular signatures provide targets for high-energy neutrino and gamma-ray searches.

Boson stars are self-gravitating solitons of the Einstein-Klein-Gordon equations for a massive complex scalar field, and arguably the simplest horizonless compact objects arising in General Relativity. Beyond spherical symmetry, their construction requires solving a system of nonlinear elliptic partial differential equations, a difficult task per se and that each group has traditionally addressed with its own numerical implementation. A systematic comparison of different methods applied to the same physical model has so far been lacking. In this work, we carry out such a comparison for the two simplest non-spherical configurations: rotating boson stars and static dipolar boson stars. We employ three independent codes, based respectively on finite differences (FIDISOL/CADSOL), finite elements (FreeFem), and spectral methods (Kadath), and assess their accuracy through different diagnostics. The three solvers agree on the global observables to typically eight significant digits. We further compare the runtime of each code on identical hardware and provide precise benchmark values of the relevant physical quantities, intended to serve as reference data for future numerical studies of boson stars. As a further proof of concept, we also present the use of physics-informed neural networks to construct a rotating Q-ball solution.

Inflation driven purely by the quantum running of the curvature-squared couplings of quadratic gravity was shown to accommodate the high scalar tilt favored by recent cosmic microwave background observations, starting from a Euclidean four-sphere at a maximum of the running $R^2$ coupling. That maximum exists only in one renormalization scheme, and is not stationary once the Euler trace anomaly is included. We show that the standard one-loop running, with the usually neglected Gauss–Bonnet coefficient retained, recovers the missing de Sitter state: the Euler running balances the scale dependence of the $R^2$ term at a unique coupling ratio, giving a de Sitter solution that is stationary for the gravitational constraint and for the compact Euclidean action alike, and whose scalaron potential is an extremely flat hilltop ($m^2/H^2\simeq-5\times10^{-10}$) joined to an inverse-linear inflationary plateau. The last $N_*\simeq50$–$60$ $e$-folds are scheme independent, with scalar tilt $n_s\simeq1-4/(3N_*)$, while the tensor-to-scalar ratio, $r$, is set by the number of matter fields that enhance the running. The current tensor bound excludes pure gravity and sets a minimum matter content, some $4\times10^6$ conformally coupled scalars or $3\times10^5$ vectors—$2.6$ times fewer than the momentum-induced scheme requires—while one-loop control to the end of inflation sets a maximum about ten times higher. Across that window the model predicts $r\gtrsim0.008$ with $0.973\lesssim n_s\lesssim0.978$, within reach of upcoming CMB polarization surveys.

We present three-dimensional general relativistic magnetohydrodynamic simulations of a precessing supermassive black hole binary with mass ratio q=1/7, embedded in a circumbinary disk. We investigate how dynamics within the binary cavity launch and shape a relativistic jet to thousands of gravitational radii. The primary black hole dominates both accretion and jet power, while the smaller black hole repeatedly crosses and shocks the inner accretion flow. These passages of the secondary drive magnetized gas alternately into the upper and lower jet funnels, producing disturbances that propagate outward as quasi-periodic outflows. Although the inner flow is perturbed twice per orbit, each jet lobe shows one dominant outflow per orbit. On longer timescales, the jet precesses, reverses its magnetic handedness, and undergoes two weak phases. The first results from a reorientation of the primary spin and is followed, after the jet recovers, by a reversal in the circulation of the projected magnetic field. The second weak phase occurs as the secondary's orbit becomes nearly coplanar with the circumbinary disk, reducing the gas and magnetic flux reaching the primary. Together, these results connect cavity dynamics to large-scale jet variability and predict a set of correlated jet signatures whose relative timing and causal ordering may provide stronger evidence for a small-mass-ratio supermassive black hole binary than any one feature alone.

