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Recent Progress on the Black Hole Information Paradox

Jørstad, Eivind Hilmen LU (2021) FYTM04 20211
Theoretical Particle Physics
Department of Astronomy and Theoretical Physics
Abstract
The black hole information paradox is of central importance in the study of quantum gravity. The paradox states that quantum fields surrounding a black hole behave in ways that run into conflict with the unitarity of quantum mechanical time evolution. In the course of the past two years, new theoretical discoveries have made progress towards the paradox’s resolution, suggesting that unitarity can be saved. The central result is that a generalized entanglement entropy, originally arising in the anti-de Sitter/conformal field theory correspondence, gives entanglement dynamics for the quantum fields that is consistent with unitarity. In this thesis, we review the black hole information paradox and the recent results. In addition, we explore a... (More)
The black hole information paradox is of central importance in the study of quantum gravity. The paradox states that quantum fields surrounding a black hole behave in ways that run into conflict with the unitarity of quantum mechanical time evolution. In the course of the past two years, new theoretical discoveries have made progress towards the paradox’s resolution, suggesting that unitarity can be saved. The central result is that a generalized entanglement entropy, originally arising in the anti-de Sitter/conformal field theory correspondence, gives entanglement dynamics for the quantum fields that is consistent with unitarity. In this thesis, we review the black hole information paradox and the recent results. In addition, we explore a puzzling feature of the generalized entropy and show a novel result regarding the entanglement entropy in the interior of an evaporating black hole in the Russo-Susskind-Thorlacius model. We also apply an approximation scheme from condensed matter physics in a novel way, using a quasiparticle description to compute entanglement entropy in a moving-mirror model of black hole evaporation. (Less)
Popular Abstract
Black holes are arguably the most extreme objects in the universe. The strength of their gravitational attraction is such that if you get too close and here “you” can refer to anything from a human in a spaceship to a single particle of light – you will be pulled in towards its center without any possibility of escape. Due to the intensity of these gravitational forces, physicists have often wondered whether one can make sense of quantum mechanics – our best description physics at very small length-scales – in the presence of black holes. In other words, one can ask: how does quantum mechanical matter behave around black holes, and can a black hole itself be considered a quantum system?

In 1975, the physicist Stephen Hawking published a... (More)
Black holes are arguably the most extreme objects in the universe. The strength of their gravitational attraction is such that if you get too close and here “you” can refer to anything from a human in a spaceship to a single particle of light – you will be pulled in towards its center without any possibility of escape. Due to the intensity of these gravitational forces, physicists have often wondered whether one can make sense of quantum mechanics – our best description physics at very small length-scales – in the presence of black holes. In other words, one can ask: how does quantum mechanical matter behave around black holes, and can a black hole itself be considered a quantum system?

In 1975, the physicist Stephen Hawking published a now famous calculation, in which he looked at quantum mechanical matter near the surface of a black hole, called its event horizon. What he found is that the black hole should not be completely black; quantum effects will produce a small amount of radiation which causes the black hole to evaporate. It was soon realized that this has significant consequences. In particular, Hawking noted that if the black hole evaporates away completely then quantum mechanics appears to be violated. In other words, the evolution process that starts with a black hole and ends with only a cloud of radiation is not allowed by the equations of quantum mechanics. This apparent contradiction was named the black hole information paradox.

Almost 20 years later, in 1993, the information paradox was sharpened by Don Page, who realized that black hole evaporation leads to trouble even before the black hole evaporates away completely. The issue has to do with quantum entanglement, a curious feature of quantum mechanics in which properties of quantum systems can be correlated even though the systems are located far apart from each other. In particular, throughout the evaporation process the amount of entanglement between the black hole and the radiation increases steadily, while at the same time the black hole’s capacity for entanglement decreases due to energy loss in the form of radiation. The conflict arises around the so-called Page time, where the radiation appears to grow more entangled with the black hole than what should be possible according to quantum mechanics.

Finally, in 2019 it was discovered that Page’s issue might be avoided in a surprising manner. A new method for computing the entropy of the black hole was conjectured based on a deep connection between gravity and certain quantum theories, and the resulting entropy narrowly avoids Page’s paradox. Moreover, it does so by showing the exact behaviour Page predicted for quantum mechanical black holes. In this thesis we review these recent developments, and discuss a puzzling result of the conjectured entropy formula. In addition, we show that a certain useful approximation scheme known from condensed matter physics can be applied to a class of models describing black hole evaporation. (Less)
Please use this url to cite or link to this publication:
author
Jørstad, Eivind Hilmen LU
supervisor
organization
course
FYTM04 20211
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Black Holes, Hawking Radiation, Entanglement Entropy, Black Hole Information Paradox, Dilaton Gravity, Quasiparticles
report number
LU-TP 21-29
language
English
id
9060679
date added to LUP
2021-08-03 14:38:30
date last changed
2022-06-28 11:56:52
@misc{9060679,
  abstract     = {{The black hole information paradox is of central importance in the study of quantum gravity. The paradox states that quantum fields surrounding a black hole behave in ways that run into conflict with the unitarity of quantum mechanical time evolution. In the course of the past two years, new theoretical discoveries have made progress towards the paradox’s resolution, suggesting that unitarity can be saved. The central result is that a generalized entanglement entropy, originally arising in the anti-de Sitter/conformal field theory correspondence, gives entanglement dynamics for the quantum fields that is consistent with unitarity. In this thesis, we review the black hole information paradox and the recent results. In addition, we explore a puzzling feature of the generalized entropy and show a novel result regarding the entanglement entropy in the interior of an evaporating black hole in the Russo-Susskind-Thorlacius model. We also apply an approximation scheme from condensed matter physics in a novel way, using a quasiparticle description to compute entanglement entropy in a moving-mirror model of black hole evaporation.}},
  author       = {{Jørstad, Eivind Hilmen}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Recent Progress on the Black Hole Information Paradox}},
  year         = {{2021}},
}