We show that retarded Green’s functions of black hole spacetimes can be expressed as a convergent mode sum everywhere in spacetime. At late times a quasinormal mode sum converges, while at early times a Matsubara (or Euclidean) mode sum converges. The two regions are separated by a light cone that scatters from the black hole potential. The Matsubara sum is a Fourier series on the Euclidean thermal circle associated with the early time region. We illustrate our results for the Pöschl-Teller model, the Bañados-Teitelboim-Zanelli black hole, and the Schwarzschild black hole. In the case of the Schwarzschild black hole, we express the branch cut contribution as a convergent sum of de Sitter quasinormal modes as $\mathrm{\Lambda }\to 0^{+}$ and exploit recent exact solutions to the Heun connection problem. In each case, we analytically show convergence by studying the asymptotics of residue sums and also provide numerical demonstrations.

We study two singular spectral components of the Green’s function of a Schwarzschild black hole and their interpretation in the frequency domain: (i) the low-frequency branch cut, which yields corrections to Price’s law tails in the form of inverse power laws weighted by logarithmic terms; and (ii) the quasinormal-mode spectrum, which generates a redshifted response for sources extended toward the horizon. We show that the frequency-domain Green’s function admits a natural interpretation in terms of graybody factors, providing the first analytical justification of graybody-based ringdown models for sources at generic locations. For sources localized outside the peak of the potential barrier, we identify two tail contributions activated with a time delay, arising from backscattering of the prompt response and of the ringdown signal. We show that corrections to Price’s law can be relevant at intermediate times, when the ringdown still dominates the waveform. For sources localized inside the potential barrier peak, the tail is suppressed and the signal is instead dominated by quasinormal frequencies. In this regime, these spectral components produce both the ordinary quasinormal-mode ringdown and an infinite tower of exponentially decaying terms governed by the horizon surface gravity, the so-called redshift terms. We demonstrate that this component is not screened by geometric features of the background spacetime and persists up to late times, as supported by numerical investigations of perturbative waveforms. Our results provide a mathematical foundation for phenomenological modeling of the branch-cut contribution at intermediate times, which is relevant for prospective observations of tails, and strong evidence for the presence of redshifted components from intermediate to late times.

In this work, we explore the quasinormal modes (QNMs) of the Bonanno-Reuter black hole, one of the first regular black hole metric suggested by the asymptotically safe gravity (ASG) program. The running parameter $\alpha$ is set to a positive value, the related running Newton coupling vanishes at high energies, fully achieving an ultraviolet fixed point and eliminating nonphysical UV divergences. This yields a singularity-free geometry. Hence, we focus on the resulting renormalization-group-improved Schwarzschild metric, which naturally produces an (anti–)de Sitter nonsingular core. On the basis of this background, we compute the QNM spectrum for scalar, electromagnetic, and gravitational perturbations by employing the spectral method (SM). This method, recognized for its enhanced precision compared to high-order WKB methods, allows the identification of fundamental modes, extensive collections of overtones, and purely imaginary overdamped modes that were entirely missed in previous analyses. These characteristics, resolved here for the first time in the Bonanno-Reuter black hole, underscore the crucial importance of high-precision spectral methods in investigating delicate signatures of black hole models inspired by quantum gravity.

We examine extreme mass-ratio inspirals (EMRIs) as probes of beyond-vacuum general relativistic effects, accounting for both astrophysical environments and scalar Gauss-Bonnet (sGB) gravity. In beyond-vacuum scenarios, the evolution of an EMRI immersed in a cold dark matter environment modifies the gravitational wave flux and introduces additional dissipative effects such as dynamical friction. In parallel, in the beyond-general-relativistic settings such as in sGB gravity, the inspiraling object carries an effective scalar charge and emits scalar radiation. Both environmental and modified-gravity effects modify the flux-balance law, thereby inducing changes in the EMRI dynamics. Using a two-timescale analysis within the fixed-frequency formalism, we compute leading-order corrections to the energy fluxes for quasicircular, equatorial orbits in static, spherically symmetric spacetimes and construct the corresponding gravitational waveforms, which are used to quantify the accumulated gravitational wave dephasing and waveform mismatch relative to the vacuum general relativistic case. We further perform the Fisher information matrix analysis to estimate parameter correlations and the ability of future space-based detectors such as the Laser Interferometer Space Antenna to disentangle environmental and modified-gravity effects. Our results show that both dark matter and scalar-field effects can leave measurable imprints on EMRI waveforms and that a consistent beyond-vacuum treatment is essential for robust tests of gravity.

