Papers

The memory-burden scenario of black hole evaporation proposes that Hawking emission may become increasingly suppressed as maintaining stored quantum information becomes dynamically costly. In this work, we revisit this scenario and investigate the conditions under which information retention can produce a genuine dynamical burden. We derive general scaling conditions for incremental memory accumulation at a fixed fractional mass loss and establish a conditional no-go result: entropy-suppressed, zero-mean deposits with subextensive integrated correlations cannot produce an order-one luminosity modification through unamplified accumulation and bounded feedback. We identify three essential requirements for dynamical memory: a record of the past must be written, retained, and coupled back to subsequent evaporation. We illustrate these requirements with concrete toy models that exhibit either a prolonged but finite black hole lifetime or an asymptotically approached finite-mass state (an effective remnant). We further distinguish kinetic-memory, thermodynamic-memory, and spectral-memory sub-categories of possible memory-burden mechanisms. In particular, we demonstrate that an independently evolving memory variable can generate evaporation-accretion hysteresis, such that a black hole returning to the same mass may possess a different retained memory and consequently a different luminosity. This history dependence may have implications for primordial black hole phenomenology. Finally, we briefly discuss the possibility of "merger rejuvenation", in which black hole mergers reorganize or reset the effective memory state.

In General Relativity, axial and polar black-hole perturbations share identical quasinormal-mode spectra, a property known as isospectrality. New physics can break this degeneracy, producing a spectral splitting analogous to atomic fine structure. We perform a theory-agnostic search for such splitting in gravitational-wave observations. We find no evidence for isospectrality breaking and place a combined $90\%$ upper limit of $<28.5\%$ on the relative frequency splitting. We map these constraints onto several modified-gravity theories, constraining the coupling-lengths to be $\lesssim 28\,\mathrm{km}$.

We study a phenomenological cosmological model of black-hole growth in which a finite baryonic reservoir and a bosonic scalar cloud feed the black hole simultaneously. The baryonic component accretes through an Eddington-like channel, while the scalar cloud transfers mass through an effective quasibound-state decay rate. Evolving the system directly in redshift within a flat $\Lambda$CDM background, we scan over $\mu$, $M_0$, $M_{c,0}$, and $M_{b,0}$ to assess whether scalar-assisted accretion can accelerate the formation of $10^9M_\odot$ supermassive black holes. We find that the scalar contribution is highly selective in parameter space. For the mass scales explored here, scalar transfer is most efficient for $\mu\sim10^{-19}-10^{-16} \mathrm{eV}$, producing rapid cloud depletion and significantly earlier black-hole growth, while outside this interval the evolution remains mainly baryonic. More generally, this efficient window reflects a preferred range of the dimensionless coupling $\alpha=\mu M_{\rm BH}$ and therefore shifts approximately as $\mu\propto M_{\rm BH}^{-1}$. Comparison with observed quasar masses and luminosities instead favors lower boson masses, broadly around $\mu\sim10^{-21}-10^{-20}\mathrm{eV}$. These results are not necessarily in tension, since the boson mass that maximizes early growth depends on the characteristic black-hole mass and evolutionary stage. This separation between dynamical efficiency and observational compatibility leaves open complementary roles for different bosonic mass scales in supermassive black hole growth and dark-matter phenomenology.

The diffraction integral formalism has been greatly successful in describing gravitational wave lensing effects in scenarios where the wavelength of the signal is comparable to the characteristic length scale of the lens, known as the wave optics regime. However, the assumptions required to construct its integrand break down as the source approaches the strong gravity region of a black hole lens. In particular, we are interested in the lensed signal from a binary (the source) near a massive black hole (the lens). We present a new formalism for obtaining low frequency corrections to sources being lensed in the strong field regime of gravity by leveraging the fact that null geodesics obey the Hamilton–Jacobi equations. In doing so, we are able to construct a time delay surface without relying on the thin lens approximation, and solve the diffraction integral for the resulting surface directly. For a stationary source at $10M$, deep in the strong field regime, when comparing the results with a relativistic wave scattering model, we find $6.5\%$ and $0.3\%$ agreement in the peak amplification and first diffractive fringe, respectively. Furthermore, we find a $< 1\%$ agreement with the amplitude of the point mass lens with a source at $10^4 M$ in the weak field, but noticeable dephasing between the peaks of the amplification function at higher frequencies. This work allows for clean interpolation between otherwise separate regimes, valid for sources from $\sim 6M \to \infty$. It provides a transparent, physically motivated framework for computing beyond-geometric optics lensing effects in the strong field regime.

