Papers

In this paper, we investigate the periodic orbits around a black hole (BH) in Einstein-Maxwell-scalar (EMS) theory and the corresponding gravitational waveforms. First, we study the test particle dynamics around the BH by using the Lagrangian formalism. Using the corresponding conditions, we explore the effect of the spacetime parameters on the marginally bound orbit (MBO) and innermost stable circular orbit (ISCO). The results indicate that MBO and ISCO quantities decrease with the rise of the $\beta$ parameter and BH charge $Q$, and vice versa for the $\gamma$ parameter. Subsequently, we plot the different zoom-whirl orbits around the BH in EMS theory by finding the test particle's corresponding energy and angular momentum. Finally, the gravitational waveforms of the extreme mass ratio inspirals, which contain a supermassive BH in EMS theory and a stellar mass object, are demonstrated. It is shown that the zoom-whirl orbits shrink as the BH charge increases, and, as a result, gravitational waveforms shift towards shorter times.

Considering a cylindrically symmetric spacetime, a novel exact $\kappa$-deformed Schwarzschild-AdS black string solution is derived in General Relativity in the presence of a negative cosmological constant. The geometric properties of the resulting solution are systematically investigated by computing the Ricci and Kretschmann curvature scalars. The analysis reveals the existence of a curvature singularity at the origin, which remains enclosed by an event horizon provided that the $\kappa$-deformation parameter satisfies a specific constraint. Subsequently, the influence of various model parameters on the horizon structure and configuration is examined in detail. The thermodynamic properties of these black strings are thoroughly evaluated; in this regard, the Hawking temperature, entropy, mass, isobaric heat capacity, and Gibbs free energy are self-consistently extracted. The effects of the parameters, particularly the $\kappa$-deformation parameter, on these thermodynamic quantities are comprehensively explored. Furthermore, it is demonstrated that these state variables fundamentally satisfy the extended first law of black hole thermodynamics and yield a modified Smarr relation. Finally, the temporal profile of the Hawking radiation is probed via the dimensionless sparsity parameter, through which the impacts of the underlying parameters on the quantum emission rate are systematically analyzed.

The Teukolsky Master Equation (TME) is a powerful technique used to study perturbations of a spacetime with gravitational, electromagnetic, and neutrino components. The well-known Kerr metric is a suitable candidate for this formalism because it is a Petrov type D metric. However, the Kerr metric represents the exterior spacetime of a perfect sphere and only black holes are described using this metric. For another astrophysical object, such as fast-spinning neutron stars, the Kerr metric is not valid due to the rotation induced deformations to the gravitational source. The main goal of the present work is to show a TME for a Kerr-like metric (KL) with a mass quadrupole moment parameter $q$. This new parameter will represent deformations from a perfect sphere; therefore, KL is a better candidate to study perturbations surrounding spinning stars.

We investigate the validity of the sub-horizon approximation (SHA) and quasi-static approximation (QSA) for linear matter perturbations in interacting scalar-field dark-energy models. We consider both quintessence and phantom scalar fields and derive their full relativistic perturbation evolution to compare with the corresponding SHA and QSA solutions. We find that, while the SHA reproduces the full evolution with percent-level accuracy for non-interacting and weakly interacting models on sufficiently sub-horizon scales, its accuracy progressively deteriorates with increasing interaction strength and towards larger scales. Moreover, unlike in $\Lambda$CDM and non-interacting scalar-field models, applying the SHA to interacting models does not fully recover the standard Newtonian fluid equations. The QSA generally provides a closer description of the full relativistic evolution than the SHA over the scales considered. By comparing the scalar-field model with $\Lambda$CDM using the full relativistic equations and, separately, using the SHA system, we evaluated whether the SHA is capable of capturing the full extent of the physical differences introduced by the alternative model. We find that the difference between these two comparisons becomes increasingly important for stronger interactions and smaller wavenumbers. Finally, we demonstrate that the resulting differences can reach several percent on scales accessible to large-volume hydrodynamical simulations, implying that the validity of the SHA cannot be assumed solely from the sub-horizon condition. Our results highlight the need to benchmark the approximation over the relevant interaction parameter and wavenumber ranges before employing interacting-dark-energy models in large-volume structure-formation simulations and precision comparisons with large-scale-structure observations.

