Abstract We present a four-qubit quantum circuit model of black-hole evaporation with a controlled violation of semi-causality, understood as the condition that information may fall into the black hole but cannot propagate back across the horizon. Building on Broda’s semi-causal evaporation circuit, we introduce a controlled-unitary gate CU ( σ ) that allows tunable information leakage from the interior to the exterior while preserving global unitarity. We compute the single-qubit reduced entropies, together with the mutual information and entanglement negativity for the BH-GR and IN–OUT bipartitions, at each discrete time step. For σ = 0 , the model reproduces Broda’s Page-like entropy evolution with complete late-time purification. For any σ > 0 , however, nonzero residual single-qubit entropies and persistent late-time entanglement remain, indicating incomplete purification of the outgoing radiation despite the global unitary evolution. In the small- σ regime, the residual entropy exhibits a characteristic − σ 2 ln σ 2 scaling that bears qualitative similarity to logarithmic entropy corrections in generalized-uncertainty-principle inspired evaporation scenarios. For larger values of σ , the persistence of finite residual entropy invites comparison with remnant-like endpoint configurations in regular or extremal black-hole models. Our results show how controlled departures from the semi-causal limit modify information recovery in a minimal analytically tractable model of black-hole evaporation.
Abstract We present the canonical quantization of Weyl-invariant gravity in a specific conformal gauge. Fixing the scale factor as a ( η ) = 1 / ( H 0 η ) yields an effective geometric cosmological term M ( η ) = α / η 2 on the left-hand side of the Einstein equations, guaranteeing an equation of state w = − 1 by construction. The Bianchi identity requires a compensator scalar field; we show that this compensator is the conformal mode of the metric, a gauge artifact that does not propagate ghost instabilities in the full quantum theory. We develop the complete Arnowitt–Deser–Misner Hamiltonian formulation and prove that the constraint algebra closes in standard first-class form. Canonical quantization yields a well-defined Wheeler–DeWitt equation where the M ( η ) term acts as a potential barrier dynamically suppressing the quantum creation of small-scale universes. The physical reduced Hamiltonian is demonstrated to be bounded from below, time evolution is strictly unitary in the physical Hilbert space, and microcausality is preserved. In the pure vacuum regime, the model admits an exact analytical solution with Ω DE = 1 , resolving the cosmic coincidence problem without fine-tuned parameters. In the matter-dominated era, the comoving horizon scales as R H ∝ η , so our result M ∝ η − 2 ∝ R H − 2 reproduces the central Compton Mass Dark Energy (CMaDE) hypothesis from first principles and establishes n = − 2 as the theoretical benchmark for the conformal holographic dark energy parametrization M ∝ η n . From a pure conformal symmetry principle, the model delivers an effective geometric cosmological term that drives the accelerated expansion with w = − 1 , providing the missing action principle for CMaDE.
Abstract We present a simple derivation of the exact Planck spectrum of the quadrupole radiation from point masses moving apart nonrelativistically, essentially an analog for gravitational radiation. The standard Einstein quadrupole radiation formula gives emitted power proportional to the square of the third derivative of x ( t ) 2 . In our moving-mass picture, imaginary-time periodicity appears as a product-log trajectory of a quadrupole source. In the frequency domain, the power becomes proportional to the Planck distribution, ω 3 / ( e 2 π c ω / κ − 1 ) . The resulting Planckian graviton energy spectrum has finite total energy and finite mean graviton number. The emitted spectrum is purely kinematic in origin: no equilibrium, horizon, or stochastic source is assumed.
