This work analyzes the degradation of continuous-variable entanglement between an inertial reference mode (Alice) and a mode accessible to a noninertial observer (Rob) when horizon-induced mode splitting renders part of Rob's degrees of freedom inaccessible. Within an effective single-mode Gaussian description, tracing the inaccessible sector induces on Rob a local phase-insensitive Gaussian amplifier with gain g = cosh²r (quantum-limited when the environment is in vacuum), where r is the Unruh squeezing parameter. For a standard-form two-mode input we provide closed-form output covariance matrices and the logarithmic negativity E_N, and we derive an exact threshold separating (i) a persistent large-r exponential tail E_N ~ C·exp(−2r) from (ii) finite-r sudden death when additional thermal noise is present. In the quantum-limited pure-input case the prefactor is C(s) = 8·tanh²(s)/ln 2. We further show that, within this Gaussian truncation, the asymptotic scale of the entanglement tail is controlled by the effective modular temperature β_R of Rob's reduced single-mode state. All quantitative claims are verified numerically. Connections to type-III algebraic modular theory and to semiclassical gravitational entropy are discussed as a delineated program rather than derived results; in particular, no identification of C(s) with A/4G or with the Bekenstein–Hawking entropy is claimed. A falsifiable analogue-gravity prediction (BEC or optical horizons) is given in terms of the time decay of the Hawking–partner logarithmic negativity. This preprint develops quantitatively a mechanism from the author's earlier work, "Incomplete Causal Transactions: Black Holes as Permanently Frustrated Couplers" (DOI: 10.5281/zenodo.18736657). AI use disclosure: AI systems were used as tools for symbolic and numerical verification of the Gaussian calculations and for reference checking; all quantitative claims were independently verified by direct computation, and the author takes full responsibility for the work and its delimited scope.
Entanglement degradation appears to be a generic prediction in relativistic quantum information whenever horizons restrict access to a region of spacetime. This property has been previously explored in connection with the Unruh effect, where a bipartite entangled system composed of an inertial observer (Alice) and a uniformly accelerated observer (Rob) was studied, with entanglement degradation caused by the relative acceleration---and with equivalent results for the case when Alice is freely falling into a black hole and Rob experiences a constant proper acceleration as a stationary near-horizon observer. In this work, we show that a similar degradation also occurs in the case of an entangled system composed of an inertial observer (Alice) and a ``diamond observer'' (Dave) with a finite lifetime. The condition of a finite lifetime is equivalent to the restriction of Dave's access within a causal diamond. Specifically, if the system starts in a maximally entangled state, prepared from Alice's perspective, entanglement degradation is enforced by the presence of the diamond's causal horizons.
We study entanglement degradation near the horizons of regular, Reissner-Nordström, and Schwarzschild-de Sitter black holes, considering the Bardeen, Hayward, and generalized Hayward metrics as regular black holes. To this end, we compute the entanglement negativity,
N, for two Unruh-like modes of a scalar field shared by Alice, who is inertial, and Rob, who hovers at a fractional offset
ρ outside the horizon of the backgrounds under consideration. For each geometry, we locally approximate the metric by a Rindler patch characterized by Rob's proper acceleration
a0. Because this Rindler approximation breaks down near the extremal limit, we also compute a near-extremal cutoff. Tracing over the inaccessible Rindler wedge yields a mixed Alice-Rob state, from which we evaluate
N as a function of the mode frequency
ω and the acceleration
a0. In all geometries considered, except for one,
N increases monotonically with the parameter distinguishing that geometry form the Schwarzschild one. The exception is the Reissner-Nordström metric, for which
N exhibits a shallow local minimum at a particular value of the charge. We also find that the Reissner-Nordström metric is the only background for which the negativity falls below that of the Schwarzschild case. Among all cases studied, the Schwarzschild-de Sitter spacetime provides the strongest protection of entanglement. Finally, across all backgrounds, high-frequency modes undergo less degradation than low-frequency modes. These results suggest that entanglement may serve as a useful probe for distinguishing Schwarzschild spacetime from other geometries.
The influence of Hawking radiation on quantum entanglement for bimodal Gaussian states near a Schwarzschild black hole is investigated. It is shown that for a thermal squeezed state of a bimodal bosonic system the Hawking radiation reduces and even can destroy the entanglement between the mode of a Kruskal observer Alice and the mode of Bob, who is an accelerated observer hovering outside the event horizon of black hole. By contrary, the Hawking radiation increases and even can generate quantum entanglement between Bob and anti-Bob, who is a hypothetical observer inside event horizon. We show that in both these scenarios the competition between the contrary influences produced by Hawking temperature, squeezing and field frequency, may favour the preservation of the quantum entanglement. We investigate also the influence of the thermal environment on the behaviour in time of the entanglement between the considered observers and show that the entanglement is destroyed in a finite time for both considered bipartite scenarios of observers Alice and Bob, and respectively Bob and anti-Bob, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. For a zero temperature of the thermal bath the initial existing entanglement is decreasing over time, but it keeps for all finite times a non-zero value and the logarithmic negativity tends to zero only in the limit of infinite time.
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.
This preprint poses, and does not solve, an open problem concerning the relative-entropy source near a Schwarzschild horizon. The central object is the finite-region thermal modular Hamiltonian on the Schwarzschild exterior: the modular Hamiltonian of a finite ball at finite radius in the Hartle–Hawking (KMS) state. Its strictly near-horizon, conformal limit is known — it is the Cardy–Tonni thermal-interval Hamiltonian of the two-dimensional s-wave reduction — but its finite-distance form, away from that limit, is not. Two independent obstructions force this object. First, the second-order Blanco–Casini–Hung–Myers stress-tensor factorisation of the relative entropy, valid near the vacuum, degrades once the ball is large compared with the local (Tolman-redshifted) thermal length. Second, the squeezed-state coincidence wall survives the Type II crossed-product renormalization as the Jafferis–Lewkowycz–Maldacena–Suh invariant. The two obstructions are logically independent. In the two-dimensional s-wave reduced sector, the finite content that the missing operator would govern is exhibited in closed form for non-squeezed states (where the wall is absent): a finite, cutoff-independent remainder R[σ] lying below the wall. In four dimensions, the operator itself is absent from the canonical relevant-deformation and modular-Hamiltonian toolkit — existing constructions either compute entanglement entropy from an already-known modular Hamiltonian, or supply an operator-level first-order deformation only for a vacuum reference, and neither applies to a finite-region thermal KMS reference. The paper therefore states, as its open problem, the construction of this operator — or its first-order deformation off the conformal limit — and claims no resolution of the squeezed-state wall. This work is part of the Informational Gravity Framework series and continues the capstone deposit (concept DOI 10.5281/zenodo.20804927).
We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a ``sudden death'' and the steering from anti-Bob to Bob experiences a ``sudden birth'' with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed
ln2, which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) $s=\mathrm{arccosh}\frac{{\mathrm{cosh}}^{2}r}{1\ensuremath{-}{\mathrm{sinh}}^{2}r}$ is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.