We derive the junction conditions for spherically symmetric thin shells in Lovelock and Quasi-topological gravities along two independent routes: from the distributional form of the field equations, and from the boundary term that makes the variational problem well-posed in the non-null case. The former method is ambiguous as it stands, since the equations contain products of Heaviside step functions with a Dirac delta. We show that the singular parts of the field equations are exact differentials in the jumping variables, so that the Vol'pert chain rule for functions of bounded variation fixes these singular combinations uniquely and no products of two deltas survive for a single shell, finding that both routes then agree. The same rule yields the null junction conditions, for which no boundary term is available in Quasi-topological gravities, together with the mass conservation law of the shell. These results clarify recent questions concerning the existence of thin shells in these theories. In particular, we show that previous claims that the junction conditions force the shell mass to vary with radius are incorrect and arise from treating a trapezoidal approximation to the relevant distributional products as exact. Our results also provide a basis for the recent analyses of mass inflation in these theories.

While the spin vectors of binary black holes offer insight into the astrophysical formation channels of these systems, individual spins are less precisely measured through gravitational-wave observations than the effective inspiral spin $\chi_\mathrm{eff}$ and the effective precession spin $\chi_\mathrm{p}$. Reducing to effective parameters discards information in the data, but how much information is lost has yet to be demonstrated. Here we show how to quantify whether individual mergers carry information about component spins beyond the constraints implied by effective parameters (a.k.a. spinformation) and apply the technique to GWTC-5. Thresholding on information loss $\gtrsim 0.25$ bits, over $80\%$ of gravitational-wave events in GWTC-5 have component spin posteriors described by $\chi_\mathrm{eff}$ alone. Only $\sim3\%$ of gravitational-wave events have substantial spin information not explained by $\chi_\mathrm{eff}$ and $\chi_\mathrm{p}$. The catalog's component spin information is effectively two-dimensional in $\chi_\mathrm{eff}$ and $\chi_\mathrm{p}$. Using simulated signals, we find the noise realization can create or destroy over a bit of beyond-$\chi_\mathrm{eff}$ information: the structure in real data may therefore be driven by noise. At current sensitivity, component spins provide interpretive\textemdash rather than informational\textemdash advantage over effective parameters.

Extreme mass ratio inspirals (EMRIs) are expected to be a major source of gravitational waves (GWs) for the future Laser Interferometer Space Antenna (LISA). An EMRI occurs when a compact object, driven by the emission of gravitational radiation, slowly inspirals into a massive black hole (MBH). The classical formation channel involves repeated two-body interactions within dense nuclear star clusters. However, both EMRI event rates and the expected distribution of their orbital parameters remain highly uncertain. A major source of this uncertainty is the poorly constrained ratio between gradually inspiraling EMRIs and direct plunges, which do not produce detectable GWs. While most studies of astrophysical EMRI production focus on the Schwarzschild limit, previous work examining the Kerr metric found that the spin of the central MBH can significantly affect the EMRI-to-plunge ratio. This enhancement depends sensitively on orbital inclination, yet earlier studies held inclination fixed. In this work, we develop the mathematical framework describing inclination evolution driven by two-body encounters evolving along Kerr geodesics. By implementing 3D diffusion into Monte Carlo simulations, we show that initially prograde orbits may evolve into retrograde states, thereby converting potential EMRIs into plunges or vice versa. We estimate the EMRI-to-plunge ratio and find that substantial MBH spin enhances the EMRI rate by a factor of $\sim 2.5$. Additionally, even for a non-spinning MBH, modeling the orbits as relativistic geodesics rather than Newtonian trajectories increases the number of EMRIs by a similar factor of $\sim 2.5$. The distribution of Kerr EMRI inclinations has a substantial prograde bias that may aid in identifying the subset of loss cone EMRIs within large future EMRI samples.