We compute deviations from observed gravitational-wave signals, where the amplitude of the signal is unchanged. As an example, we consider the detectability of low-lying dynamical tides in binary neutron star or neutron star black hole mergers. Tidal forces can excite oscillatory modes of one or both of the stars in the binary when the orbital frequency of the binary system sweeps through the resonant mode frequency dissipating energy into the vibrational mode. The orbital energy loss to the vibrational mode extracts energy from the orbital motion, advancing the time to merger. The inspiral then continues with an excess phase and a time advance. Both will cause a mismatch when fitting to a system that has not gone through the resonance. To resolve this effect, we compute the mismatch for current and planned detectors using both a quasianalytical approach that relies on the computation of moment integrals and an optimized version of the standard numerical match function. We conclude that detectability can occur for time advances of the order of 1 ms with advanced LIGO-Virgo-KAGRA detectors for an excess energy flux that is a few percent of the gravitational-wave emission. Our results contrast with previous work, which model this effect solely as a phase shift of the waveform or by using the difference in the number of cycles induced by the resonant behavior. We show that tidal resonance effects primarily cause a time advance of the merger, rather than a phase difference, and that the single-frequency approximation commonly used in the literature significantly overestimates the detectability of this effect.

We study the cosmological impact of ultralight dark matter (ULDM) with a quadratic coupling to Standard Model particles. In addition to the suppression of small-scale power from ULDM itself, the coupling induces a variation of fundamental constants that is modulated by the ULDM oscillatory field value. In this work, we consider the ULDM-induced, time-dependent variation of the fine structure constant and the mass of the electron. These variations modify the predicted abundance of light elements during big bang nucleosynthesis (BBN) and the process of recombination, thereby affecting the anisotropies of the cosmic microwave background (CMB). We use CMB anisotropy data and baryon acoustic oscillation measurements to obtain constraints on the variation of couplings over a wide range of ULDM masses. We self-consistently account for the modification of the primordial helium abundance during BBN in computing the CMB power spectra. We find that the allowed ULDM fraction of total dark matter abundance is more constrained for ULDM masses $\lesssim {10}^{-26}\mathrm{eV}$ in the presence of the variations. Moreover, our constraints on the variational couplings for ULDM masses $\lesssim {10}^{-27}\mathrm{eV}$ are stronger than the ones derived from the primordial helium abundance at BBN. Under our ULDM model, the variation of fundamental constants has no appreciable impact on the Hubble constant inferred from CMB data.

Current pulsar timing array (PTA) analyses are phase incoherent and thus to not take full advantage of pulsar distance information, thereby missing out on improved angular resolution and on a potential factor-of-two gain in detection sensitivity for individual gravitational-wave (GW) sources. In this work, we investigate the impact of precise pulsar distance measurements on angular resolution as an extension to previous work measuring the angular resolution of a dense isotropic PTA [D. L. Jow et al., How many pixels are there in a polarized pulsar timing array map?, Phys. Rev. D 113, 043034 (2026)]. We present a coherent map-making technique that utilizes precise pulsar distance measurements to reach a diffraction-limited resolution of an individual source: $\delta {\theta }_{\mathrm{diff}}\times (1/\mathrm{SNR})\approx 1\mathrm{arcmin}$, where $\delta {\theta }_{\mathrm{diff}}={\lambda }_{\mathrm{GW}}/r$ is the diffractive angle and SNR refers to the detection strength of the source. With this level of angular resolution, identifying an electromagnetic counterpart may become feasible, enabling multimessenger follow-up. We show that for SNR = 10, which may be the current sensitivity level using a coherent analysis, the diffraction limit is reached with approximately ten equidistant pulsars with distances of about 300 parsecs. Moreover, angular resolution scales sharply with the number of known pulsar distances as $\sim (1/\mathrm{SNR}{)}^{N_{\mathrm{dist}}/2}$. Thus, each additional pulsar with high signal-to-noise timing and precise distance measurement can improve PTA resolution by an order of magnitude. The distance to the best-timed millisecond pulsar (PSR $\mathrm{J}0437-4715$) is already constrained to sub-parsec levels. We argue, therefore, that a coherent analysis of PTA data, fully incorporating pulsar distance information, is timely.