Abstract In this work we give a thorough derivation of the spherically symmetric Einstein–Vlasov system in Bondi coordinates. The system of partial differential equations obtained differs significantly from the Schwarzschild-coordinate formulation, and it is naturally adapted to the study of radiation and null infinity. This paper provides the raw material whose exploitation, in forthcoming investigations, will give rise to characteristic counterparts of some important previous results known for the standard Cauchy problem associated to the spherically symmetric Einstein–Vlasov system. As the first such results in Bondi coordinates for the characteristic initial value problem, we establish the global well-posedness of the characteristic initial value problem obtained. Furthermore, we prove a nonlinear stability result: for sufficiently small initial data, the solution decays polynomially to the Minkowski spacetime. More precisely, we obtain the decay estimates | λ | , | ν | ⩽ C ε ( 1 + u ) − 1 for the metric coefficients, | ρ | ⩽ C ε ( 1 + u ) − 2 for the matter density, and | m ( u , ∞ ) − m ( 0 , ∞ ) | ⩽ C ϵ for the Bondi mass, which remains bounded and converges to its initial value at late retarded time. To illustrate the physical relevance of our formulation and complement the theoretical analysis, we present numerical simulations comparing the behavior of solutions, both in Bondi and Schwarzschild coordinates. These simulations highlight key phenomena such as the radiative mass loss via the Bondi mass, the outgoing particle trajectories toward null infinity, the characteristic quadrupole gravitational wave pattern, and the contrasted dynamics of gravitational collapse. This work lays the foundation for further investigations of fundamental problems such as black holes formation, gravitational collapse and cosmic censorship in Bondi coordinates.
Abstract Expansion of the Universe can be interpreted as a tendency for achieving the holographic equipartition. This principle, the law of emergence, first postulated in the context of Einstein’s gravity has been extended successfully to more general gravity theories like Gauss–Bonnet and Lovelock gravity. We derive the law of emergence for brane world models of gravity, starting from the more fundamental and well established principle, the first law of thermodynamics. More specifically, we derive the law of emergence in the context of RS II brane world, warped Dvali, Gabadadze and Porrati model and Gauss–Bonnet brane world model, with the help of corresponding Friedmann equations. We further show that the law of emergence leads to the maximization of horizon entropy in all these brane world models. Our results suggest that the horizon thermodynamics is the backbone of the law of emergence in the brane world scenarios. Following this, we analyze the evolution of the horizon energy fluctuations in the context of brane world gravity. Interestingly, the fluctuations in horizon energy attain a constant value in the long run, when ω = − 1 , which corresponds to an equilibrium state of maximum entropy.
Hawking radiation away from stationarity is governed, at the ray tracing level, by the retarded time evolution of the null mapping. We consider an extracted massless conformal channel whose outgoing directions are labelled on a fixed reference horizon slice. Balanced uniformisation, after fixing a nondegenerate balanced branch, defines an induced antipodal involution on this slice. We prove that creation and erasure of centred antipodal odd structure in the channel labelled peeling field enforce a lower bound on the time integrated spatial norm of the conformal channel defect. The forcing scale depends only on the largest intermediate mismatch and the intrinsic Jacobian distortion of the induced antipode, while greybody filtering, angular and frequency mixing, mass effects, spin dependence, and residual propagation or extraction corrections enter through a remainder whose integrated norm must be controlled independently. Round sphere odd scalar harmonics provide analytic calibrations, with the compact dipole pulse saturating the geometric and temporal estimates. A time-averaged form identifies a transient conformal channel scale proportional to the antipodal peeling amplitude divided by the episode duration.
