Quantum geometry and gravitational entropy

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.

29 pages, 2 figures; references added

References in corpus (5)

• Fuzzballs with internal excitations
• Anatomy of bubbling solutions
• Integrability vs. Information Loss: A Simple Example
• The Gravitational Description of Coarse Grained Microstates
• On the existence of supergravity duals to D1--D5 CFT states

Cited by in corpus (7)

• Black Holes as Effective Geometries
• Anatomy of bubbling solutions
• Quantitative approaches to information recovery from black holes
• Local bulk operators in AdS/CFT and the fate of the BTZ singularity
• The electrostatic view on M-theory LLM geometries
• Studies on 1/4 BPS and 1/8 BPS geometries
• Coarse-graining of bubbling geometries and the fuzzball conjecture