Classical Limit of Black Hole Quantum N-Portrait and BMS Symmetry

TL;DR

This paper explores the classical limit of black hole quantum states, linking the infinite-N entropy and Goldstone modes to BMS symmetries, and discusses implications for black hole information recovery.

Contribution

It connects the classical limit of black hole quantum portrait with BMS symmetry, providing a geometric interpretation of the quantum critical state of gravitons.

Findings

Infinite-N limit corresponds to classical BMS super-translations.

Black hole information recovery is only possible at finite N.

Classical limit involves broken BMS symmetry in black hole geometry.

Abstract

Black hole entropy, denoted by N, in (semi)classical limit is infinite. This scaling reveals a very important information about the qubit degrees of freedom that carry black hole entropy. Namely, the multiplicity of qubits scales as N, whereas their energy gap and their coupling as 1/N. Such a behavior is indeed exhibited by Bogoliubov-Goldstone degrees of freedom of a quantum-critical state of N soft gravitons (a condensate or a coherent state) describing the black hole quantum portrait. They can be viewed as the Goldstone modes of a broken symmetry acting on the graviton condensate. In this picture Minkowski space naturally emerges as a coherent state of infinite-N gravitons of infinite wavelength and it carries an infinite entropy. In this paper we ask what is the geometric meaning (if any) of the classical limit of this symmetry. We argue that the infinite-N limit of Bogoliubov-Goldstone modes of critical graviton condensate is described by recently-discussed classical BMS super-translations broken by the black hole geometry. However, the full black hole information can only be recovered for finite N, since the recovery time becomes infinite in classical limit in which N is infinite.