The mean Hawking flux does not determine how quantum stress fluctuations perturb a black-hole geometry. That information resides in field correlations, including vacuum contributions absent from the outgoing luminosity. Here we connect the complete exterior Unruh Wightman function to a finite-band stochastic reconstruction of Schwarzschild geometry. We retain the incoming vacuum and both outgoing frequency branches, form the connected stress covariance before angular projection, and propagate its monopole through a density-driven radial response. A shared Gaussian reconstruction then resolves how the value and derivative of the lapse control different geometric observables. For the specified covariance and noise amplitude, 2,200 realizations give relative widths of 0.0185 for the local horizon radius and 0.0483 for the surface-gravity temperature parameter, consistently across histograms and reconstruction checks. Covariance derivatives explain this unequal sensitivity. The construction separates the quantum-state input from the gravitational closure and spatial sampling assumptions, providing a reproducible finite-resolution description of how Hawking-field correlations affect horizon positions and surface-gravity statistics.
The mean Hawking flux does not determine how quantum stress fluctuations perturb a black-hole geometry. That information resides in field correlations, including vacuum contributions absent from the outgoing luminosity. Here we connect the complete exterior Unruh Wightman function to a finite-band stochastic reconstruction of Schwarzschild geometry. We retain the incoming vacuum and both outgoing frequency branches, form the connected stress covariance before angular projection, and propagate its monopole through a density-driven radial response. A shared Gaussian reconstruction then resolves how the value and derivative of the lapse control different geometric observables. For the specified covariance and noise amplitude, 2,200 realizations give relative widths of 0.0185 for the local horizon radius and 0.0483 for the surface-gravity temperature parameter, consistently across histograms and reconstruction checks. Covariance derivatives explain this unequal sensitivity. The construction separates the quantum-state input from the gravitational closure and spatial sampling assumptions, providing a reproducible finite-resolution description of how Hawking-field correlations affect horizon positions and surface-gravity statistics.
Black holes are usually described either as classical geometries on which quantum fields propagate or as objects whose complete quantum description lies beyond semiclassical gravity. Hawking radiation already shows, however, that a black hole is not an exactly isolated system: the horizon carries a thermal scale and, after coarse graining, may be associated with fluctuations, dissipation and environmental correlations. Whether this horizon-scale openness can be encoded directly in the gravitational background, before any stochastic treatment of the metric, remains an open question. Here we answer it by introducing, for the first time, a conserved Hawking-scale anisotropic source representing the coarse-grained near-horizon atmosphere and solving the Einstein equations for a static black hole at fixed ADM mass. The dressed geometry has a renormalized mass function, a self-consistently shifted horizon and a modified surface gravity. Because the same lapse governs the horizon and timelike geodesics, the thermal response is accompanied by a correlated orbital restructuring: the effective potential is renormalized, the ISCO moves inward and the near-horizon residence time increases. The construction adds no Langevin force to a fixed Schwarzschild background; rather, it defines a deterministic dressed mean geometry, providing a controlled background on which stochastic metric fluctuations may subsequently be treated in the Einstein-Langevin framework. This establishes the deterministic mean-field sector as the necessary first step for future stochastic gravity programs addressing horizon-scale openness.
Stress-tensor fluctuations carry information that is absent from the mean
semiclassical Einstein equation, but their observable effect depends as much
on the response of the geometry as on the noise itself. We formulate an
effective, quasistationary spherical model organized by the response--noise
structure of a quantum Langevin equation. A prescribed mean dressing and a
horizon-localized colored source are varied independently. For every source
realization we reconstruct the lapse, locate its outer trapping horizon, and
evaluate the adiabatic Hayward--Kodama temperature from the slope at that same
root. As the mean lapse approaches an inner--outer root merger, its inverse
slope acts as a geometric susceptibility: a fixed source covariance produces
enhanced horizon fluctuations, horizon--temperature covariance, and a
positively skewed, greybody-filtered luminosity. The specific advance is a
single-realization map from colored metric noise to correlated geometric,
thermal, and radiative statistics, together with an explicit separation of
reservoir strength from near-critical amplification. The model is a
stochastic-semiclassical testbed, not a microscopic evaluation of Unruh-state
response and noise kernels.
