Extremal black holes, Holography & Coarse graining

TL;DR

This work investigates how gravitational thermodynamics arises from quantum information coarse graining and holography, illustrating the mechanism with half-BPS states in N=4 SYM and their LLM gravity duals to explain spacetime emergence, entropy, and singularities. It then develops extremal black hole microscopics, proposing a four-constituent non-BPS model in STU gravity and a Kerr/CFT/AdS3/CFT2 perspective that accounts for microscopic entropy via CFT central charges and near-horizon symmetries. The review also discusses the holographic encoding of non-local gravity features on holographic screens, arguing for approximate CFT descriptions near horizons and exploring local thermodynamics through Jacobson-like arguments and Verlinde’s entropic gravity. Collectively, the papers’ approaches link black hole thermodynamics, information coarse graining, and holography to a broader framework in which spacetime and gravitational dynamics emerge from underlying quantum information structures. The insights have potential implications for the information paradox, the emergence of spacetime, and the universality of entropy across gravitational horizons, including extensions to non-extremal and cosmological settings.

Abstract

I review some of the concepts at the crossroads of gravitational thermodynamics, holography and quantum mechanics. First, the origin of gravitational thermodynamics due to coarse graining of quantum information is exemplified using the half-BPS sector of ${\cal N}=4$ SYM and its LLM description in type IIB supergravity. The notion of black holes as effective geometries, its relation to the fuzzball programme and some of the puzzles raising for large black holes are discussed. Second, I review recent progress for extremal black holes, both microscopically, discussing a constituent model for stationary extremal non-bps black holes, and semiclassically, discussing the extremal black hole/CFT conjecture. The latter is examined from the AdS${}_3$/CFT${}_2$ perspective. Third, I review the importance of the holographic principle to encode non-local gravity features allowing us to relate the gravitational physics of local observers with thermodynamics and the role causality plays in these arguments by identifying horizons (screens) as diathermic walls. I speculate with the emergence of an approximate CFT in the deep IR close to any horizon and its relation with an effective dynamical description of the degrees of freedom living on these holographic screens.

Figures (6)

• Figure 1: Set of concepts and relations discussed in these notes.
• Figure 2: From black holes to statistical mechanics & CFT and back using fuzzball ideas.
• Figure 3: From pure states, to typical states and their coarse grained phase space density description providing a gravity boundary condition.
• Figure 4: RG-transformation in phase space giving rise to entropy.
• Figure 5: Relation between different local AdS${}_3$ geometries, their near horizon limits and their dual interpretations.