Periodic Reporting for period 2 - SPINBHMICRO (New Horizons for Holography)
Periodo di rendicontazione: 2024-05-02 al 2025-05-01
Black holes are elusive celestial objects: they are formed by collapse of heavy stars and are characterized by an event horizon that prevents us from seeing the atoms they are composed of. Black holes are thermodynamic ensembles, and they possess entropy proportional to the area of the event horizon: the latter is a precious clue in unravelling the degrees of freedom of quantum gravity, whose formulation is one of the outstanding problems in modern Theoretical Physics.
One of the main objectives of the project was the study of the spectrum of microstates of the rotating black holes. These investigations encompass cases where symmetry is enhanced (so-called “supersymmetric” configurations) and more realistic Kerr black holes, which exist in our universe. Due to lack of supersymmetry, the latter case requires the development of a new framework that renders the problem computationally tractable. One of the objectives of the proposal is making use of the horizon geometry, and a regulated near-extremal geometry, to tackle this problem. At the same time, another objective of the proposal is to investigate the deformation properties of black hole horizons, and the characteristics of horizons in spacetimes with positive cosmological constant (de Sitter black holes), relevant for cosmological scenarios.
These studies connect to recent results that found chaotic behavior near a black hole horizon, and aim at understanding what are the building blocks of spacetime, how they are organized and how they interact, providing a new window into the fundamental constituents of a theory of quantum gravity.
One of the main objectives of the project was the study of the spectrum of microstates of the rotating black holes. These investigations encompass cases where symmetry is enhanced (so-called “supersymmetric” configurations) and more realistic Kerr black holes, which exist in our universe. Due to lack of supersymmetry, the latter case requires the development of a new framework that renders the problem computationally tractable. One of the objectives of the proposal is making use of the horizon geometry, and a regulated near-extremal geometry, to tackle this problem. At the same time, another objective of the proposal is to investigate the deformation properties of black hole horizons, and the characteristics of horizons in spacetimes with positive cosmological constant (de Sitter black holes), relevant for cosmological scenarios.
These studies connect to recent results that found chaotic behavior near a black hole horizon, and aim at understanding what are the building blocks of spacetime, how they are organized and how they interact, providing a new window into the fundamental constituents of a theory of quantum gravity.
For supersymmetric setups the counting makes use of holography and known techniques such as localization. The presence of supersymmetry usually makes computations more tractable, for instance removing some unwanted divergencies. In the first part of the project we studied the thermodynamics in the BPS limit of AdS black holes, including the definition of a correct limiting procedure to reach extremality. We computed the density of near-BPS states by making use of an effective 2d theory that takes into accounts fluctuations close to extremality: we showed the presence of a gap between the BPS black holes and the lightest near-BPS ones. In addition, we have found a remarkable behaviour displayed by black holes in a particular M-theory truncation. Their spectrum is altered due to the presence of anomalies, and both the gap and index are reduced. Their density of states can be qualitatively reproduced by an SYK model with an odd number of fermions.
For more realistic Kerr black holes (such as the ones seen at the Event Horizon Telescope) we instead developed a strategy for regulating divergencies (due to so-called "zero-modes") in the gravitational path integral in the four-dimensional geometry near the black hole horizon. Our techniques make use of a near-extremal geometry, and render the path integral finite. We find that the quantum-corrected near-extremal entropy exhibits 3/2logT behavior, predicting a lifting of the ground state degeneracy for the extremal Kerr black hole, and the absence of a mass gap. We have corroborated these results via a computation of the quantum corrections that makes use of the full black hole geometry, by making use black hole quasinormal modes. This simple 3d computation confirmed the 3/2logT behaviour.
Further studies concern the physics of black holes in presence of positive cosmological constant (de Sitter black holes). These spacetimes are characterized by the presence of a cosmological horizon that bounds the black hole in size. Different extremal (zero-temperature) limits exist, and one of our goals was to study how these branches react to deformations from extremality, to investigate whether (and to which extent) the black hole response to a small temperature increase is universal. In this framework, we have computed response coefficients and mass gap, and we have identified a sector in the near-horizon theory that is responsible for the deviation from extremality and studied its dynamics. Subsequently, we focused on the quantum corrections to black hole entropy in presence of a positive cosmological constant, finding for instance that one of the limiting configurations (Nariai solution) is plagued with pathologies such as negative norm modes, and negative eigenvalue corrections. Further studies investigated the consequences of the addition of angular momentum on the horizon dynamics at small temperatures.