We study null geodesics in Reissner-Nordström-de Sitter spacetime and in its $\omega=-2/3$ Kiselev deformation through the elliptic curves defined by the radial equation. The relation of these curves to the non-critical $E_7$ Seiberg-Witten family yields differential equations for finite-distance light deflection, and explains the boundary source term through a suitable gauge of the Seiberg-Witten differential. This geometry separates the extremal point $Q^2=M^2$ from the Argyres-Douglas point $Q^2=9M^2/8$. We also determine the Kiselev critical and horizon loci, and show that, at fixed nonzero angular momentum, the Argyres-Douglas and ultracold loci meet only at zero Killing energy.

Propagation delays cause an image recorded at a single observer time to combine radiation emitted at different stages of the source evolution. Comparable changes in total intensity can accompany distinct and even opposite changes in apparent image size. Using regional intensities, centroids, and covariances, we apply the law of total covariance to separate changes in regional intensity weights from changes in internal widths and centroid separation. Ray tracing simulations of a finite Gaussian hotspot moving along a prescribed strong field trajectory show two events with comparable attenuation in screen integrated intensity but opposite changes in second moment size. In the contracting event, the regional weights move away from balance; in the expanding event, they move toward balance even as the centroids approach each other. Differential propagation delays therefore drive these opposite size responses by redistributing intensity between spatially separated image regions.

Thermodynamic descriptions of gravity involve both variational conditions for spacetime dynamics and analytic structures associated with horizons. We examine their relation while keeping their assumptions distinct. First, we present an explicit derivation of the Einstein equation from the established null-vector entropy functional, including the null constraint, the matter term, and the integration constant associated with the cosmological constant. Second, for an analytic static spherical geometry with a nondegenerate Killing horizon, we define a meromorphic radial one-form whose residue is the inverse of twice the surface gravity. Euclidean regularity then fixes the Hawking temperature. Combining this residue with the Einstein–Hilbert Noether charge gives a normalized contour representation of the Wald entropy. The construction reproduces the Schwarzschild temperature, entropy, and Smarr relation, but does not constitute an independent microscopic derivation of the area law. We establish the limits of a stronger identification between pole structure and dynamics: an asymptotically flat family can retain the Schwarzschild horizon residue, area, surface gravity, and mass while violating the vacuum Einstein equation, and an extremal charged solution possesses a higher-order pole. We also show why exponentiating an unspecified entropy functional does not produce a universal entropy residue. The resulting framework separates entropy stationarity, horizon analyticity, and charge normalization, providing explicit consistency tests for further thermodynamic interpretations of gravitational singularities.

We prove that plane waves are the only gravitational pp-wave spacetimes which are distinguishing; in particular, they are the only strongly causal ones. This is used to prove a null version of Anderson's rigidity theorem, conjectured by Costa e Silva and Flores: every geodesically complete, transversally complete, strongly causal, Ricci-flat Brinkmann spacetime of dimension $4$ is isometric to a quotient of a plane wave spacetime.

In this study, the power law form of f(Q) gravity $(f(Q)=Q+mQ^n)$ has been studied in view of statistical analysis with current observed data and irreversible thermodynamics. The best fit values of model specific parameters are found with the use of of 31point Hubble data, Patntheon type Supernva and 1721 point SH0ES data and a comparative study has been performed between $f(Q)$ and standard $\Lambda$CDM model. The thermodynamic consequence using standard Eckart theory of non-equilibrium thermodynamics has been examined independently for general form of $f(Q)$ gravity followed by power law form of $f(Q)$ where the horizon entropy is calculated using unified law of thermodynamics. Suitable range of power law model specific parameters has been explored through investigating validity of generalized second law of thermodynamics and thermodynamic equilibrium. Finally evolution nature of cosmographic parameters are studied within the specific range of $m,n$ which is compatible with the results obtained from both statistical and thermodynamical analysis.

