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The interior of a pure-state black hole is known to be reconstructed from the Petz map by collecting a sufficiently large amount of the emitted Hawking radiation. This was established based on the Euclidean replica wormhole, which comes…

The non-isometric holographic model of the black hole interior stands out as a potential resolution of the long-standing black hole information puzzle since it remedies the friction between the effective calculation and the microscopic…

We compute the black hole entropy and the entanglement entropy of Hawking radiations due to photons during the evaporation of a 4d asymptotically flat Kerr black hole. The Page curve for the Kerr black hole is obtained in the original way…

This paper summarizes recent discussions of the Page curve and the information paradox, and responds to the reasoning and examples from arXiv:2506.04311. We review arguments demonstrating that in quantum gravity the algebra of observables…

The quantum entanglement entropy of an eternal black hole is studied. We argue that the relevant Euclidean path integral is taken over fields defined on $\alpha$-fold covering of the black hole instanton. The statement that divergences of…

Unitary evolution makes pure state on one Cauchy surface evolve to pure state on another Cauchy surface. Outgoing Hawking radiation is only subsystem on the late Cauchy surface. The requirement that Hawking radiation to be pure amounts to…

In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the "black hole information paradox". Two main types of…

The black-hole information puzzle has attracted much attention over the years from both physicists and mathematicians. One of the most intriguing suggestions to resolve the information paradox is due to Bekenstein, who has stressed the fact…

We examine the basic assumptions in the original setup of the firewall paradox. The main claim is that a single mode of the lathe radiation is maximally entangled with the mode inside the horizon and simultaneously with the modes of early…

The approach of 't Hooft to the puzzles of black hole evaporation can be applied to a simpler system with analogous features. The system is $1+1$ dimensional electrodynamics in a linear dilaton background. Analogues of black holes, Hawking…

We investigate the information paradox in the four-dimensional Kerr-Newman black hole by employing the recently proposed island paradigm. We first consider the quantum field in the four-dimensional Kerr-Newman spacetime. By employing the…

The puzzles of black hole evaporation can be studied in the simplified context of 1+1 dimensional gravity. The semi-classical equations of Callan, Giddings, Harvey and Strominger provide a consistent description of the evaporation process…

We study the Page curve in the four dimensional asymptotically flat eternal Garfinkle-Horowitz-Strominger dilaton black holes by applying the "quantum extremal surface" prescription. The results demonstrate that without island, the…

We discuss the black hole information problem, including the recent claim that unitarity requires a horizon firewall, emphasizing the role of decoherence and macroscopic superpositions. We consider the formation and evaporation of a large…

We analyze a system consisting of an oscillator coupled to a field. With the field traced out as an environment, the oscillator loses coherence on a very short {\it decoherence timescale}; but, on a much longer {\it relaxation timescale},…

We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional…

After reviewing the relation of entropy to information, I derive the entropy bound as applied to bounded weakly gravitating systems, and review the bound's applications to cosmology as well as its extensions to higher dimensions. I then…

We study reflected entropy as a correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and radiation, radiation and radiation. We compute reflected…

A simple classical consideration of black hole formation and evaporation times focusing solely on the frame of an observer at infinity demonstrates that an infall cutoff outside the event horizon of a black hole must be imposed in order for…

We study the Page curve and the effect of the Hawking-Page phase transition in the Vaidya model of evaporating BTZ black holes, both with and without islands. The phase transition can occur before, at, or after the Page time. When it occurs…