Lastly, we performed studies on the deformability properties of black hole horizons, constructing for instance new solutions of composite black holes (Black Saturns) that are useful playground for the study of the equilibrium conditions between black objects in spaces with cosmological constant and studied possible contributions to the index, also in light of newly found Grey Galaxies solutions.
The results of the research were disseminated through seminars and conferences in research institutions around the world. I have presented these results in workshops in Asia, USA and Europe and I have been the lecturer in PhD summer schools in the UK and in Brazil. Finally, I have organized two workshops in my field and I have taken part in a number of outreach events (i.e. a podcast for RadioAspen, and the INFN school laboratory initiative Lab2go) and initiatives aimed at raising awareness of gender issues in physics.
For more realistic Kerr black holes (such as the ones seen at the Event Horizon Telescope) we instead developed a strategy for regulating divergencies (due to so-called "zero-modes") in the gravitational path integral in the four-dimensional geometry near the black hole horizon. Our techniques make use of a near-extremal geometry, and render the path integral finite. We find that the quantum-corrected near-extremal entropy exhibits 3/2logT behavior, predicting a lifting of the ground state degeneracy for the extremal Kerr black hole, and the absence of a mass gap. We have corroborated these results via a computation of the quantum corrections that makes use of the full black hole geometry, by making use black hole quasinormal modes. This simple 3d computation confirmed the 3/2logT behaviour.
Further studies concern the physics of black holes in presence of positive cosmological constant (de Sitter black holes). These spacetimes are characterized by the presence of a cosmological horizon that bounds the black hole in size. Different extremal (zero-temperature) limits exist, and one of our goals was to study how these branches react to deformations from extremality, to investigate whether (and to which extent) the black hole response to a small temperature increase is universal. In this framework, we have computed response coefficients and mass gap, and we have identified a sector in the near-horizon theory that is responsible for the deviation from extremality and studied its dynamics. Subsequently, we focused on the quantum corrections to black hole entropy in presence of a positive cosmological constant, finding for instance that one of the limiting configurations (Nariai solution) is plagued with pathologies such as negative norm modes, and negative eigenvalue corrections. Further studies investigated the consequences of the addition of angular momentum on the horizon dynamics at small temperatures.
Lastly, we performed studies on the deformability properties of black hole horizons, constructing for instance new solutions of composite black holes (Black Saturns) that are useful playground for the study of the equilibrium conditions between black objects in spaces with cosmological constant and studied possible contributions to the index, also in light of newly found Grey Galaxies solutions.
The results of the research were disseminated through seminars and conferences in research institutions around the world. I have presented these results in workshops in Asia, USA and Europe and I have been the lecturer in PhD summer schools in the UK and in Brazil. Finally, I have organized two workshops in my field and I have taken part in a number of outreach events (i.e. a podcast for RadioAspen, and the INFN school laboratory initiative Lab2go) and initiatives aimed at raising awareness of gender issues in physics.
The results obtained so far contribute to defining the effective setup where to correctly define quantum corrections to black hole entropy in absence of supersymmetry. By making use of the gravitational path integral in the near horizon geometry we were able to quantify the contributions of these corrections and obtain insights on the spectrum of the black hole states. This can be seen as a stepping stone towards a complete calculation of the widths of the microstates for the Kerr black hole,
which likely requires connecting the horizon geometry to asymptotically flat space. The latter will allow us to quantify the effect of energy extraction via superradiance and obtain the full density of resonances in the complex plane.
Black holes in spacetimes with positive cosmological constant (de Sitter ones) are of phenomenological interest since our universe is expanding, but are much less studied with respect to their Anti-de Sitter counterpart, due to the fact that a holography for de Sitter spaces is not as well developed. In a broad sense, our results make also allow new steps in this direction. At the same time, our effective two-dimensional dilaton-gravity framework allows to probe universal aspects of physics near extremality, answering crucial questions on how the dynamics close to the horizon is influenced by the environment in which the black hole lives.
which likely requires connecting the horizon geometry to asymptotically flat space. The latter will allow us to quantify the effect of energy extraction via superradiance and obtain the full density of resonances in the complex plane.
Black holes in spacetimes with positive cosmological constant (de Sitter ones) are of phenomenological interest since our universe is expanding, but are much less studied with respect to their Anti-de Sitter counterpart, due to the fact that a holography for de Sitter spaces is not as well developed. In a broad sense, our results make also allow new steps in this direction. At the same time, our effective two-dimensional dilaton-gravity framework allows to probe universal aspects of physics near extremality, answering crucial questions on how the dynamics close to the horizon is influenced by the environment in which the black hole lives.