Quasinormal modes of black holes provide a central avenue for confronting general relativity with gravitational-wave observations from the ringdown stage of compact binary coalescence. However, inferring black-hole properties or the background spacetime requires theory-dependent input. In this work, we connect a calibrated eikonal method, which relates quasinormal mode shifts to local metric properties near the light ring, with the underlying rotating black hole metric. Using Bayesian inference, we compare a metric-specific model based on the global Konoplya-Rezzolla-Zhidenko parametrization with a metric-agnostic approach based on local values and radial derivatives of the metric functions at the light ring. For each model, we perform both one-parameter and simultaneous multi-parameter analyses and quantify how their priors map onto the same local quantities. We find that uniform priors on the metric-specific coefficients can induce strongly nonuniform and skewed priors on these local metric quantities. For an injection compatible with general relativity, both models remain consistent with Kerr and yield similar posteriors for the orbital frequency and Lyapunov exponent despite their different induced priors. For injections representing deviations from general relativity, one-parameter analyses can fail to recover the injected local deviations and, in the metric-specific case, can bias the global metric reconstruction. The multi-parameter analyses of both models yield consistent constraints, suggesting sufficient robustness. However, they introduce substantial degeneracies and differences in marginalized parameters, demonstrating practical limitations when considering more flexible models. Finally, we apply the framework to approximate posterior information from the ringdown analysis of GW250114 and find that both models are consistent with the Kerr metric in general relativity.

The effective-field-theory interpretation of generalized uncertainty principle (GUP) deformations does not by itself establish whether their tree-level operator content is closed under renormalization. We investigate this question in massless GUP-deformed quantum electrodynamics at one loop and to first order in the deformation parameter. We compute the ultraviolet divergences of the relevant Green functions and determine the counterterm structure. Our central result is that, after eliminating redundant operators, renormalization requires only one independent physical counterterm beyond those associated with the tree-level theory: an axial-axial four-fermion interaction. The original deformation therefore admits a minimal radiative completion at this order. We derive the leading logarithmic running of the induced Wilson coefficient and discuss its operator-level correspondence with the contact interaction arising in Einstein-Cartan gravity.

Going beyond the traditional Hubble-normalized framework, we formalize a unified dynamical system formulation for $f(R)$ and coincident gauge $f(Q)$ gravity using three distinct sets of dimensionless variables: (1) kinematical cosmographic parameters, (2) the dark energy equation of state parameter $w$ (with its $N=\ln a$ derivatives) and matter density abundance $\Omega_m$, and (3) theory space parameters $\{m_i\}$ characterizing the shape of the theory function. Our formulation is free of auxiliary variables, closing via three equivalent ways: (1) specifying a theory, (2) requiring a specific cosmological evolution, or (3) requiring a specific dark energy equation of state evolution. Each closure strategy is illustrated with explicit examples. The theory closure approach studies a case of Hu-Sawicki $f(R)$ and $f(Q)=-2\Lambda+Q+\beta\sqrt{-Q}$ models, where traditional formalisms fail. A heteroclinic trajectory from a GR-matter-dominated epoch to a late-time de-Sitter epoch is general for $f(Q)$, but sensitive to initial conditions for $f(R)$. The cosmographic and equation-of-state closure approaches compare $f(R)$ and $f(Q)$ gravities kinematically equivalent to $\Lambda$CDM ($j(z)=1$) and dynamically equivalent to $\Lambda$CDM ($w(z)=-1$). In both, GR acts as a cosmological past attractor for $f(Q)$ gravity, but not for $f(R)$.

Arm-locking is an important technique for suppressing laser frequency noise in space-based gravitational-wave detection. However, stronger noise suppression inevitably increases the magnitude of frequency pulling, thereby prolonging the lock-acquisition time and increasing the risk of system instability. To address this issue, this paper proposes a real-time Doppler-frequency measurement and frequency-pulling suppression method based on a linear-quadratic-gaussian controller. To achieve a balance between noise suppression and pulling suppression, a time-varying control strategy is adopted. At the initial stage of the time-varying control process, the primary objective is to rapidly limit frequency pulling. Subsequently, the level of pulling suppression is gradually relaxed while the capability for laser frequency-noise suppression is progressively enhanced, so that the residual frequency noise satisfies the time-delay interferometry (TDI) requirement by the end of the transition. Comprehensive performance simulations are conducted for several arm-locking configurations. The results show that the proposed suppressor can reduce frequency pulling within approximately 1000 s while limiting its magnitude to below 100 MHz, thereby eliminating the need for the conventional Doppler frequency pre-estimation stage. When a Fabry-Perot laser is used, the amplitude spectral density (ASD) of the closed-loop laser frequency noise meets the requirements of second-generation and first-generation TDI after 2000 s and 9200 s of closed-loop operation, respectively. These results demonstrate that the proposed suppressor provides both rapid frequency-pulling suppression and a high level of laser frequency-noise suppression. This new method provide a feasible way for rapid acquisition and locking of arm-locking.