Mass distributions of binary black hole mergers inferred from gravitational-wave observations offer clues to how binaries form. These distributions conventionally label the heavier component as the primary, with mass $m_1$, and the lighter as the secondary, with mass $m_2$, such that $m_1 \geq m_2$. This ordering folds the physically labeled mass distribution along the equal-mass line, potentially reshaping the underlying population structure. In this Letter, we determine which population features can arise from mass ordering and which require genuine astrophysical structure. We show that ordering alone can produce (1) an $m_2$ distribution that declines more rapidly than the $m_1$ distribution, without intrinsic differences between the physically labeled components, and (2) an apparent concentration along equal masses, without correlations that preferentially pair black holes of equal mass. Moreover, different physically labeled populations can produce the same ordered mass distribution. Crucially, however, a preferred companion mass that remains constant as $m_1$ increases requires a characteristic mass scale already present in the physically labeled population. Applied to binary black hole mergers in the fifth Gravitational-Wave Transient Catalog, our model recovers such a scale near $m_2 \simeq 50\,\mathrm{M}_\odot$. Around this scale, the merger-rate density declines much more rapidly toward higher $m_2$ than toward lower $m_2$, ruling out an equal or weaker high-$m_2$ decline at 99.45% credibility. This structure therefore requires a characteristic mass scale in at least one physically labeled component, but masses alone cannot determine which component carries it. Any formation model reproducing the observed high-mass binary black hole merger population must contain such a scale.

Compact binaries evolving in the vicinity of massive black holes may be commonplace in the Universe, and their gravitational waves carry signatures of their environment. We study the strong lensing of these signals by the massive companion, a configuration that violates the standard assumptions of the lensing literature: geometric optics and thin lenses. Using a perturbative framework, we compute the full wave optics amplification factors for face-on and edge-on binaries, including spinning lenses. In the edge-on configuration, peak amplification does not occur at perfect source–lens–observer alignment, even for a non-spinning lens. This is a consequence of the anisotropic, coherent quadrupolar emission of the stellar-mass binary breaking the axisymmetry of the system. Restricting to the equatorial plane near the optical axis, we then find that the frequency dependence of the amplification factor is universal across every configuration studied, persisting deep into the wave optics regime. Comparing against a strong-field ray tracing calculation, we find agreement at the $\sim10\%$ level for a face-on binary lensed by a Schwarzschild black hole. In the less symmetric edge-on case only the angular peak shift and fringe spacing is reproduced to this accuracy. For a Kerr lens, the face-on amplification factor is described by its Schwarzschild counterpart to the same $\sim 10 \%$ accuracy once the effect of frame dragging is corrected for. A point mass lens, by contrast, fails to reproduce the features of the system, which may have strong implications for forecasts that adopt it for lensing by massive black holes in the strong field.

Gravitational perturbations of rotating black holes in higher dimensions generally obey coupled partial differential equations. We show that scalar gravitational perturbations invariant under rotations of the transverse sphere of a singly spinning Myers-Perry black hole separate, despite the obstruction to a decoupled Teukolsky equation. Two commuting, second-order angular operators organise the three gauge-invariant curvature components into joint eigenfunctions. The physical radial problem is a $2\times2$ first-order system, equivalent to a single second-order equation. This gives a separation of the sector containing both the bar-mode and axisymmetric ultraspinning instabilities. Using only ordinary differential equations, we compute the bar-mode quasinormal spectrum in $d=5,6,7$ and find instability onsets at $a/r_+=0.90498$ and $0.83228$ in $d=6,7$. We also compute the growing axisymmetric modes and their onset rotations in $d=6,\ldots,9$. The construction shows how separability can survive the coupling between gravitational polarisations.