We investigate whether the coalescence of long-lived quasinormal modes enhances the boundary response of rotating BTZ black holes. Using exact scalar solutions with mixed Robin boundary conditions and the retarded boundary correlator, we compare frequency-domain resonances and time-domain signals at fixed source and operator normalizations. An exceptional point (EP) can be crossed by varying the spin alone in a suitably selected fixed theory. Along a distinct near-extremal path that tracks the co-rotating EP surface by tuning the scalar mass and boundary coupling, a taller, narrower resonance coexists with a weaker but longer-lasting double-pole impulse response. The frequency-domain enhancement persists away from the EP and is therefore not unique to mode coalescence. Thus, the EP determines the double-pole structure and Jordan relaxation, but does not by itself determine the response strength, which also depends on the physical path and excitation protocol.

The Weyssenhoff fluid expands the ordinary perfect-fluid description of general relativity by taking into account the intrinsic spin of its constituent particles. Within the linearized regime of Einstein-Cartan theory, we investigate the exterior geometry produced by isolated slowly rotating Weyssenhoff fluids, i.e., sources endowed with both macroscopic and microscopic angular momenta. Our work represents an extension of the foundational analysis of Arkuszewski, Kopczyński and Ponomariev, which was restricted to the static fluid configuration. Under the assumptions of stationarity and axial symmetry, we derive the explicit expression for the linearized stress-energy tensor of the source and obtain the corresponding metric through a multipole expansion. The ensuing solution exhibits a generalized Lense-Thirring structure, with both the gravitoelectric and gravitomagnetic sectors affected by the quantum spin and macroscopic rotation. We also discuss some phenomenological implications of the model, including the gyroscope precession and the Sagnac effect, along with potential experimental probes of the predicted corrections.

de~Sitter spacetime plays a central role in modern cosmology, providing an excellent approximation to both inflation and the present accelerated expansion. It also offers a particularly simple setting in which gravity, spacetime symmetry, and quantum field theory depart qualitatively from their Minkowski-space counterparts. These lecture notes introduce de Sitter spacetime, from its geometry and symmetries to quantum fields and perturbations on a fixed \(3+1\)-dimensional de Sitter background. We cover coordinate systems, causal structure, unitary representations, particle production in time-dependent backgrounds, and cosmological perturbations, with emphasis on physical interpretation, applications to cosmology, and how curvature reshapes the notions of mass, vacuum, particles, and late-time observables.

In this work, we investigate quasinormal modes and the shadow of a Schwarzschild-Tangherlini black hole in $(d+1)$ dimensions, incorporating corrections arising from the Generalized Uncertainty Principle (GUP). Using the WKB approximation up to sixth order, we calculate the quasinormal frequencies for $l=1, 2$ and $d=3, 4, 5, 6$, and analyze the effects of the dimensionless linear and quadratic GUP parameters $\bar{\alpha}$ and $\bar{\beta}$, respectively. We find that the linear correction increases the oscillation frequency and the damping rate, whereas the quadratic correction produces the opposite behavior within the parameter range considered. Using the finite difference scheme, we obtain the time-domain evolution and find that higher dimensions lead to faster damping and that the visibility of GUP-induced modifications to the time-domain waveform depends on the excitation profile of the initial perturbation, whereas the underlying quasinormal spectrum remains determined by the black hole geometry.Furthermore, we investigate the shadow and establish its correspondence with the quasinormal spectrum in the eikonal limit through the properties of the unstable circular null geodesics. Finally, we confront the predicted shadow size with Event Horizon Telescope observations of Sagittarius A* and use these constraints to investigate the allowed GUP parameter space.

This paper concerns the geometry of gravitational pp-wave spacetimes. We give a counterexample to the Ehlers–Kundt conjecture. In fact, we show that geodesic completeness is generic, in the sense of Baire category, among gravitational pp-waves. We also define a concept of “universal pp-wave”, i.e. a pp-wave whose metric approximates that of every other gravitational pp-wave arbitrarily closely on arbitrarily large compact sets, and we show that there are geodesically complete universal pp-waves. Our machinery also suffices to give a new proof of the polynomial case of the Ehlers–Kundt conjecture (previously proved by Flores and Sánchez).

