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In the early 1970s, Jacob Bekenstein discovered that black holes have entropy, which became one of the greatest scientific revolutions of the second half of the 20th century. The objective of this paper is to present a simple derivation --…

Popular Physics · Physics 2026-02-27 Jorge Pinochet

In this invited review, we discuss the evaporation of a black hole, with emphasis on the resulting macroscopically distinct patterns of Hawking radiation. The density matrix of this radiation can approach a pure final state in the form of a…

High Energy Physics - Theory · Physics 2024-12-19 Xavier Calmet , Stephen D. H. Hsu

The black hole information paradox is a contradiction between fundamental principles which has puzzled physicists for over forty years. The crux of the problem lies in an assumption about the structure of entanglement across the event…

Popular Physics · Physics 2019-01-07 Ro Jefferson

By applying Rosen's quantization approach to the historical Oppenheimer and Snyder gravitational collapse and by setting the constraints for the formation of the Schwarzschild black hole (SBH), in a previous paper [1] two of the Authors (CC…

General Relativity and Quantum Cosmology · Physics 2022-11-28 C. Corda , F. Feleppa , F. Tamburini , I. Licata

We give a method in which a quantum of mass equal to twice the Planck mass arises naturally. Then using Bose-Einstein statistics we derive an expression for the black hole entropy which physically tends to the Bekenstein-Hawking formula.

General Relativity and Quantum Cosmology · Physics 2009-10-31 B. Ram

In this paper, we analyze whether quantum correlations between successive steps of evaporation can open any way to resolve the black hole information paradox. Recently a celebrated result in literature shows that `small' correction to…

High Energy Physics - Theory · Physics 2014-12-18 Avik Roy , Moinul Hossain Rahat , Mishkat Al Alvi , Md. Abdul Matin

Trieste Spring School Lectures describing the author's opinions about black hole evaporation and information loss. The remnant, or cornucopion scenario for the endpoint of Hawking evaporation is described in detail. In this picture…

High Energy Physics - Theory · Physics 2009-10-28 Thomas Banks

First, the relation between black holes and limitations on information of other systems is developed. After reviewing the relation of entropy to information, we derive the entropy bound, review its applications to cosmology and its…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Jacob D. Bekenstein

If a black hole (BH) is initially in an approximately pure state and it evaporates by a unitary process, then the emitted radiation will be in a highly quantum state. As the purifier of this radiation, the state of the BH interior must also…

High Energy Physics - Theory · Physics 2015-09-30 Ram Brustein , A. J. M. Medved

We argue that a process where a fuzzy space splits in two others can be used to explain the origin of the black hole entropy, and why a "generalized second law of thermodynamics" appears to hold in the presence of black holes. We reach the…

General Relativity and Quantum Cosmology · Physics 2015-05-18 C. A. S. Silva , R. R. Landim

Suppose a black hole forms from a pure quantum state $\ket{\psi}$. The black hole information loss paradox arises from semiclassical arguments suggesting that, even in a closed system, the process of black hole formation and evaporation…

General Relativity and Quantum Cosmology · Physics 2025-04-15 Kiran Adhikari

The conservation of information of evaporating black holes is a very natural consequence of unitarity which is the fundamental symmetry of quantum mechanics. In order to study the conservation of information, we need to understand the…

High Energy Physics - Theory · Physics 2022-09-02 Jeong-Myeong Bae , Dong Jin Lee , Dong-han Yeom , Heeseung Zoe

The evaporation of black holes into apparently thermal radiation poses a serious conundrum for theoretical physics: at face value, it appears that in the presence of a black hole quantum evolution is non-unitary and destroys information.…

High Energy Physics - Theory · Physics 2011-07-11 Vijay Balasubramanian , Bartlomiej Czech

We provide a simple way for calculating the entropy of a Schwarzschild black hole from the entropy of its Hawking radiation. To this end, we show that if a thermodynamic system loses its energy only through the black body radiation, its…

General Relativity and Quantum Cosmology · Physics 2017-03-13 Sajad Aghapour , Kamal Hajian

Hawking's radiance, even as computed without account of backreaction, departs from blackbody form due to the mode dependence of the barrier penetration factor. Thus the radiation is not the maximal entropy radiation for given energy. By…

High Energy Physics - Theory · Physics 2009-10-22 Jacob D. Bekenstein

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here…

High Energy Physics - Theory · Physics 2015-06-12 Don N. Page

In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy $S^{BH}$ (defined by the response of the free energy of a system containing a black hole on the change…

High Energy Physics - Theory · Physics 2007-05-23 Valeri Frolov

The complete gravitational collapse of a body in general relativity will result in the formation of a black hole. Although the black hole is classically stable, quantum particle creation processes will result in the emission of Hawking…

High Energy Physics - Theory · Physics 2017-08-02 William G. Unruh , Robert M. Wald

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general,…

High Energy Physics - Theory · Physics 2009-11-11 Vijay Balasubramanian , Donald Marolf , Moshe Rozali

A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Steven Carlip