We extend the general relativistic Lagrangian perturbation formalism of Friedman and Schutz [Astrophys. J. 200, 204 (1975)] beyond linear order, retaining full time dependence of the perturbations. We provide general formulae to relate the Lagrangian and Eulerian perturbations to any general perturbative order. As a proof of principle, we apply the framework to tidally perturbed relativistic stars in Regge-Wheeler gauge and reduce the second-order field and conservation equations to master equations with a nonlinear source. Projecting the source onto the star's eigenmodes, we obtain a nonlinear equation of motion for the mode amplitudes and the coupling coefficients, which describe the interactions among the eigenmodes and with the external tidal field. Approximating the tidal field and the coupling coefficients, we compute the static quadratic Love number from the quadrupolar fundamental mode alone and find that it reproduces the direct metric-matching value to a reasonable accuracy of $4\%$, up to a further correction arising from the Hamiltonian and momentum constraints of the second-order tidal field.

The spin-induced quadrupole moment (SIQM) of a compact object provides a direct null test of the Kerr hypothesis. Most existing gravitational-wave tests of SIQM assume quasi-circular binaries, although dynamical formation channels can produce measurable eccentricity that may persist in the sensitive band of third-generation (3G) detectors. We extend the symmetric SIQM test to eccentric, aligned-spin binaries using a post-Newtonian spinning-eccentric phasing model, and forecast its measurability with Cosmic Explorer (CE) and Einstein Telescope (ET). Single-event Fisher-matrix forecasts show that the impact of eccentricity on SIQM measurement precision depends on the binary parameters and detector configuration, rather than uniformly degrading the measurement. A population study with a truncated eccentric expansion indicates that ET's additional low-frequency eccentric cycles tighten $\Delta\kappa_s$ by roughly a factor of two relative to CE (median $0.11$ to $0.12$ versus $0.20$ to $0.23$); the absolute values are indicative only. We further show that quasi-circular template banks can lose significant effectualness for moderately eccentric signals, motivating the development of eccentric-spin template families. Accounting for eccentricity is therefore important both for SIQM measurements and for avoiding systematic losses in searches, and it strengthens tests of the nature of compact objects with 3G gravitational-wave detectors.

Gravitational waves (GWs) propagating across the Universe can be distorted by intervening lenses, producing characteristic wave-optics signatures. These effects are not incorporated into current matched-filtering searches and can therefore substantially reduce detection efficiency. The underlying mechanism is the signal-consistency test, which measures deviations between the observed and expected signal-to-noise ratio (SNR) distributions. We report a systematic study of the impact of gravitational lensing on signal-consistency tests, using a two-image interference model and representative signal-consistency statistics in both the time and frequency domains. We find that overlapping images produce sharply localized SNR residuals in the time domain, breaking the reflection symmetry of the autocorrelation about the merger time. Although interference fringes produce broadband SNR residuals in the frequency domain, both domains exhibit a minimum for high-mass signals when the fringe structure becomes comparable to the signal bandwidth. This highlights a limitation of current strategies that search for distorted lensed signals only among GW events detected by matched-filtering searches. Exploiting this asymmetry, we develop a statistic that separates selected down-ranked lensed injections from noise-background triggers and paired nonlensed injections, without extending the template bank. Our results establish the first connection between lensing observables and detection, paving the way for the discovery of lensed GWs.