Cosmological $\alpha$-attractor models are renowned for their universal predictions for inflationary observables, largely independent of the detailed form of the inflaton potential. In this work, we investigate the extent to which this universality persists for polynomial $\alpha$-attractor models, with particular emphasis on the scalar spectral index ($n_s$) and the post-inflationary reheating history. We derive an extended analytical expression for the scalar spectral index ($n_s$) and the tensor-to-scalar ratio ($r$), retaining sub-leading contributions beyond the commonly used universal approximation. Interestingly, we find that these corrections introduce an explicit dependence of $n_s$ on the parameter characterizing the polynomial attractor potential $\mu$, a dependence that is absent in the leading universal expression. We systematically investigate how this model dependence modifies the predictions in the $(n_s-r)$ plane and affects the model parameter ($\mu$). We further incorporate the Duration of reheating ($\Delta N_{rh}$) and effective equation of state parameter of the reheating epoch ($w_{rh}$), accounting for their impact on the number of e-folds between horizon crossing and the end of inflation ($\Delta N_{\mathrm{CMB}}$). By confronting the resulting predictions with current CMB observations, we identify the viable parameter space and examine the interplay between the model parameter ($\mu$) and reheating. Our results demonstrate that sub-leading corrections can provide a window into the underlying structure of polynomial attractors, offering a possible way to distinguish different members of the attractor class observationally.

Deciphering the formation channels of the observed binary black hole mergers remains a central open problem in gravitational-wave astronomy. With hundreds of detections, the inferred distribution of masses and spins reveals a rich diversity which is difficult to reconcile with traditional formation scenarios from isolated binary stars or dense stellar environments. Here, we consider the large fraction of massive progenitor stars found in hierarchical triples and investigate black hole mergers driven by gravitational perturbations from tertiary companions. Simulations of their dynamics and stellar evolution reproduce key features of the merger population, including: i) a sharp primary mass peak at $m_1\sim10\,\rm M_\odot$ dominating the population; ii) substantial fractions of systems with large spin-orbit angles within and beyond the peak, matching the skewed distributions of the spin parameters $\chi_{\rm eff}$ and $\chi_p$; iii) a mass-ratio distribution favouring equal masses with matching slopes. We further predict a sharp decline of mergers near $m_1\sim30\,\rm M_\odot$, coincident with the location of inferred features that may signal another channel dominating the high-mass tail. Our models of hierarchical triples demonstrate, for the first time, a formation scenario which simultaneously reproduces the principal properties inferred for the low-mass bulk of binary black hole mergers.

We apply physics-informed neural networks (PINNs) to recover the time-time component of static, spherically symmetric black-hole exterior metrics from a reduced ordinary differential equation (ODE). Inspired by recent work on solving Einstein field equations with deep learning~\cite{Li2023}, we encode the vacuum/charged exterior through a residual loss and an asymptotic boundary constraint—not by embedding analytic metric terms such as $2M/r$ directly into the network output. Unlike the distributed PINN (DPINN) strategy of Ref.~\cite{Li2023}, which partitions the radial domain into subdomains with separate networks, we employ a unified fully connected network over the entire interval $[r_{\min},r_{\max}]$, avoiding spurious jumps at subdomain interfaces. Moreover, whereas Ref.~\cite{Li2023} restricts training to $r\in(10,300)$—well outside the steep $1/r$ and $1/r^2$ curvature of the inner exterior—we begin at $r_{\min}=10^{-2}M$, spanning three decades in radius and covering the strongly varying region that DPINNs sidestep by domain truncation. Holding the mass fixed at $M=1$, we sweep electric charge $Q\in\{0,0.5,1.0,1.1\}$ at $\Lambda=0$ and sweep $\Lambda\in\{0,0.1,-0.1\}$ at $Q=0.5$. All configurations achieve relative $\mathcal{L}_2$ errors below $6\%$ against the analytic reference. For the representative case $Q=0.5$, $\Lambda=0.1$, three independent trainings with fixed seeds yield relative errors of $3.89\%$, $1.08\%$, and $2.76\%$ (mean $2.58\%$, standard deviation $1.41\%$), demonstrating robustness of the mesh-free approach without labeled field data.

Spontaneous scalarization of charged black holes in asymptotically flat spacetime has attracted much recent interest. It is recently reported that inside these spontaneously scalarized black holes, the Kasner parameter $\beta$ at the terminal singularity diverges as $\beta\propto(q/q_c-1)^{-\gamma}$ near the critical charge-to-mass ratio $q_c$, with an exponent $\gamma=1/2$ that appeared model independent within a wide class of couplings. In this paper we report a family of new universality classes in which $\gamma$ differs from 1/2. We show that all these critical behaviors are governed by the same emergent scaling symmetry at the would-be Cauchy horizon of the background Reissner-Nordström solution. This symmetry leads to a “seesaw amplification” to amplify exterior small scalar and produces a limiting autonomous system that is independent of the details of the theory. Our mechanism provides a unified picture of exterior scalarization and interior criticality and makes sharp numerical predictions that we test.

