## Periodic Reporting for period 2 - QBH Structure (The Quantum Structure of Black Holes and the Recovery of Information)

Reporting period: 2020-07-01 to 2021-12-31

This project addresses a foundational issue about black holes and what happens to the matter that falls into them. Conventional combinations of general relativity and quantum mechanics lead to a fundamental conflict that is best characterized through the information paradox: Hawking showed that quantum black holes will ultimately radiate away all their mass, or evaporate, into largely featureless thermal radiation. This radiation is independent of how the black hole formed and so it is impossible to use it to reconstruct the initial state of the matter that made the black hole. Such a loss of information about the initial state is fundamentally incompatible with the precepts of quantum mechanics.

This project is using string theory and higher dimensional theories of gravity, to reveal the quantum properties of black holes through the construction and analysis of “microstate geometries.” This research focusses on the construction of such geometries and the dynamics of matter falling into them and will determine the extent to which they replicate the observed properties of black holes without producing an information paradox. This work involves computing how matter is reprocessed through microstate geometries and how such geometries describe the microstructure that must emerge at the event horizons of black holes. By exploring the similarities and differences in the predictions coming from black holes and microstate geometries, the project will explore potential macroscopic, measurable signatures of the horizon-scale microstructure.

Since quantum mechanics and general relativity are essential to the technological functioning of modern society (through things like microprocessors and global positioning systems), it is essential to resolve conflicts between these two extremely important theories of Nature. By resolving the conflict, we will also learn much about behaviour of black holes, the quantum properties of matter near black holes, and perhaps even the quantum structure of space and time.

This project is using string theory and higher dimensional theories of gravity, to reveal the quantum properties of black holes through the construction and analysis of “microstate geometries.” This research focusses on the construction of such geometries and the dynamics of matter falling into them and will determine the extent to which they replicate the observed properties of black holes without producing an information paradox. This work involves computing how matter is reprocessed through microstate geometries and how such geometries describe the microstructure that must emerge at the event horizons of black holes. By exploring the similarities and differences in the predictions coming from black holes and microstate geometries, the project will explore potential macroscopic, measurable signatures of the horizon-scale microstructure.

Since quantum mechanics and general relativity are essential to the technological functioning of modern society (through things like microprocessors and global positioning systems), it is essential to resolve conflicts between these two extremely important theories of Nature. By resolving the conflict, we will also learn much about behaviour of black holes, the quantum properties of matter near black holes, and perhaps even the quantum structure of space and time.

The project has progressed extremely well, resulting in 44 publications: of which 29 have already appeared in refereed journals, another 14 are yet to be submitted and there are two sets of lecture notes.

We have also organized, and held, four Conferences/Workshops that led to new and deeper insights:

Black-Hole Microstructure Workshop – May 27-31, 2019

Black-Hole Microstructure Conference I - June 8-12, 2020 (23 speakers, 285 participants)

Black-Hole Microstructure Conference II - December 9-11, 2020 (17 speakers, 120 participants)

Black-Hole Microstructure Conference III - June 7-11, 2021 (20 speakers, 259 participants)

Warner has also organized three training programs/lecture courses for students, post-docs and researchers

Lectures on Microstate Geometries [Publication 21]: 4 x 2 = 8 hours of lectures with recordings and lecture notes. Given by Warner in May 2019

Lectures on Superstrata Construction 4 x 2 = 8 hours of lectures with recordings and lecture notes. Given by Warner in October/November 2020

Virtual Workshop on Black-Hole Information conducted by Samir Mathur, 5 x 2 = 10 hours of lectures and discussions; May, 2021

In addition, Warner, Bena, Minasian and some of the postdocs have, together, given many plenary conference talks. Bena, Mayerson and Warner attended, and have given talks at several meetings with members of the LIGO and LISA collaborations. The goal was to continue a dialogue about possible observable signatures of microstate structure. This objective has been further advanced in several publications.

There have been substantial advances in the several of the primary objectives in the original proposal. Highlights include:

1) The construction of by far the largest, most general class of supersymmetric microstate geometries ever achieved and the matching of these geometries to precise microstructure of black-hole states.

2) Establishing how microstate geometries replicate black hole behavior without information loss: how infalling matter undergoes thermal decay and is incorporated, or “scrambled,” into microstate geometries; how trapped matter can tunnel out of microstate geometries.