Abstract A matter wave propagating through curved spacetime accumulates a phase that encodes both geometry and gauge structure. We develop a semiclassical description of charged spin-$\tfrac{1}{2}$ matter-wave interferometry based on a WKB expansion of the general covariant Dirac equation. At leading order, and within the guided-arm approximation, the interferometric phase separates into three additive contributions: a dynamical phase associated with proper-time evolution, a spin phase arising from parallel transport in the local Lorentz frame, and an electromagnetic phase generated by curvature-induced perturbations of a background electromagnetic field. In a freely falling detector frame described by Fermi normal coordinates, the dynamical and spin channels are driven by the local gravitoelectric and gravitomagnetic tidal fields, while the electromagnetic channel follows from solving the detector-frame Maxwell equations for a uniform background magnetic field in the long-wavelength regime. For a weak gravitational wave, all three channels are controlled by the common tidal scale $\ddot h_{+,\times}\sim\Omega_{\rm gw}^2 h_0$, but enter through distinct couplings and geometry-dependent response kernels. Applied to an idealized square Mach--Zehnder interferometer, the dynamical channel reproduces the established tidal matter-wave response, and the spin channel is suppressed by the ratio of the Compton wavelength to the interferometer size. The electromagnetic channel is set by the applied magnetic flux rather than by the particle mass or spin: within the initial-value solution adopted here, its magnitude depends on the orientation of the background field relative to the wave, with the perpendicular configuration carrying an additional factor $c/v$, and the two orientations select different gravitational-wave polarizations.
Abstract This study analyses the WKB and Supersymmetric WKB (SWKB) methods within a closed Friedmann–Robertson–Walker minisuperspace model to determine whether these approaches yield different results in modelling tunnelling phenomena in quantum cosmology. The transition from a dust-dominated to a dark-energy-dominated epoch driven by a generalised Chaplygin gas is examined. Incorporating supersymmetric quantum mechanics requires modifying the initial phenomenological potential, which in turn influences late-time cosmological evolution. Specifically, after the dust-dominated phase, the Universe enters a dark-energy-dominated dynamical regime. This regime decays over time and eventually returns to another dust-dominated period. Analytic approximations for the superpotential, including power series and the Picard approximation, yield closed-form SWKB tunnelling expressions. These expressions facilitate the calculation of transmission probabilities as functions of the Chaplygin parameters A , B , and α . The SWKB and WKB methods can both be employed for a concrete range of the scale factor, a and the Chaplygin gas parameters, but quantitatively they provide different tunnelling probabilities. In more detail, they diverge for suppressed barriers: standard WKB systematically underestimates the tunnelling probability, while SWKB mathematically avoids the turning-point singularity but physically overcompensates due to the lack of shape-invariance. A backward numerical integration method is introduced as a numerical benchmark, confirming that the true transmission probabilities lie strictly between the two semiclassical approximations ( T WKB < T num < T SWKB ). Crucially, by confirming that the actual tunnelling probabilities are higher than estimated by standard WKB, these results demonstrate that quantum transitions into cosmological models with transient late-time acceleration are probabilistically more viable. Therefore, SWKB provides a valuable complementary approach for studying barrier transmission in quantum cosmology. It is suggested that a functional form for the decaying dark energy density should be derived. This would enable a test of the supersymmetric quantum mechanics modified potential and of its implications with current observational data.
Abstract We study static, spherically symmetric stellar configurations in the power-law class of energy-momentum squared gravity defined by F ( R , T ) = R + η T n using the covariant 1 + 1 + 2 semi-tetrad formalism. For perfect physical fluids, we show that the nonlinear matter corrections can be reinterpreted as an effective perfect fluid, so that the stellar equilibrium equations retain the standard Tolman–Oppenheimer–Volkoff (TOV) form when written in terms of effective variables. The resulting covariant structure equations are formulated in both metric and dimensionless variables and, whenever an effective closure relation exists, reduce to an autonomous planar dynamical system. This provides a global qualitative description of the stellar phase space in terms of finite and asymptotic critical points. Specializing to linear physical equations of state, we recover the general relativistic benchmark and identify sectors that are exactly, asymptotically, or piecewise equivalent to general relativity, as well as sectors for which the planar reduction breaks down and the full three-dimensional covariant flow must be considered. We further recover the standard metric TOV equation in terms of effective variables and show that, although the exterior spacetime remains Schwarzschild, the natural matching condition at the stellar surface is p eff ( R ) = 0 , which need not coincide with p ( R ) = 0 for self-bound matter. Finally, in the appendix, we show how our procedure can be applied to a realistic neutron-star equation of state.