In this paper, we examine the new black holes of Einsteinian cubic gravity within the framework of Born-Infeld-type electrodynamics. Initially, we establish the differential equations of motion that characterize an innovative collection of charged black hole solutions in Einsteinian cubic theory. Next, we compute the thermodynamic quantities of these black holes for the case of vanishing bare cosmological constant. We consider this situation because the model is unitary only for the asymptotically flat solutions that allow horizons with spherical topology. We also present that the first law of thermodynamics is fulfilled for these objects. Finally, we examine how the nonlinearity of electric field, electric charge and cubic coupling parameter can impact the local thermal stability of our simulated black holes in both canonical and grand canonical ensembles.

Kehle and Unger have recently shown that self-gravitating charged classical scalar fields can collapse to form extremal Reissner-Nordström (eRN) black holes in finite time, thus violating the third law of thermodynamics (TLT). Reall has subsequently proved that the formation of an eRN black hole in gravitational collapse is impossible if the mass-to-charge ratio of the field exceeds unity, $m/e\geq1$. In the present compact paper we conjecture, using quantum considerations, that the Reall bound is not sharp. In particular, we point out that the electric field of a charged system with charge $Q$ will spontaneously polarize the vacuum in the regime $(eQ/\hbar)^2>(mQ/\hbar)^2+1/4$, thereby creating pairs of charged particles that discharge the black hole and ensure the quantum validity of the TLT in this regime. Motivated by the TLT, we conjecture that the classical Reall bound can be strengthened such that classical considerations would prevent eRN black holes from forming dynamically in the regime $m/e\geq\sqrt{1-\big({{\hbar}/{2eQ}}\big)^2}$, where quantum polarization effects are unable to protect the TLT.

Excitations of the neutron star (NS) fundamental mode (f-mode) during a binary NS inspiral or from a glitching pulsar can produce gravitational waves (GWs) that will be detectable with the next generation of detectors, opening the door to GW asteroseismology of neutron stars. There exist approximately equation-of-state (EOS)-insensitive, or "universal," relations that relate the f-mode to other NS properties. These universal relations have typically been identified with relatively small, selective EOS samples. To more thoroughly explore the parameter space, we examine the f-modes for a large sample of piecewise-parametric EOSs by solving the linearized fluid perturbation equations for the f-mode frequency and damping time in full general relativity. We utilize our sample to evaluate the EOS-sensitivity of previously-proposed universal relations (URs) for both the f-mode frequency and damping time. We find that URs that depend on combinations of only NS mass and radius have significant residuals, as previously reported; but that these residuals are strongly correlated with the overall stiffness of the EOS. We account for this residual dependence on the EOS by introducing linear correction terms that depend on the characteristic radius predicted by the EOS and the slope of the mass-radius curve at intermediate masses. To assess the impact of our new correction terms on observables, we consider the case of GW emission due to a glitch in a Vela-like pulsar and demonstrate that the predicted signal-to-noise ratio for such an event is over/under-estimated by up to ~10% when using an existing, single-parameter UR, but is recovered nearly exactly with our improved 3-parameter UR. In contrast, we find that URs between the f-mode and tidal deformability exhibit only minimal EOS-dependent correlations in their residuals and overall remain highly EOS-insensitive.

The time-domain gravitational waveform emitted during the scattering of two nonspinning compact bodies is computed in the extreme-mass-ratio limit. It provides a time-domain description of the gravitational radiation emitted during the encounter and complements previous first-order self-force calculations, which have primarily been formulated in the frequency domain. In this way, the present results provide a complementary representation of the radiative dynamics and facilitate a direct comparison between time-domain and frequency-domain approaches to the gravitational-wave signal. The waveform is accurate to the fifth post-Minkowskian (three-loop) level and seventh post-Newtonian order, and will serve as a benchmark for future calculations by other methods, to first order in the mass ratio. The results have been already tested in a previous work by constructing the energy and angular momentum fluxes, thereby computing the corresponding radiative losses at the 5PM and 4PM level, respectively, with the same PN accuracy, which are in agreement with recent amplitude-based calculations.