Abstract We introduce a local operational protocol for measuring quantum information scrambling in a curved spacetime background. In this framework, two Unruh-DeWitt (UDW) detectors, coupled to a massless conformally coupled scalar field in the Hartle–Hawking vacuum of the non-rotating ( 2 + 1 ) -dimensional Banados–Teitelboim–Zanelli (BTZ) black hole, serve as local probes. Evaluating the detector out-of-time-ordered correlator requires a fourth-order Dyson series expansion. Within the scrambling regime, this correlator exhibits exponential growth with Lyapunov exponent, exactly saturating the Maldacena–Shenker–Stanford bound at the global Hawking temperature. Governed by the black hole surface gravity, the Lyapunov exponent is universal and independent of detector positions, energy gaps, and coupling strengths. Furthermore, the scrambling amplitude shows a monotonic dependence on the radial positions of the detectors, vanishing at the event horizon and increasing outward. Local two-level probes thus witness the maximal chaos of the BTZ geometry without reconstructing the global quantum field state.
Black holes are conjectured to be maximally chaotic, with their quantum spectra expected to exhibit universal random-matrix correlations. This expectation, however, has so far rested largely on holographic descriptions or on many-body models in which randomness is introduced rather than derived from the microscopic degrees of freedom of the horizon itself. In the horizon matrix model, the fuzzy sphere supports highly degenerate parton states whose multiplicity accounts for the black-hole entropy. We show that quantum fluctuations of the horizon geometry lift this degeneracy and generate an ensemble of one-parton Hamiltonians. Both the operator structure and the rank-dependent covariance of this ensemble are determined by the microscopic model, rather than fixed by quenched couplings.
Despite this structured covariance, the resulting spectra exhibit GOE, GUE, and GSE statistics dictated by their antiunitary symmetry classes, with the adjacent-gap statistic becoming increasingly self-averaging with matrix size. The model also realizes the universal Pandey--Mehta orthogonal-to-unitary crossover, with the crossover scale determined by the microscopic geometric covariance. A rank-resolved variance analysis shows that the fluctuation strength remains broadly distributed across tensor ranks up to the microscopic cutoff, providing a microscopic basis for the observed Wigner--Dyson universality and effectively nonlocal dynamics. The antiunitary symmetry acts directly on the fuzzy-sphere geometry, so the Dyson class of a conditional Hamiltonian is determined by the antiunitary symmetry of the underlying quantum geometry. This provides a microscopic counterpart of the Stanford--Witten relation between geometry and random-matrix universality in JT gravity. These results establish a microscopic route from quantum horizon geometry to black-hole spectral chaos.
A bstract The effect of black holes on entanglement harvesting has been of considerable interest over the past decade. Research involving stationary Unruh-DeWitt (UDW) detectors near a (2+1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole has uncovered phenomena such as entanglement shadows, entanglement amplification through black hole rotation, and differences between bipartite and tripartite entanglement. For a (1+1)-dimensional Schwarzschild black hole, it has been shown that two infalling UDW detectors can harvest entanglement from the scalar quantum vacuum even when separated by an event horizon. In this paper, we calculate the mutual information between two UDW detectors coupled to a massless quantum scalar field, with the detectors starting at rest and falling radially into a non-rotating (2+1)-dimensional BTZ black hole. The trajectory of the detectors includes regions where both detectors are switched on outside of the horizon; where one detector is switched on inside of the horizon while the other switches on outside; and where both detectors switch on inside of the horizon. We investigate different black hole masses, detector energy gaps, widths and temporal separations of the detector switching functions, and field boundary conditions. We find that black holes — even the simplest kind having constant curvature — significantly affect the correlation properties of quantum fields in the vacuum state. These correlations, both outside and inside the horizon, can be mapped out by infalling detectors.
We show that implementing a generalized uncertainty principle (GUP) with both minimal length and maximal momentum directly on the reduced phase space of the Schwarzschild black hole (BH) leads to a finite and discrete mass spectrum, a strict upper bound on the BH mass, a bounded entropy, and a fully regulated Hawking temperature. We further construct a GUP-deformed lapse function that preserves the ADM mass and horizon radius while exactly reproducing the GUP temperature through the surface gravity. Using the most massive observed supermassive BHs, we derive the constraint on the GUP parameter, β≲10−98, showing that present astrophysical data already impose robust bounds on minimal length quantum gravity.