Gravitational tail-of-tail corrections arise when radiation scatters twice from the mass-monopole field of its source. In the multipolar effective field theory, one of the two-loop topologies contributing to this process involves genuinely coupled loop momenta, preventing its evaluation through nested one-loop integrations. After tensor reduction, this nonfactorizing structure leads to a particularly challenging family of scalar integrals with unbounded numerator powers as the multipole rank increases. We derive exact closed-form expressions for the entire relevant integer numerator domain, valid in generic dimension and accommodating Feynman, retarded, and advanced prescriptions through consistent analytic continuation. Near $d=3+\epsilon$, we also obtain explicit Laurent expansions through $O(\epsilon)$, retaining the subleading information needed in higher-order radiative calculations. While these expansions determine the dimensional poles, identifying their ultraviolet (UV) or infrared (IR) origin requires a separate analysis of momentum regions. We carry out this analysis throughout the integral domain and apply it directly to the coupled tail-of-tail emission diagram for arbitrary electric and magnetic multipoles. In this way, we independently determine the UV and IR residues, and explicitly verify that the complete infrared pole structure, including both double and simple poles, agrees with the exponentiation of the one-loop gravitational tail. The UV residues, calculated directly from hard-momentum regions, reproduce the established multipole anomalous dimensions when combined with the known contributions of the remaining diagrams.

We constructed a (2+1)-dimensional gravastar whose interior region was characterized by a noncommutative geometry with Gauss-Bonnet corrections, while the exterior region was described by a Gauss-Bonnet-modified BTZ solution. The two geometries were joined across a thin shell using the generalized junction formalism, from which we derived the surface equations of state. We investigated the energy conditions at the shell, determining the parameter regimes under which the null, weak, and strong energy conditions were satisfied. We also analyzed the thermodynamic properties of the noncommutative interior region, including the temperature, entropy, and heat capacity.

Current and upcoming galaxy-redshift surveys offer a promising path for constraining inflationary physics. These constraints are often imposed by relating correlations of the primordial curvature perturbation to the late-time galaxy correlation functions. The primordial correlators can either be computed analytically, or via realizations of the primordial curvature perturbations that are initialized on a grid and evolved numerically according to the classical equations of motion. In this work we take a hybrid approach, initializing the fields in the Bunch-Davies vacuum; and then imposing time evolution through direct numerical integration. Our method efficiently generates realizations of the inverse decay primordial curvature perturbations for axion inflation—an inflationary model in which a pseudoscalar inflaton field couples to a $U(1)$ gauge field via a Chern-Simons interaction. Depending on the choice of parameter $\xi\in\{2, 2.5, 3\}$, which controls gauge field particle production in this model, our method generates realizations with an average runtime of a few hours on 1 CPU core. We compute the power spectrum and bispectrum from these realizations and find a surprisingly large discrepancy between our result and previous work that used an approximation for the gauge field mode functions—up to a factor of $\sim4$ difference for the bispectrum in the case of $\xi=2$. This new method enables not only rapid computation of higher order polyspectra, but also generation of initial conditions for large-scale structure analyses.

The Klein-Gordon equation is a second order differential equation that appears in a variety of applications in mathematics, physics and engineering. This equation is often solved using numerical methods, since a general analytical solution is unattainable. However, one can find very useful analytical solutions for some special cases. In cosmology, the Klein-Gordon equation of a field can explain the physics of inflation and has important consequences on understanding the origin and evolution of the universe. An analytical solution to the Klein-Gordon equation in cosmology has been obtained in the small-field excursion approximation, and it turns out that the solution can be written in terms of the confluent hypergeometric limit function. In this work, we derive this result again while showing the details of the calculations and then generalize to the case of two coupled Klein-Gordon equations. We show that the solution of this coupled system can be written in terms of Kummer's hypergeometric limit function while considering minimal assumptions. We carry out a full numerical calculation of the coupled system and compare it to the results from the analytical expressions.

The work presents a canonical Hamiltonian system in a classical scenario and further extend the analysis to a quantum mechanical framework for a homogeneous and isotropic universe governed by Bumblebee gravity, in which spontaneous Lorentz symmetry breaking is triggered by a vector field acquiring a vacuum expectation value (VEV). Starting from the full four-dimensional covariant action, the derivation has been carried out for the one-dimensional mini-superspace Lagrangian density for a flat Friedmann-Lemaître-Robertson-Walker (FLRW) background with a purely temporal bumblebee field configuration. Further, the work focuses on to construct the classical Hamiltonian system through a canonical Legendre transformation, identifying the lapse function $N(t)$ as a Lagrange multiplier enforcing a primary Hamiltonian constraint. Apart form that, the conservation of phase-space volume via Liouville's theorem, locate and classify the critical points of the resulting dynamical system, and examine the stability of the Lorentz-violating vacuum has been carried to test the classical Hamiltonian system in the work. Furthermore, the modified first and second Friedmann equations and discuss the resulting time-dependence of the effective gravitational coupling, illustrating the results with numerical phase-space has been discussed in this work. Finally, the work extended to construct the Wheeler-DeWitt equation through the canonical quantization and obtain the approximate solutions in the deep-quantum ($a\to0$) and near-vacuum regimes for it.