Extending the work presented in a workshop “From Quarks to Neutron Stars: Insights from kHz gravitational waves”, we discuss some limiting cases of the moment of inertia, tidal deformability, and spin-induced quadrupole moment for relativistic stars. First, conjecturing that a hierarchy of the length scale is the key to proposed universality among these second-order moments, we revisit the relation for incompressible relativistic stars (known as Schwarzschild's interior solution) as a candidate of the possible stiff limit. Second, we present the limiting form for the weak-field limit. In particular, we demonstrate how relativistic computations of tidal deformation are related to the traditional Newtonian counterpart, which might not have been presented explicitly in the literature.
Abstract This paper investigates the perturbation problem of a spherically symmetric black hole surrounded by perfect fluid matter in Rastall gravity. Assuming that the black hole is subjected to axial perturbations, we derive the governing equation for perturbation evolution, namely the Regge–Wheeler (RW) equation, and discuss the properties of the perturbation potential V RW ( r ) . From this, a constraint condition on the Rastall gravity parameter k λ is deduced. Furthermore, we solve the quasinormal mode frequencies ( QNMs ) of the equation using the WKB approximation. Subsequently, we distinguish two regions: the region near the perturbation center and the region far from the perturbation center. For these two regions, we separately solve the spatial distribution and time evolution functions of gravitational perturbations satisfying the RW equation under the WKB approximation. Among them, with the help of the analysis of the trajectories of equiphase points, we discuss the problem of the finiteness of the perturbation amplitude. Finally, given the specified perturbation frequencies and the spatiotemporal distribution of perturbations, we solve the variation of the particle’s effective potential curve under perturbations and discuss the influence of gravitational perturbations on the corresponding innermost stable circular orbit.
Abstract We present novel solutions to the Klein–Gordon equation in a black string spacetime immersed in a Kiselev-like quintessence fluid and surrounded by a cloud of strings (BCK spacetime). The solutions are shown to depend on the quintessence state parameter α Q and extend to a broader radial domain than previously reported. Explicit analytical results are provided for α Q = 0 , 1 / 2 , 1 , thereby encompassing all relevant physical scenarios. These analytical radial solutions are derived using the confluent and biconfluent Heun equations, as well as Bessel equations in specific cases. Constraints on the Heun parameters that produce spectral restrictions are examined, resulting in the δ N -subclass of solutions, which includes the polynomial cases. More importantly, quintessence-induced ‘dark phases’ are identified for several scenarios; in particular, the regime α Q = 1 is emphasized for future comparison with alternative spacetime geometries. These findings contribute to the understanding of scalar particle dynamics and the influence of dark energy on quantum systems in curved spacetime backgrounds.
Abstract Fast neutrino flavor conversion is a crucial yet poorly understood process in core-collapse supernovae due to its dependence on neutrino angular distributions and the microscopic scales. In this study, I present the general relativistic \textit{multiangle} Boltzmann neutrino radiation hydrodynamics simulations incorporating a quantum-kinetically motivated subgrid model based on the Bhatnagar-Gross-Krook relaxation scheme. First, a comparative testing of various subgrid methodologies in 1D simulations is performed, validating the robustness of the angular-dependent approach against simpler models. Furthermore, following the recent findings that the flavor conversion exerts a bifurcated impact on shock revival, I investigate how these flavor conversion induced changes affect the resulting gravitational wave signatures. The analysis shows that the flavor conversion can indeed affect the high-frequency gravitational wave emission. In particular, an equation of state dependent suppression of the high-frequency ($\gtrsim600\,\mathrm{Hz}$) gravitational wave power is identified.
