We expand the Einstein-Hilbert action to cubic order about the Schwarzschild horizon, in the even Regge-Wheeler gauge of the Gaddam-Groenenboom-'t~Hooft (GGV) near-horizon framework, and derive the cubic graviton self-interaction. Our central result is a `vanishing theorem': at leading soft order the self-coupling of the purely traceless longitudinal polarizations is identically zero, because with the trace/transverse-scalar sector switched off the fluctuation reduces to a two-dimensional block whose $\sqrt{-g}\,R$ is a total (Euler) derivative at every order in $κ$. We prove this by an explicit closed-form reduction and exhibit the cancellation term by term. It is a `framework-specific' statement, even RW gauge, GGV sector, leading soft order, not a gauge-invariant theorem of general relativity. The theorem is exact, but the quantized vertex inherits a $\sim\!20\%$ soft/scheme systematic at the only simulable multiplet ($\ell=2$), which we state explicitly. We then simulate the real-time dynamics of the resulting Hamiltonian on IBM Qiskit/Aer with exact cross-checks. Two structural facts, a conserved charge that only the cubic vertex violates, opening $φφ\to hh\to4φ$, and a provably resonance-free boost spectrum (gap $\to1/2$), already predict that the longitudinal channel is perturbatively rigid; the simulation confirms this quantitatively and measures the residual dressing ($d_{\rm eff}=1.06$; multiplicity far from thermal, Poisson, and Haar references) rather than discovering it. A symmetry-exact total-occupation truncation yields the first sector-resolved level statistics, indicative of intermediate behaviour on Hilbert spaces too small to be decisive. All circuit results agree with exact diagonalization, every headline number carries a stated systematic, and hardware execution is deferred behind a quantified noise budget. less

We apply the parabolic-hyperbolic formulation of the Einstein constraint equations to generate cosmological initial data. The freely specifiable geometric data correspond to flat Friedmann--Lemaître--Robertson--Walker background, while the matter sector contains localized anisotropic perturbations of a perfect fluid. Unlike the standard approach, our method evolves the constraints outward from regular data at the origin and therefore requires no boundary conditions. This makes our method well suited as a starting point in investigating systematic biases introduced by commonly adopted boundary conditions, such as periodic boundaries. A second advantage concerns uniqueness: standard elliptic solvers may fail when multiple solutions exist, whereas solving the constraints as a well-posed evolutionary system always yields a unique solution. To demonstrate our method, we implement it numerically and generate cosmological initial data with localized anisotropic perfect fluid perturbations. less

Within theoretical frameworks such as loop quantum gravity, black holes may evolve into white holes through a quantum bounce. This paper uses general relativistic ray-tracing techniques to calculate the ray-traced imaging of accretion disks from the previous cosmic stage during the Kerr black hole and post-bounce Kerr white hole phases. Calculations show that the black hole image presents a crescent emission ring and a central shadow. In contrast, after radiation from the previous universe penetrates the rotating white hole, eccentric and asymmetric nested intensity ring structures form in the synthetic image due to frame-dragging and lensing effects. We analyze the influence of spin parameters, observation inclinations, and accretion disk geometric configurations on the distribution of this nested ring structure using synthetic images and intensity profiles. Building upon this, we introduce polarized ray-tracing calculations for radiation across evolutionary stages. This process results in the polarization image features after the polarization vector is subjected to the gravitational field and spacetime spin dragging during the photon propagation through the white hole horizon and internal spacetime. The spatial rotation patterns and concentric interference fringes in the white hole polarization images exhibit a distinct inter-ring polarization discontinuity. This phenomenon differs from the polarization behavior of black holes. The intensity ring structures and polarization inter-ring discontinuity features provide multi-band and polarimetric interferometry baselines to overcome morphological observational degeneracies. This provides theoretical guidance for future very-long-baseline interferometry (VLBI) to distinguish black holes and white holes. less