3) A huge reduction in the complexity of the construction of new families of far more generic, non-supersymmetric microstate geometries leading to a breakthrough paper [Publication 44] that pioneers the systematic construction of non-extremal microstate geometries. These geometries are expected to have properties that more closely replicate the behavior of astrophysical black holes, and these geometries, when embedded into flat space should exhibit Hawking radiation.

Prior to my team’s work in the last year, it seemed that the construction of such generic microstate geometries would be out of reach of even the most advanced numerical algorithms and supercomputers. Our work has developed a much simpler route to achieving this important goal for a simple class of microstate geometries. The next phase of the project will expand upon this success and use our newly-developed techniques to complete some the major objectives of the project.

4) Finding and computing new, potentially-measurable signatures, or multipole moments, that characterize different classes of horizon-scale black-hole microstructure.

We have also organized, and held, four Conferences/Workshops that led to new and deeper insights:

Black-Hole Microstructure Workshop – May 27-31, 2019

Black-Hole Microstructure Conference I - June 8-12, 2020 (23 speakers, 285 participants)

Black-Hole Microstructure Conference II - December 9-11, 2020 (17 speakers, 120 participants)

Black-Hole Microstructure Conference III - June 7-11, 2021 (20 speakers, 259 participants)

Warner has also organized three training programs/lecture courses for students, post-docs and researchers

Lectures on Microstate Geometries [Publication 21]: 4 x 2 = 8 hours of lectures with recordings and lecture notes. Given by Warner in May 2019

Lectures on Superstrata Construction 4 x 2 = 8 hours of lectures with recordings and lecture notes. Given by Warner in October/November 2020

Virtual Workshop on Black-Hole Information conducted by Samir Mathur, 5 x 2 = 10 hours of lectures and discussions; May, 2021

In addition, Warner, Bena, Minasian and some of the postdocs have, together, given many plenary conference talks. Bena, Mayerson and Warner attended, and have given talks at several meetings with members of the LIGO and LISA collaborations. The goal was to continue a dialogue about possible observable signatures of microstate structure. This objective has been further advanced in several publications.

There have been substantial advances in the several of the primary objectives in the original proposal. Highlights include:

1) The construction of by far the largest, most general class of supersymmetric microstate geometries ever achieved and the matching of these geometries to precise microstructure of black-hole states.

2) Establishing how microstate geometries replicate black hole behavior without information loss: how infalling matter undergoes thermal decay and is incorporated, or “scrambled,” into microstate geometries; how trapped matter can tunnel out of microstate geometries.

3) A huge reduction in the complexity of the construction of new families of far more generic, non-supersymmetric microstate geometries leading to a breakthrough paper [Publication 44] that pioneers the systematic construction of non-extremal microstate geometries. These geometries are expected to have properties that more closely replicate the behavior of astrophysical black holes, and these geometries, when embedded into flat space should exhibit Hawking radiation.

Prior to my team’s work in the last year, it seemed that the construction of such generic microstate geometries would be out of reach of even the most advanced numerical algorithms and supercomputers. Our work has developed a much simpler route to achieving this important goal for a simple class of microstate geometries. The next phase of the project will expand upon this success and use our newly-developed techniques to complete some the major objectives of the project.

4) Finding and computing new, potentially-measurable signatures, or multipole moments, that characterize different classes of horizon-scale black-hole microstructure.

This is partially covered by the highlights above, and particularly by the advances we have made towards the construction of far more generic, non-supersymmetric, non-extremal microstate geometries.

In the next phase of the project we anticipate

1) The construction of broader classes non-trivial, non-supersymmetric microstate geometries corresponding to black holes. These are expected to exhibit many of the features of Hawking radiation from black holes but without an information paradox.

2) The probing and analysis of the non-supersymmetric microstate geometries, determining how they trap and scramble matter, and how these geometries decay via some form of Hawking radiation.

3) Additional progress on the other objectives of the project, especially on new horizon-scale physics

4) Constructing the holographic duals of geometric processes, building on the dual field theory understanding of tidal forces.

In the next phase of the project we anticipate

1) The construction of broader classes non-trivial, non-supersymmetric microstate geometries corresponding to black holes. These are expected to exhibit many of the features of Hawking radiation from black holes but without an information paradox.

2) The probing and analysis of the non-supersymmetric microstate geometries, determining how they trap and scramble matter, and how these geometries decay via some form of Hawking radiation.

3) Additional progress on the other objectives of the project, especially on new horizon-scale physics

4) Constructing the holographic duals of geometric processes, building on the dual field theory understanding of tidal forces.