We investigate the cosmological dynamics of gravitational particle creation in a spatially flat FLRW Universe comprising radiation, baryons, dark matter (DM), and a separately conserved dark-energy component. The DM sector is described as an effective open thermodynamic fluid incorporating intrinsic pressure and particle-creation-induced negative pressure. Introducing the compact variable $u=H_0/(H_0+H)$, we construct a four-dimensional autonomous system and systematically investigate its critical points, dynamical stability, and physical admissibility. The model is constrained using three observational combinations: PPS+BAO+OHD, Union3+BAO+OHD, and DES-DOV+BAO+OHD. The observationally preferred parameter regions exclude the nontrivial DM-dominated de Sitter-like branches from the physical phase space, while identifying a stable, physically admissible, dark-energy-dominated accelerating attractor. The reconstructed cosmological evolution consistently reproduces the radiation–matter–acceleration sequence, with a transition redshift $z_{\rm tr}\simeq0.71$–$0.73$. Posterior-level analysis reveals that approximately $92\%$–$97\%$ of the samples support this accelerating attractor. The asymptotic evolution approaches a quintessence-like power-law expansion with $H\rightarrow0$, rather than a de Sitter state. These findings establish a connection between observational constraints, gravitational particle creation, and the global dynamical structure governing the distant cosmic future.

Modifications of gravity beyond (vacuum) General Relativity have a subtle impact on the physics around black holes. Describing these effects across different observables is, however, a priori strongly model dependent. While effective descriptions of the geometry allow to efficiently capture deviations from benchmark predictions, they sometimes lack a clear passage towards (effective) new physics. Inspired by linear response theory, in this work I therefore propose a formalism that allows to calculate leading corrections of observables relative to the Schwarzschild black hole anywhere in space-time (outside of the horizon): the order of corrections is fixed through an eigenvalue $\mathcal{E}$ of the Einstein tensor, which is identified with an external energy momentum tensor that generates the deformation of the geometry. In this ways, $\mathcal{E}$ can be linked to effective physics models. Focusing on spherically symmetric and static black holes, I illustrate the approach at the hand of a number of observables in the vicinity of the horizon, such as characteristic quantities of particles moving around the black hole (e.g. the black hole shadow or the radius of the innermost stable circular orbit) or the spectrum of scalar quasi-normal modes. Reversing the logic, I argue that the knowledge of such observables provides non-trivial constraints on $\mathcal{E}$, which in turn grant insights into the effective physics in the vicinity of the black hole.

How a relativistic star responds to a time-dependent tide has lacked a first-principles counterpart of the Newtonian normal-mode expansion. In general relativity, the tidal field is gauge sensitive, radiative modes are non-Hermitian and incomplete, and the direct and late-time responses are intrinsically nonmodal. In this work we present, to our knowledge, the first causal relativistic theory that treats all of these components on equal footing. We first develop the spectral decomposition of the retarded Green function of the matched stellar interior–Schwarzschild exterior, which classifies four separate regimes in time domain: acausal region, prompt wave, surface-reflected wave, and mode+tail. The prompt signal is identical to that of a Schwarzschild black hole with the same mass, which is combined with the surface-reflected wave to be referred as the "direct part". With the Green function and a complex bilinear form on the full metric–fluid phase space, we decompose the linear response of a nonrotating perfect-fluid star into direct, quasinormal-mode, and late-time-tail sectors. Crucially, every sector admits an explicit first-order driven evolution equation: discrete bilinear projections determine the dynamically evolving quasinormal-mode amplitudes, while continuum projections of the same tidal source onto branch-cut states determine the direct and tail amplitudes. The result is a complete modal–nonmodal decomposition of the spacetime and fluid perturbations, which is physically described by the dynamics of a discrete and a continuous-frequency set of oscillators. We verify the decomposition numerically under generic time-dependent tidal driving and discuss applications to black hole perturbations.