Cosmological-collider signals are usually interpreted as clean probes of massive particles present during inflation. In this work, we study a massive spectator field excited by a spatially quenched random source, which may arise from a frozen realization of a light field or environmental sector whose relaxation time is long compared with the inflationary timescale. We determine which features of the collider signal remain reliable probes of the heavy field. After Gaussian disorder averaging, the random source modifies only the statistical component of the propagator, leaving the spectral function and heavy-field poles unchanged. The particle spectrum is therefore preserved, and the logarithmic frequency of the collider oscillations remains fixed by the heavy-field mass. What changes is how the massive modes are excited and imprinted on cosmological correlators: the temporal profile of the source controls the amplitude, phase, and envelope of the oscillations. For a power-law source, the fixed-realization problem is exactly solvable in terms of Lommel functions. Decaying sources can make the nonanalytic clock signal dominant in the squeezed limit, while spatial white noise can destructively interfere with the standard collapsed-trispectrum signal. Thus, mass measurements remain robust against this class of quenched disorder, whereas amplitude-based inferences can depend sensitively on the random environment.

Élie Cartan established that the metric and intrinsic curvature of a $D$ dimensional embedded manifold $M$ could be determined by tracing the response of another surface $N$ of the same dimensionality, as it is rolled without slipping and twisting on $M$. In the context of spacetime geometry, this construction underpins the MacDowell-Mansouri formulation of General Relativity. We consider extensions of this framework that correspond to rolling of a shape with twisting and with shape evolution; it is shown that these naturally describe torsion and non-metricity respectively. Cartan-geometric formulations of teleparallel gravity and symmetric teleparallelism are discussed in addition to further manifestations of non-metricity in first-order formulations of gravity.

We extend a previous study of the radial stability of solitonic boson stars by nonlinearly evolving them under aspherical perturbations, and by studying their formation from the collapse of scalar clouds. We focus in particular on models previously identified as radially stable, despite having positive binding energy, which ordinarily suggests that dispersion of all scalar matter is energetically preferred. A mode analysis of our 3+1 evolutions produces no evidence for the presence of a non-radial instability in any radially stable model, including those with positive binding energy. However, we do find evidence that such models do not generically form via gravitational cooling. We also find that it is possible to form another kind of compact object, which undergoes long-lasting radial oscillations and hence cannot be described as a stationary boson star. These objects may be characterized, we suggest, by energetically favoured multi-oscillating solutions to the Einstein-Klein-Gordon equations, present in certain regions of the parameter space.

We analyze the radiative properties of a general class of static and spherically symmetric black holes described by three independent shape functions, that encompass a broad family of regular and quantum-corrected geometries. We consider a minimally coupled massless scalar field, and derive the Hawking temperature and graybody factor for the different geometries. While the Hawking temperature is determined by the near-horizon geometry, the graybody factor depends on the scattering properties of the entire exterior spacetime, and therefore exhibits a richer dependence on the deformation parameters, frequency, and angular mode. Then we particularize to geometries that describe slight deformations of the Schwarzschild black hole, and obtain analytic expressions for the leading corrections to the graybody factor. Finally, we apply our results to several specific well-known black-hole models, including Reissner-Nordström, Bardeen, Hayward, Simpson-Visser, as well as geometries inspired by loop quantum gravity. In general, the deformations lead to colder horizons than Schwarzschild, and their effect on the graybody factor is frequency-dependent: the transmission of low-frequency modes is suppressed, whereas it is enhanced for high-frequency modes. This behavior is found for all but one of the geometries considered, which exhibits just the opposite trend. The analyzed modifications to the Hawking spectrum may therefore have relevant observational consequences, potentially providing signatures of deviations from the Schwarzschild geometry.

