The information paradox: a pedagogical introduction

By Samir D. Mathur. 2009

994 citations recorded by the source corpus.

The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a ‘theorem’: assuming ‘traditional’ physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking AdS/CFT duality. We conclude with recent results on the quantum physics of black holes which show that the interior of black holes have a ‘fuzzball’ structure. This nontrivial structure of microstates resolves the information paradox and gives a qualitative picture of how classical intuition can break down in black hole physics.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2e69d56dedc2c30f0867e60a3152dcb44d3126cb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Harlow
2. S. Raju
3. D. Stanford
4. R. Myers
5. J. Maldacena
6. L. Susskind
7. S. Shenker
8. J. Polchinski

In Nuclear and High Energy Physics

1. D. Harlow
2. S. Raju
3. D. Stanford
4. R. Myers
5. J. Maldacena
6. L. Susskind
7. S. Shenker
8. J. Polchinski

In Statistical and Nonlinear Physics

1. D. Harlow
2. S. Raju
3. D. Stanford
4. R. Myers
5. J. Maldacena
6. S. Shenker
7. Ahmed Almheiri
8. D. Marolf

Citations in the corpus

• The Holographic Nature of Null Infinity (2020, background): “lization, where information on dierent parts of a spacelike slice is distinct, and then travels along causal trajectories, this leads to a paradox. A closely related paradox, rst described by Mathur [44] and later popularized by AMPS [45], is the strong subadditivity paradox. Here, the early Hawking”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “Many people were reasonably satisfied with this state of affairs, but there were always some lingering doubts and in particular there was a sizeable contingent of people who were never convinced [6, 141, 142].”
• Quantum computation vs. firewalls (2013, background): “One way to see this more precisely, again following AMPS, who themselves were motivated by a similar argument due to Mathur [31], is to note that strong subadditivity requires”
• State-Dependent Bulk-Boundary Maps and Black Hole Complementarity (2013, background): “4), since this is the context in which the claim of [10] was formulated.”
• Black holes: complementarity or firewalls? (2012, methodology): “The arguments that we have given for the firewall are largely built on those that have been used to support the fuzzball picture [12], and one might wonder whether the fuzzball provides the actual dynamical picture of the firewall.”
• Habemus superstratum! A constructive proof of the existence of superstrata (2015, background): “See [30–45] for some developments in that area.”
• Entanglement islands in higher dimensions (2019, background): “As explained nicely in [25], the intuitive reason behind this is the stretching of space behind a black hole horizon [40, 41].”
• The Page curve of Hawking radiation from semiclassical geometry (2019, background): “The early growth of the boundary entropy is related to the growth of the entropy of the quantum fields inside the black hole, which is manifest using the nice slices picture of [10,11].”
• An apologia for firewalls (2013, methodology): “For example, it could instead take the form of the large tidal forces that would naively seem to be present in the so-called fuzzball solutions advocated in [4] to replace old black holes.”
• Time Dependence of Hawking Radiation Entropy (2013, background): “Interest in black hole information [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 6”
• Replica wormholes and the black hole interior (2019, background): “However, if the interior partner is secretly part of the early radiation, then the arguments of [28, 29] do not apply [30, 31, 32, 33, 34].”
• Remarks on the necessity and implications of state-dependence in the black hole interior (2015, background): “Recent work by Mathur [1], Almheiri et al. [2, 3] and then by Marolf and Polchinski [4] has sharpened the information paradox [5, 6] and highlighted some of the difficulties in analyzing questions about local bulk physics in the AdS/CFT correspondence.”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “This tension is colloquially known as the black hole information paradox [8].”
• Black Hole Remnants and the Information Loss Paradox (2014, neutral): “[See also the argument in [275]].”
• Comments on black holes I: the possibility of complementarity (2012, methodology): “But in [27] it was shown that this hope is false; the change in entanglement δSent, compared to the entanglement Sent of the leading-order Hawking process, is bounded by δSent Sent < 2ǫ .”
• An infalling observer in AdS/CFT (2012, background): “This is also the statement that we seem to find in the recent literature [2, 1, 41, 11].”