We study the algebraic and geometric structures of gravitational decoupling within a fixed class of globally static, spherically symmetric spacetimes with non-vanishing areal-radius differential. We show that (minimal and extended) geometric deformations of the seed metric define a groupoid of partial transformations. We also draw a connection between the geometric deformation procedures and disformal transformations. It is shown that every admissible minimal geometric deformation admits a disformal representation using the areal radius as an auxiliary scalar. For extended deformations, we derive a necessary condition and exhibit a global obstruction that persists under diffeomorphisms preserving the areal radius and the static Killing direction up to constant normalization. Finally, we verify that the disformal construction reproduces the standard minimal geometric deformation source equations and separate conservation law, including anisotropic seeds.

We consider vacuum spatially homogeneous models in Hořava-Lifshitz gravity, which are expected to describe generic singularities for these modified gravity theories. These models perturb the well-known Bianchi models in general relativity (GR) by a parameter $v\in (0,1)$, in which GR occurs at $v=1/2$. We show that all periodic heteroclinic chains of Bianchi type II orbits are robust for small perturbations of GR, i.e. they exist for any $v\approx 1/2$. Moreover, we prove the existence of a stable manifold for each heteroclinic chain within a Cantor set for the supercritical case, $v\in (1/2,1)$. In particular, we discuss the heteroclinic chains of periods three and four in detail.

We study Dirac mini-stars in modified $R^2$ gravity, where gravity is sourced by both linear and nonlinear spinor fields. Two-dimensional (2D) and three-dimensional (3D) profiles of the mini-star mass are constructed as functions of the spinor frequency (for the 2D profiles) and the central value of the spinor field (for the 3D profiles) in general relativity and modified gravity for various values of the spinor nonlinearity parameter. We show that the modification of gravity alters the properties of these configurations, while increasing the nonlinearity parameter within the framework of $R^2$ gravity significantly changes the profiles of the spinor and metric functions, the effective energy density, and the dependence of the total mass on the oscillation frequency. The most pronounced changes occur at large values of the nonlinearity parameter.

We study a massive scalar field in flat spacetime written in a time-dependent accelerated frame whose fixed-coordinate observers have maximal proper acceleration at $t=0$ and become asymptotically inertial without forming a horizon. The Klein-Gordon equation separates into a modified Mathieu equation in time and a confining Schrödinger problem in space with a discrete spectrum. We impose an adiabatic vacuum at the instant of maximal acceleration and compute the particle number in the inertial future. For the zeroth-order adiabatic state it falls as the inverse eighth power of the initial mode frequency, and raising the adiabatic order cancels successive terms of the endpoint expansion, in analogy with the switching transients of finite-time detectors. Analytic continuation of the spatial eigenfunctions gives the out modes in closed form and an exact expression for the particle number, which is entirely the mismatch at $t=0$ between the initial state and the out vacuum. The spectrum is algebraic rather than Planckian.

Quantum mechanics and general relativity are remarkably successful, yet their joint predictions remain beyond direct experimental reach. Photonic interferometers operating in a gravitational field offer a promising route to test this regime: gravitational redshift differentiates photon propagation between vertically separated arms, leading to a predicted phase shift and reduction in interference visibility. These effects are minute on laboratory scales, motivating existing proposals to consider large interferometer areas to accumulate them geometrically. Indeed, such schemes typically require kilometre-scale optical paths to produce appreciable interferometric signals. Here, we propose a strategy that replaces geometric accumulation with spectral enhancement by coupling the two interferometer arms to optical scatterers based on ultranarrow atomic transitions. These transitions serve as local spectral references: gravitational redshift changes the photon's detuning from each resonance, producing large differences in reflection amplitude and hence substantial visibility loss and interferometric phase shift already for centimetre-scale height differences. We quantify the experimental requirements and assess the feasibility of implementation with current or near-term technology. Our proposal thus opens a route to tabletop optical tests of the interplay between quantum mechanics and general relativity.

