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Journal of High Energy Physics

, 2019:197 | Cite as

Emergent classical spacetime from microstates of an incipient black hole

  • Vijay Balasubramanian
  • David Berenstein
  • Aitor Lewkowycz
  • Alexandra Miller
  • Onkar ParrikarEmail author
  • Charles Rabideau
Open Access
Regular Article - Theoretical Physics
  • 20 Downloads

Abstract

Black holes have an enormous underlying space of microstates, but universal macroscopic physics characterized by mass, charge and angular momentum as well as a causally disconnected interior. This leads to two related puzzles: (1) How does the effective factorization of interior and exterior degrees of freedom emerge in gravity?, and (2) How does the underlying degeneracy of states wind up having a geometric realization in the horizon area and in properties of the singularity? We explore these puzzles in the context of an incipient black hole in the AdS/CFT correspondence, the microstates of which are dual to half-BPS states of the \( \mathcal{N} \) = 4 super-Yang-Mills theory. First, we construct a code subspace for this black hole and show how to organize it as a tensor product of a universal macroscopic piece (describing the exterior), and a factor corresponding to the microscopic degrees of freedom (describing the interior). We then study the classical phase space and symplectic form for low-energy excitations around the black hole. On the AdS side, we find that the symplectic form has a new physical degree of freedom at the stretched horizon of the black hole, reminiscent of soft hair, which is absent in the microstates. We explicitly show how such a soft mode emerges from the microscopic phase space in the dual CFT via a canonical transformation and how it encodes partial information about the microscopic degrees of freedom of the black hole.

Keywords

AdS-CFT Correspondence Black Holes in String Theory Spacetime Singularities 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© SISSA, Trieste, Italy 2019

Authors and Affiliations

  • Vijay Balasubramanian
    • 1
    • 2
  • David Berenstein
    • 3
  • Aitor Lewkowycz
    • 4
  • Alexandra Miller
    • 5
  • Onkar Parrikar
    • 1
    Email author
  • Charles Rabideau
    • 1
    • 2
  1. 1.David Rittenhouse LaboratoryUniversity of PennsylvaniaPhiladelphiaU.S.A.
  2. 2.Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay InstitutesBrusselsBelgium
  3. 3.Department of PhysicsUniversity of California at Santa BarbaraSanta BarbaraU.S.A.
  4. 4.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordU.S.A.
  5. 5.Department of PhysicsWellesley CollegeWellesleyU.S.A.

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