The notion of a spatiotemporal quantum state extends the conventional concept of a spatial quantum state to the spatiotemporal domain. Such states are represented by unit-trace operators that encode correlations among quantum events distributed across space and time. In this work, we use the spatiotemporal Kirkwood-Dirac phase space to provide a unified characterization of spatiotemporal quantum states. Spatiotemporal states obtained from Kirkwood-Dirac distributions are generally non-Hermitian and nonnormal; whereas those constructed from Margenau-Hill distributions are Hermitian. We provide a unification via (quasi)probabilistic mixture of Kirkwwod-Dirac spatiotemporal states which encompasses almost all existing formulations of spatiotemporal quantum states. We derive recursive expressions for spatiotemporal states and elucidate the relation between Kirkwood-Dirac nonclassicality and the temporality of spatiotemporal states. We further extend the construction to many-fold correlation functions and establish its connection with out-of-time-ordered correlators (OTOCs). We also develop a more general unifying framework based on (quasi)probabilistic mixture of $s$-parametrized spatiotemporal states and establish their Petz time reversal and application in studying Kubo-Martin-Schwinger (KMS) condition in two-time setting. Finally, we apply this framework to characterize quantum entanglement in spacetime and analyze spatiotemporal entanglement using several complementary entropy measures.

The black hole zeroth law asserts the thermal equilibrium of a stationary Killing horizon, yet its status beyond general relativity remains limited. We demonstrate that its validity is not governed by a universal mechanism: distinct gravitational theories enforce constancy of the surface gravity through different horizon-projections of their field equations. In general relativity, $f(R)$-gravity, and Lovelock theories, the zeroth law is known to follow from the mixed (null-transverse) horizon equations. By contrast, we show that in non-Lovelock theories the zeroth law is enforced by qualitatively different mechanisms. In generalized quadratic gravity, for instance, the null-null component of the field equations dictates its validity. Exploiting this novel diagnostic, we obtain the first exact proof of the zeroth law in the broader landscape of higher-curvature gravity, without relying on a perturbative expansion around general relativity. Our result establishes the zeroth law as a sharp probe of the underlying thermodynamic structure of gravity, and points toward a classification of modified theories according to the mechanism responsible for its validity.

Next-generation ground based gravitational wave detectors will enable precision standard-siren cosmology, making systematics increasingly important. We investigate how line-of-sight acceleration, as may arise for compact binaries in dense astrophysical environments, biases measurements of the Hubble constant $H_0$. We simulate a catalogue of 50 binary neutron star bright sirens with known host redshifts, assuming the signals have been impacted by line-of-sight acceleration and analysing them with vacuum waveforms. Unmodelled line-of-sight acceleration biases the inferred luminosity distances and shifts the individual $H_0$ posteriors systematically towards lower values. Consequently, combining events narrows the posterior around a biased value rather than averaging away the systematic, even when the acceleration signs are assigned randomly. For our 50-event catalogues, affected fractions of approximately $10\%$ at $|a_\parallel|/c=10^{-6}\,\mathrm{s^{-1}}$, or $30\%$ at $|a_\parallel|/c=10^{-7}\,\mathrm{s^{-1}}$, produce offsets exceeding three posterior standard deviations in at least one quarter of the realisations. Considering larger catalogues further increases the significance of the effect. Our results indicate that environmental effects may constitute an important systematic for precision standard-siren cosmology and should be incorporated into future population analyses.