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 (17)

• Bubbling AdS space and 1/2 BPS geometries
• Giant Gravitons in Conformal Field Theory
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• A toy model for the AdS/CFT correspondence
• "Double-trace" Deformations, Boundary Conditions and Spacetime Singularities
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• The Library of Babel: On the origin of gravitational thermodynamics
• Fuzzballs with internal excitations
• Multiple-Trace Operators and Non-Local String Theories
• Superstars and Giant Gravitons
• Anatomy of bubbling solutions
• Non-local string theories on AdS_3 times S^3 and stable non-supersymmetric backgrounds
• Integrability vs. Information Loss: A Simple Example
• Singularities and closed time-like curves in type IIB 1/2 BPS geometries
• The Gravitational Description of Coarse Grained Microstates
• Stretched Horizon and Entropy of Superstars
• On the existence of supergravity duals to D1--D5 CFT states

Cited by in corpus (31)

• Understanding shape entropy through local dense packing
• Black Holes as Effective Geometries
• Anatomy of bubbling solutions
• Quantum Information in Holographic Duality
• New D1-D5-P geometries from string amplitudes
• Entropy of near-extremal black holes in AdS_5
• Quantitative approaches to information recovery from black holes
• From configuration to dynamics -- Emergence of Lorentz signature in classical field theory
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Chaotic Fast Scrambling At Black Holes
• Entanglement shadows in LLM geometries
• Emergent classical spacetime from microstates of an incipient black hole
• Typicality, Black Hole Microstates and Superconformal Field Theories
• Local bulk operators in AdS/CFT and the fate of the BTZ singularity
• The electrostatic view on M-theory LLM geometries
• Detecting topology change via correlations and entanglement from gauge/gravity correspondence
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Strings on Bubbling Geometries
• Coherent state excitations and string-added coherent states in gauge-gravity correspondence
• Small Black holes vs horizonless solutions in AdS
• Reconstructing spacetime from the hologram, even in the classical limit, requires physics beyond the Planck scale
• Non-geometric States in a Holographic Conformal Field Theory
• Correlations vs connectivity in R-charge
• Studies on 1/4 BPS and 1/8 BPS geometries
• Interior analysis, stretched technique and bubbling geometries
• Holographic entanglement entropy beyond coherent states
• Coarse-graining of bubbling geometries and the fuzzball conjecture
• Quantum curves as quantum distributions
• Coherent state superpositions, entanglement and gauge/gravity correspondence
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Entanglement and mixed states of Young tableau states in gauge/gravity correspondence