Extended bodies in general relativity do not necessarily fall along geodesics, but can be accelerated. These accelerations depend on an object's angular momentum, as well as on its quadrupole, octupole, and higher-order moments. However, these multipole moments can evolve differently from one body to another. Different bodies can thus fall differently, even with identical initial data. This paper examines how octupole moments contribute to the non-universality of free-fall in general relativity. We begin by showing that in arbitrary vacuum spacetimes, only the trace-free component of an octupole moment can affect an object's motion. It follows that at least 16 out of 40 octupole components decouple from the laws of motion. Then, we obtain two decompositions for trace-free octupole moments, one in terms of a timelike frame vector and the other in terms of a null tetrad. These decompositions are applied to motion both in generic Newtonian spacetimes and in fully-relativistic vacuum spacetimes that are of Petrov type D. In Newtonian spacetimes, the mass moments are shown to have their ordinary Newtonian effects, while the momentum moments determine a body's hidden momentum---the misalignment between its momentum and its velocity. In Petrov type D spacetimes (such as Kerr), we show that some torques that are impossible with quadrupole moments are possible with octupole moments. Octupole moments can thus have qualitatively-different effects from quadrupole moments. less

In this paper, we show that the robustness of black hole stability is not preserved when the perturbations are disposed on some critical values of the coupling constant in two non-minimally coupled scalar-tensor models, in particular for a number of regular black holes. Using an analytical demonstration in the near-horizon approximation, we obtain exact expressions for the critical coupling constant in two models for which the instability will occur. The numerical analysis show that these critical values are consistent with the threshold points in time-domain profiles of field perturbations. At that threshold value, the effective potential of the Regge-Wheeler equation exhibits an extremum exactly on the location of event horizon. We also show that the real part of the quasi-normal frequencies vanish in the near-horizon regime at critical coupling constant -- recently addressed as purely imaginary modes. Finally, we recover the general area quantization of the spherical black holes at that critical coupling without invoking to highly-damped mode approximation and the result is independent of a specific coupling model. less

We investigate the thermodynamic properties of the cosmological apparent horizon in Gauss-Bonnet quasi-dilaton massive gravity. We derive the modified Friedmann equations and reformulate them in standard form, thereby allowing us to study the first and second laws of thermodynamics for the apparent horizon. Both equilibrium and non-equilibrium states are considered. In the equilibrium description, the first law retains the conventional form with the Bekenstein-Hawking area law for the horizon entropy, and we show that the generalized second law is satisfied under the null energy condition. In the non-equilibrium description, the Wald entropy receives a correction from the Gauss-Bonnet coupling, and the first law acquires an additional term associated with using the Wald entropy representation of the Gauss-Bonnet sector. We demonstrate that the total entropy change is non-negative provided the null energy condition, the positive horizon temperature condition, and the Gauss-Bonnet positivity constraints $ξ(σ)\ge0$ are simultaneously satisfied. Furthermore, we investigate the holographic entropy bound $S_{\text{inside}} \le S_{\text{horizon}}$. We demonstrate that while the idealized local thermal equilibrium assumption leads to a formal saturation or apparent breakdown during dust-dominated eras, the bound is robustly preserved across all cosmological epochs when utilizing realistic physical fluid temperatures. The condition $ξ(σ)\ge0$ is shown to be compatible with the stability constraints derived from tensor perturbations in our previous work. Our results establish that Gauss-Bonnet quasi-dilaton massive gravity is a consistent modified gravity theory from the perspective of horizon thermodynamics and the holographic principle. less

A graviton can be converted into a phonon in a resonant bar detector. First-order perturbation theory predicts a strong enhancement of this conversion for coherent and squeezed graviton states, but the probability can exceed unity when the coherent or squeezing parameter is large. Since a conversion probability must satisfy the unitarity bound, we solve the graviton-phonon quantum dynamics exactly within the rotating-wave approximation. For an initial coherent state, we find that the conversion occurs intermittently through narrow bursts separated by intervals of strong suppression. For an initial squeezed state, the departure from perturbative behavior occurs earlier, and the conversion is strongly suppressed after its initial growth. These effects may provide signatures of quantum graviton-phonon dynamics relevant to single-graviton detection. less

