Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1908.06363

The Particle and Energy Cost of Entanglement of Hawking Radiation with the Final Vacuum State

Robert M. Wald
View original source ↗Read source document ↗Export metadata ↓

Abstract

A semiclassical analysis shows that in the process of black hole formation and evaporation, an initial pure state will evolve to a mixed state, i.e., information will be lost. One way of avoiding this conclusion without invoking drastic modifications of the local laws of physics in a low curvature regime would be for the information to be restored at the very end of the evaporation process. It is normally envisioned that this would require a final burst of particles entangled with the early time Hawking radiation. This would imply the emission of an extremely large number of particles from an object of Planck size and mass and would appear to be blatantly ruled out by energy considerations. However, Hotta, Schutzhold, and Unruh have analyzed a $(1+1)$-dimensional moving mirror analog of the Hawking process and have found that, in this model, information is restored via entanglement of the early time Hawking radiation with vacuum fluctuations in the spacetime region to the future of the event where the mirror returns to inertial motion. We analyze their model here and give a precise formulation of this entanglement by introducing the notion of "Milne particles." We then analyze the inertial particle and energy cost of such an entanglement of Hawking radiation with vacuum fluctuations. We show that that, in fact, the entanglement of early time Hawking radiation with vacuum fluctuations requires the emission of at least as many late time inertial particles as Hawking particles. Although the energy cost can be made small in the $(1+1)$-dimensional mirror system, this should not be the case for the $(3+1)$-dimensional evaporating black hole system. Thus, vacuum entanglement has the same difficulties as the more usual burst scenarios for attempting to avoid information loss.

Explore related subjects

gr-qchep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Robert M. Wald. 2019-09-27. The Particle and Energy Cost of Entanglement of Hawking Radiation with the Final Vacuum State. https://doi.org/10.1103/physrevd.100.065019

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

gr-qc↗
arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