We study the spinoptics equations for test electromagnetic wave in the Reissner-Nordström spacetime. The explicit and hidden symmetries of this background allow the complex null tetrad parallel-propagated along the null geodesic to be constructed explicitly. From this tetrad we obtain the evolution equations for the deviation of the ray from the null geodesic and for the tilting angle of its orbital plane. In these equations the charge term enters with a sign opposite to the mass term. Numerical integration confirms that the gravitational spin Hall effect becomes weaker with increasing charge: at a fixed impact parameter away from the critical value, the magnitude of the dimensionless tilting angle decreases with $Q$. As the turning point approaches the photon sphere, its magnitude grows firstly, and then exhibits an oscillatory behavior. Since the physical tilting angle is proportional to the reduced wavelength, it remains small whenever the spinoptics approximation is applicable. A divergence occurs only when the ray travels on the photon sphere.

We derive analytic response functions for Unruh–DeWitt detectors coupled to real, massless, conformally coupled scalar fields, to distinguish the effects of the field spectrum and global geometry from those of the interaction protocol. For Gaussian-switched static pairs in Minkowski, anti-de Sitter, and de Sitter spacetimes, we obtain the leading-order excitation probabilities and two-detector coherences in spacetime dimension $\mathcal D=d+1\ge3$. Time-ordered coherence requires distinct spatial worldlines; the local response and single-excitation coherence also admit coincidence. For equal-redshift pairs, Gaussian switching separates the gap dependence of the time-ordered coherence. In de Sitter space, KMS detailed balance fixes the gap that maximizes the ratio of nonlocal coherence to local excitation, giving a single-gap test for the existence of leading-order entanglement and restricting any entangling gaps to one bounded interval. When entanglement is present, the concurrence itself peaks at a smaller positive gap. In the three-dimensional BTZ black hole, an integrated Legendre series gives the sharply switched response of a radially infalling detector. A uniform image-sum estimate establishes logarithmic growth near the singularity and determines its coefficient from the covering-AdS response. A sufficiently smooth monotone onset removes the finite-time onset glitches but leaves a positive logarithmic coefficient; the accumulated leading-order response remains finite. Independent numerical calculations test the analytic expressions, their convergence properties, and these physical distinctions.

The observed cosmological constant is set by the deepest infrared scale of the present universe rather than by the microscopic scales that contribute to the vacuum energy. We show that this emerges as the quantum fluctuations of the gravitational field are progressively taken into account. Considering the Einstein-Hilbert+$R^2$ truncation of gravity, we find that in a wide region of the parameter space the theory develops instabilities that give rise to large amplitude quantum fluctuations which govern the renormalization group flow. Once the flow enters this region, it remains there all the way towards the infrared and progressively loses memory of its boundary conditions. The running cosmological constant $\Lambda_k$ ($k$ is the running scale) is driven towards the universal infrared scaling $\Lambda_k\sim \lambda_{_{\rm IR}}\,k^2$, with $\lambda_{_{\rm IR}}= \frac{1}{2(\pi-2)}$. At the deepest infrared scale $k_{_{\rm IR}}\sim H_0$ (the current Hubble scale), the cosmological constant is then screened to its observed value $\Lambda_{_{\rm IR}}\sim H_0^2$.

We study the Petrov classification and Weyl double copy of the four-dimensional bulk metric dual to a $2+1$-dimensional relativistic Rindler fluid at first order in the relativistic gradient expansion. Upon imposing the fluid equations, the leading Weyl curvature is determined by the fluid vorticity and shear. At this order, the bulk geometry is generically of Petrov type II, with a type D branch for shear-free flows with nonzero vorticity and a type N branch for irrotational flows with nonzero shear. For the type D branch, we construct a purely magnetic Maxwell single copy on a fixed Rindler background and distinguish exact source-free solutions with a constant magnetic field from local perturbative solutions valid through first order in gradients. For the type N branch, we obtain a family of algebraic Weyl double copies parametrized by $\beta$. We derive explicit field strengths and gauge potentials for $\beta=0$ and $\beta=1$, together with the local Cauchy-Riemann conditions imposed by Maxwell's equations. These choices encode the fluid shear differently: for $\beta=0$, the shear dependence resides entirely in the zeroth-copy scalar, whereas for $\beta=1$, it enters the Maxwell field directly. Finally, using the non-relativistic hydrodynamic expansion with explicit $\epsilon$ counting, we derive the non-relativistic limits of the type D single copy and both type N choices, and compare the resulting structures with existing non-relativistic constructions.