Deviations from vacuum general relativity (such as modified theories or the presence of an environment) produce small shifts in black hole quasinormal mode (QNM) spectra. These effects are becoming increasingly relevant for gravitational wave astronomy as observations of ringdown spectra become more precise. The first-order frequency shift (in a small dimensionless coupling parameter) is now well understood, but no systematic framework exists to compute higher order corrections. The major obstacle is that QNMs do not form a complete basis due to the non-self-adjointness of the system. Nevertheless, it was recently shown that QNMs are orthogonal with respect to an appropriate bilinear form. In this work, we use the bilinear form to systematically lift Schrödinger perturbation theory to the black hole setting. We obtain a formula for quasinormal frequency shifts to any order, in terms of lower order mode shifts. We also provide a spectral decomposition of the first-order mode shift, which involves projections onto unperturbed QNMs along with continuous-spectrum contributions -- making incompleteness explicit. We illustrate the framework on slowly-spinning Kerr and Pöschl-Teller examples, where we find that the QNM sum itself diverges. less

We extend the polynomial construction of parity-violating spatially covariant gravity (SCG) to total derivative order $d=5$, where $d=d_{\mathrm{t}}+d_{\mathrm{s}}$ counts the total number of temporal and spatial derivatives. After organizing the monomials by $(d_{\mathrm{t}},d_{\mathrm{s}})$ and reducing them using integrations by parts, tensor symmetries, three-dimensional curvature identities, the Schouten identity, and the Cayley-Hamilton relation, we obtain a $59$-element basis: $2$, $40$, and $17$ monomials in the sectors $(0,5)$, $(2,3)$, and $(4,1)$, respectively. A direct inspection separates $35$ monomials containing neither the lapse velocity $\mathcal{L}_{\bm{u}}\ln N$ nor $\mathcal{L}_{\bm{u}}K_{ij}$ from $11$ lapse-velocity monomials and $13$ monomials containing higher normal derivatives of the spatial metric. The latter two sectors require a dedicated degeneracy analysis. For tensor perturbations about a spatially flat cosmological background, the acceleration-free part of the manifestly first-order-in-time sector contains $16$ basis elements, whose quadratic action depends on only four combinations of coefficients. These combinations generate helicity-odd corrections proportional to $k/a$ and $(k/a)^3$ in the kinetic and gradient functions. We derive two relations that enforce luminal phase velocity for both circular polarizations while still allowing helicity-dependent kinetic normalization and damping. less

Matched filtering remains the most sensitive method for detecting gravitational waves from compact binary coalescences. The efficiency of such searches depends on how well a discrete template bank covers the underlying parameter space. Conventional geometric, stochastic, and hybrid placement methods can lead to uneven coverage and redundant templates in higher dimensions. Hybrid methods are generally the most efficient among these, while stochastic methods are simpler to implement, particularly when the parameter-space metric is difficult to compute. In practice, both approaches rely on uniform random sampling, which often requires a large number of proposal points to achieve adequate coverage. We find that stochastic template banks constructed using low-discrepancy sequences achieve comparable recovery fractions while requiring 27.5\% fewer proposal points in two dimensions and 12\% fewer in three dimensions. The final template count changes only marginally ($\sim 1\%$), consistent with the metric-volume constraints of the covering problem. The primary benefit of low-discrepancy sampling is therefore a reduction in the size of the initial proposal set, leading to lower memory usage and reduced bookkeeping during bank generation. Since the final template count is governed mainly by the metric volume of the target parameter space, the wall-clock speed-up is more modest than the reduction in proposal count. Nevertheless, low-discrepancy sampling provides a simple and scalable improvement to stochastic template-bank generation for current and future gravitational-wave searches. less