In the present paper we study the evolution of a homogeneous and anisotropic Kantowski Sachs cosmological model coupled with radiation and a generalized Chaplygin gas. Our main objective is verifying if this model evolves to a homogeneous and isotropic Friedmann Robertson Walker cosmological model, which is the more accepted model to describe our present Universe. If this is the case, we may imagine that the Kantowski Sachs cosmological model could had been an early stage of our Universe.

Gravitational lensing is usually treated as an initial value problem: for a given impact parameter of an unbound orbit, one computes the resulting deflection angle. In this paper we advocate the inverse point of view. For a prescribed deflection angle, the orbit is selected by two boundary conditions at spatial infinity, so that the lensing problem becomes a well-defined two-point boundary value problem, with the impact parameter playing the role of a nonlinear eigenvalue. We show that pseudo-spectral methods based on Chebyshev collocation solve this boundary value problem accurately at modest computational cost, and that the parallel transport equations governing the spin precession of the particle reduce to a single linear system on the same grid. As a concrete application, we compute the spin precession of massive particles in backward scattering off two black hole spacetimes from loop quantum gravity: the covariant effective metric and the self-dual loop quantum black hole. All equations are written for a general static, spherically symmetric line element with three free functions, so that both spacetimes are handled on the same footing. We find that the quantum corrections are most pronounced for slowly moving particles, while in the ultra-relativistic limit the universal spin flip is always recovered. The flip itself is universal, but the rate at which it is approached is not: the derivative of $\cos\xi$ with respect to the particle speed at $v=1$ is a strong-field quantity in every backward channel and depends clearly on the quantum parameters of both spacetimes. The framework is not restricted to the models studied here and applies to any static, spherically symmetric spacetime.

We construct the rotating counterpart of a black hole embedded in a dark-matter halo with the exponential-sphere profile $\rho=\rho_0e^{-r/r_0}$, using the Newman–Janis algorithm in the Azreg-Aïnou form, and study its imprints on test-particle motion and quasiperiodic oscillations (QPOs). We derive closed-form orbital and epicyclic frequencies valid for any Kerr-like metric with a mass function and show that, to first order, the halo enters them only through its central density, acting as an effective cosmological constant $\Lambda_{eff}=8\pi\rho_0$; the corrections are therefore universal for all cored profiles. The halo moves the innermost stable circular orbit outward and produces an outer boundary of stable orbits, while the sign of the frequency shift depends on the assumed equation of state of the halo. Fitting the relativistic precession model to the simultaneous QPO triplets of GRO~J1655$-$40 and XTE~J1859+226 with Markov-chain Monte Carlo sampling yields spins and emission radii consistent with Kerr and $\rho_0M^2<2.9\times10^{-5}$ and $3.0\times10^{-5}$ (95%), respectively. In physical units these limits exclude only ultra-dense dark cores, $\rho_0\gtrsim10^{11}$~g\,cm$^{-3}$.

We use microlocal tools to define distinguished incoming and outgoing vacuum states of the quantum theory of massive Klein–Gordon fields in non-trapping asymptotically flat spacetimes, including radiative perturbations of Minkowski space. The asymptotic vacuum states satisfy the Hadamard condition, and the incoming and outgoing particle representations are unitarily equivalent, or in other words the quantum S-matrix is well-defined. These results are based on a description of scattering of classical fields which keeps track of the asymptotic distinction between positive- and negative-frequency solutions of the Klein–Gordon equation. Our emphasis is on developing the theory without recourse to explicit asymptotics for classical waves.