We show that black hole horizons with non-constant curvature can be constructed in any even dimension, when the source of the Einstein equations is given by the stress-energy tensor of a non-linear sigma model of a particular class
The tilted dipole cosmology extends the standard model by incorporating a preferred spatial direction and separate bulk velocities for matter and radiation, offering a potential explanation for observed large-scale bulk flows and the CMB dipole. We conduct a comprehensive analysis of this anisotropic framework using Big Bang Nucleosynthesis (BBN) and Gravitational Baryogenesis (GB) to impose stringent constraints on the radiation tilt parameter β_r, which quantifies the magnitude of the radiation bulk flow. By deriving the modified expansion rate H(T) and its impact on light element abundances, we find that the combined 2σ BBN limits from primordial helium-4 and deuterium are |β_r| ≲ 0.03 for maximal shear (tightest bound) and |β_r| ≲ 0.2 for minimal shear (weakest bound). These bounds are consistent with, but tighter than, those inferred from the effective neutrino species count |ΔN_eff| ≲ 0.4. Importantly, both bounds are upper limits; β_r = 0 is always allowed by the BBN constraints. The lithium-7 problem persists, as the β_r values required to resolve it are excluded by helium-4 data. Furthermore, GB – operating at decoupling temperatures T_D ≳ 10^12 GeV under the scaling β_r ∝ T – yields far more severe constraints, limiting |β_r^BBN| ≲ 10^-8 for such high-scale baryogenesis scenarios.
Abstract Flat Minkowski space (M 4 ) and AdS 4 can both be conformally mapped to the Einstein cylinder. The maps may be judiciously chosen so that some null generators of the I + boundary of M 4 coincide with antipodally-terminating null geodesic segments on the boundary of AdS 4 . Conformally invariant nonabelian gauge theories in M 4 have an asymptotic S -algebra generated by a tower of soft gluons given by weighted null line integrals on I + . We show that, under the conformal map to AdS 4 , the leading soft gluons are dual to light transforms of the conserved global symmetry currents in the boundary CFT 3 . The tower of light ray operators obtained from the S O ( 3 , 2 ) descendants of this light transform realize a full set of generators of the S -algebra in the boundary CFT 3 . This provides a direct connection between holographic symmetry algebras in M 4 and AdS 4 .
We constrain the Emergent Fractional Fractal (EFF) cosmological model through a joint likelihood analysis of recent cosmological observations at the background and perturbation levels. In this framework, an effective fractal dimension d is introduced to parameterize possible fractional deviations from the standard cosmological model. We consider three combinations of datasets: (i) late-time (LT) observations including PantheonPlus Type Ia supernovae, H(z) measurements, and growth-rate measurements fσ_8; (ii) LT combined with DESI DR2 BAO and Big Bang nucleosynthesis (BBN); and (iii) LT combined with DESI DR2 BAO and CMB distance priors. With the inclusion of CMB distance priors, the fractal dimension is constrained to d = 2.0004^+0.0006_-0.0003 at the 1σ confidence level. Model comparison using the Akaike Information Criterion (AIC) shows that the EFF and ΛCDM models fit the observational data equally well, while the Bayesian Information Criterion (BIC) favors the simpler ΛCDM model because of its smaller parameter space. These results show that current cosmological observations place strong constraints on fractal extensions of the standard cosmological framework and possible deviations from the ΛCDM model.
Abstract This Corrigendum reports three corrections to the published article: (i) clarification of the heavy-mediator resonance mass used for the two-mediator benchmark in table 1, (ii) correction of a typo in the scaling exponent for the light-mediator mass in figure 2 (left panel) and appendix I, and (iii) availability of a public reproducibility package.
Abstract In this paper, working in a geometrical, frame-independent and ansatz-independent formalism, we analytically investigate the gravitational collapse of a mass-less scalar field in a spherically symmetric space-time. This is one of the fundamental matter fields determined by the Lagrangian formulation. We identify a single dimensionless parameter, that determines the end-state to be a black-hole or complete dispersal and a locally naked null singularity, which exists as a critical case between the previous two end-states. The governing parameter, being dimensionless, makes the result scale independent, thus confirming the universality and criticality that was observed in extensive numerical studies by various authors.
