2007/05/31 by Vijay Balasubramanian, Bartłomiej Czech, Bartlomiej Czech +4 · 50 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Geometry #Hilbert space #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #hep-th
paper · pdf · doi:10.1088/1126-6708/2007/12/067
published in Journal of High Energy Physics 2007(12), 067 (Springer Nature) · 29 pages, 2 figures; references added
openalex publication_date 2007/12/19 · arxiv created 2009/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 AdS5 x S5 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.