Understanding the hydrodynamics of out-of-equilibrium dense viscous fluids is of key importance to accurate descriptions of physical systems such as compact stars, particularly their mergers. We consider a near-equilibrium relativistic fluid with $n$ independent and small chemical potentials restoring the system back toward equilibrium. By diagonalizing the evolution equation for the out-of-equilibrium chemical potentials, we construct an explicit evolution equation for the bulk scalar of the system in second-order hydrodynamics in terms of equilibrium quantities. We find expressions for the $2n$ transport quantities and show that, in the rest frame of the fluid, the system admits a Green’s function corresponding to an $n$-component fluid.

We analyze how the geodesic motion in the three- and four-vortex sectors of the Abelian-Higgs model at critical coupling is deformed by the excitation of a massive bound mode. We find that the geodesics corresponding to Bogomol’nyi-Prasad-Sommerfield (BPS) solutions with enhanced symmetry remain unchanged, although the direction of the actual motion depends on the mode-generated force, i.e., a force arising from the change of the mode frequency along the geodesic. In a generic case, for example, in head-on collisions between the axially symmetric one- and two-vortex or between two two-vortices, the vortex trajectories can differ strongly from the BPS geodesic. This enhances the chaotic behavior in the formation of the final state.

We investigate the thermodynamic and transport properties in hot nuclear matter accounting for the medium modifications of the nucleons within a chiral SU(3) model including effects from isospin asymmetry. Using the relaxation time approximation, the transport coefficients of the shear viscosity and thermal conductivity are studied. The shear viscosity $\eta$ calculated within the chiral SU(3) model is observed to be smaller than the values calculated for free nucleon gas, whereas the thermal conductivity $\kappa$ is appreciably larger as compared to the free nucleon gas. The presence of isospin asymmetry in the medium leads to higher values of both the coefficients of shear viscosity ($\eta$) and thermal conductivity ($\kappa$), however, the effect is observed to be marginal for $\eta$. In the chiral SU(3) model, the effect of isospin asymmetry is observed to be larger for higher values of temperature. For $\mathrm{T}=150\mathrm{MeV}$, there is observed to be a drop in the value of $\kappa$ as density is increased, contrary to the increase observed for the lower values of temperature, $\mathrm{T}=50$ and 100 MeV. The shear viscosity coefficient to entropy density ratio $\eta /s$ drops with increasing baryon density that becomes more pronounced at higher temperatures in the chiral SU(3) model as compared to the case of a free nucleon gas. The present study of the thermodynamic as well as transport properties in hot nuclear matter is of relevance for relativistic heavy-ion collisions with different initial isospin asymmetry, in particular, for the compressed baryonic matter experiment at the FAIR facility at GSI.

We investigate the decay $\varphi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ in an effective-Lagrangian framework that keeps the dominant $\rho \pi$ mechanism, the direct three-pion term, and a real constant background contribution explicitly separated at the amplitude level. The resonant contribution is described with the Gounaris-Sakurai propagator, the neutral channel includes ${\rho }^0\text{−}\omega$ mixing, and the leading elastic $I=1$, $P$-wave $\pi \pi$ final-state interaction is incorporated through the complex, $s$-dependent Omnès function ${\mathrm{\Omega }}_1(s+i0)$. The Omnès factor is applied channel by channel to the three two-pion subsystems, while the direct amplitude is dressed by the averaged factor ${\mathrm{\Omega }}_{\mathrm{dir}}=({\mathrm{\Omega }}_0+{\mathrm{\Omega }}_{+}+{\mathrm{\Omega }}_{-})/3$. To avoid double counting the elastic rescattering already contained in the physical $\rho \to \pi \pi$ coupling, we introduce $g_{\rho \pi \pi }^{\mathrm{bare}}=g_{\rho \pi \pi }^{\mathrm{phys}}/|{\mathrm{\Omega }}_1(m_{\rho }^2)|$ in the Omnès-dressed $\rho$-exchange amplitude. With the final parameter set used in this work, we obtain ${\mathrm{\Gamma }}_{\mathrm{th}}=0.6915\mathrm{MeV}$, slightly above the empirical estimate ${\mathrm{\Gamma }}_{\exp }\approx 0.660\pm 0.020\mathrm{MeV}$, while the direct integrated weight is reproduced at the KLOE (K LOng Experiment) scale, $I_{\mathrm{dir}}=8.393\times {10}^{-3}$. The corresponding resonant weight is $I_{\rho \pi }=0.9619$. The resulting Dalitz distribution retains the expected $\rho \pi$-dominated three-band structure and shows the localized neutral-channel deformation induced by ${\rho }^0\text{−}\omega$ mixing. Remaining discrepancies in the $x$ and especially the $y$ projections indicate the limitations of the present minimal single-channel Omnès implementation and motivate a next-stage analysis based on a full dispersive crossed-channel treatment and a direct fit to the efficiency-corrected KLOE Dalitz-bin data.

