Black Holes, AdS, and CFTs

TL;DR

This paper explains how the AdS/CFT correspondence relates black hole entropy to boundary observables, suggesting it counts either all or only distinguishable states outside the black hole, offering insights accessible to relativists.

Contribution

It provides an accessible interpretation of AdS/CFT implications for black hole entropy, emphasizing the role of boundary observables and superselection sectors.

Findings

S_{BH} as density of boundary states

Different interpretations of what black hole entropy counts

Connection between boundary observables and interior states

Abstract

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein-Hawking entropy S_{BH} is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly, while there is a valid context in which this result can be restated as "S_{BH} counts all states inside the black hole," there may also be another in which it may be restated as "$S_{BH}$ does not count all states inside the black hole, but only those that are distinguishable from the outside." The arguments and conclusions represent the author's translation of the community's collective wisdom, combined with a few recent results. For the proceedings of the WE-Heraeus-Seminar: Quantum Gravity: Challenges and Perspectives, dedicated to the memory of John A. Wheeler.