Quantum geometry and gravitational entropy

TL;DR

This paper explores the conditions under which quantum states in the AdS/CFT framework can be described by classical geometries, linking geometric singularities to entropy and identifying the most entropic spacetimes.

Contribution

It introduces a coarse-grained metric operator in the half-BPS sector, connecting geometric singularities with entropy and characterizing when classical geometry descriptions are valid.

Findings

Half-BPS universes have non-zero entropy if and only if the metric is singular.

Entropy arises from coarse-graining the geometry.

The most entropic spacetimes are identified for fixed asymptotic moments.

Abstract

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.