Recent studies have shown that a secondary potential barrier, forming a potential well outside the event horizon, can destabilize the quasinormal mode (QNM) spectrum of black holes. We find that spectral instability may persist even after the potential well vanishes, giving rise to a distinct family of spectrally unstable QNMs that differ from the spectrally stable modes localized near the potential peak and associated with the photon sphere. Nevertheless, time-domain simulations reveal that early-time ringdown waveforms remain dominated by stable modes, while unstable modes have only a subdominant contribution. These results highlight the robustness of black hole spectroscopy, as the observable ringdown signal is primarily governed by the most stable QNMs.

We extend Maxwell electrodynamics with a Chern-Simons coupling to a dark-sector top form sourced by domain walls. Cosmic birefringence can arise from a distinct mechanism in which photon polarization is rotated when crossing vacuum interfaces rather than through adiabatic propagation in a background field. Ultrathin walls induce a finite, frequency-independent polarization rotation generated by an electromagnetic Chern-Simons term localized at the interface. The effect persists even in the absence of ultralight axions or other propagating scalar degrees of freedom. For phenomenologically viable parameters, such walls can generate cosmic microwave background polarization rotation at the level $\mathrm{\Delta }\vartheta \sim {10}^{-3}\mathrm{rad}$, providing a signature of the topological structure of the dark-sector vacuum.

We explore the mass-resonance structure that naturally arises in extradimensional models. The resonance can enhance both dark matter annihilation and self-interactions. We demonstrate such a resonance structure by considering the fermionic dark matter and dark photon models on an $S^1/(Z_2\times Z_2^{\prime })$ orbifold. We also note that this model embeds a dark matter axial-vector coupling to the dark photon, thereby opening up the viable dark matter parameter space. We then present the unique predictions for direct-detection experiments and accelerator searches.

A novel semiclassical gravity model proposed by Oppenheim et al., that consistently describes interactions between quantum systems and a classical gravitational field, has recently attracted considerable attention. However, the limitations and phenomenological viability of this model have not yet been thoroughly investigated. In this work, based on the model, we study quantum fluctuations of geodesic deviation coupled with a classical gravitational field. We analytically derive the strain spectrum expected from the fluctuations and show that the original Oppenheim et al. model can be tested with the current observational sensitivity of gravitational-wave experiments. Furthermore, motivated by the novel semiclassical model, we construct two additional models; a modified Oppenheim et al. model that is manifestly consistent with Bianchi identities, and a classical-quantum model with environment-induced noise. We analyze the strain spectra predicted by these two models through comparison with those of the original Oppenheim et al. model and perturbative quantum gravity.

We investigate the vacuum-induced current density for a charged scalar field in a ($D+1$)-dimensional cosmic dispiration spacetime threaded by a magnetic flux. This background combines a cosmic string and a screw dislocation, yielding a nontrivial helical geometry. By constructing the normalized mode functions of the Klein-Gordon equation, we evaluate the Wightman function and obtain the vacuum expectation value of the current density. We show that, in addition to the azimuthal component describing a persistent current around the defect, a nonvanishing axial component is induced as a direct consequence of the helical structure of the spacetime. Both components are periodic functions of the magnetic flux depending only on its fractional part, reflecting the Aharonov-Bohm nature of the effect. Closed expressions are obtained for massive and massless fields in arbitrary dimensions. We demonstrate that the screw dislocation parameter plays a crucial role in the behavior of the induced currents, leading to the regularization of the components at the origin and controlling their magnitude. Their asymptotic behavior is also analyzed in detail. Our results reduce to known expressions in the absence of the screw dislocation, providing a consistency check. In particular, we examine the physically relevant ($3+1$)-dimensional case, where numerical analysis reveals nontrivial features arising from the interplay between topology and gauge effects.

We investigate the behavior of black hole scalarization induced by a charged scalar field in the extended phase space of the asymptotic AdS spacetime with three distinct horizon topologies. The results indicate that in all three cases, the charged black hole spacetime undergoes scalarization at low temperatures. Notably, the spherical topology is unique in that its domain of scalarization theoretically extends to much higher temperatures under low pressure in the extended phase space. Moreover, the scalarization process in the spherical case exhibits complex phase transition behaviors without additional nonlinear terms, which are similar to those in the planar and hyperbolic topologies with the assistance of nonlinear terms. With increasing pressure in the extended phase space, the condensate of the scalarization in all three cases undergoes a transition from the first-order style to a cave-of-wind style. This study provides deeper insight into the zeroth-order phase transition during black hole scalarization and reveals the complete phase structure of black holes in the extended phase space.

We investigate the challenges of constructing neutron star (NS) solutions in $f(\mathbb{Q})$ gravity, highlighting the importance of treating the affine connection as an active, dynamical component of the theory. We begin by clarifying under what conditions standard simplifications—such as the coincident gauge or general relativity (GR)-like connections—inadvertently lead to GR behavior, even in nontrivial $f(\mathbb{Q})$ models. Building on previous work in black hole spacetimes, we adapt the formalism to NS and extend it to nonvacuum configurations. Focusing on two representative models, $f(\mathbb{Q})=\mathbb{Q}+\alpha {\mathbb{Q}}^2$ and $f(\mathbb{Q})={\mathbb{Q}}^{\beta }$, our analysis suggests that, under standard regularity assumptions, solutions with Maclaurin/Laurent-type series recover GR dynamics, pointing to more intricate structures as the likely seat of beyond-GR effects, and reflecting the constraints imposed by the connection’s dynamics on the asymptotic behavior of genuinely beyond-GR solutions. We then formulate the problem as a boundary value problem and highlight the numerical pathologies that may arise, together with possible strategies to prevent them. This work aims to provide a concrete framework for future numerical studies and outlines the theoretical consistency conditions required to construct physically meaningful beyond-GR NS solutions in $f(\mathbb{Q})$ gravity.

We develop a local and covariant framework for constraining the evolution of generalized entropy along null horizons, combining classical geometric methods with constraints from quantum field theory. Building on the quantum focusing conjecture (QFC), which restricts entropy evolution along null directions, we derive a Raychaudhuri-type differential inequality for the generalized expansion that makes its local dependence on expansion and shear explicit. The resulting relation, $\frac{d\mathrm{\Theta }}{d\lambda }\le -\theta \mathrm{\Theta }+\frac{1}{2}{\theta }^2-{\sigma }^2$, reveals a direct interplay between expansion and shear in controlling entropy flow: shear contributes negatively and yields a monotonic suppression of the generalized expansion in shear-dominated regimes, while expansion provides a competing geometric source term. This structure provides a local geometric formulation consistent with the QFC and clarifies its interpretation as a constraint on entropy evolution. We further show that quantum extremal surfaces correspond to configurations characterized by $\mathrm{\Theta }=0$, whose local stability properties are governed by the same geometric data. In addition, we derive a bound on the exponential separation of nearby null generators, indicating that the same combination of expansion and shear also controls geometric instability. Our results provide a local geometric refinement of entropy bounds in semiclassical gravity and establish a direct connection between null geometry, quantum energy conditions, and entropy flow, offering a local geometric perspective on horizon thermodynamics beyond global formulations.

Recent observations of high-redshift galaxies by the James Webb Space Telescope suggest the presence of a bright population of galaxies that is more abundant than predicted by most galaxy formation models. These observations have led to a rethinking of these models, and numerous astrophysical and cosmological solutions have been proposed, including cosmic strings, topological defects that may be remnants of a specific phase transition in the very early moments of the Universe. In this paper, we integrate cosmic strings, a source of nonlinear and non-Gaussian perturbations, into the semianalytical code zeus21, allowing us to efficiently predict the ultraviolet luminosity function (UVLF). We conduct a precise study of parameter degeneracies between star-formation astrophysics and cosmic-string phenomenology. Our results suggest that cosmic strings can boost the early-galaxy abundance enough to explain the measured UVLFs from the James Webb and Hubble Space Telescopes from redshift $z=4$ to $z=17$ without modifying the star-formation physics. In addition, we set a new upper bound on the string tension of $G\mu ⪅{10}^{-8}$ (95% credibility), improving upon previous limits from the cosmic microwave background. Although with current data there is some level of model and prior dependence to this limit, it suggests that UVLFs are a promising avenue for future observational constraints on cosmic-string physics.