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 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.
Highlights
Black hole entropy, denoted by N, inclassical limit is infinite
The multiplicity of qubits scales as N, whereas their energy gap and their coupling as 1/N. Such a behavior is exhibited by Bogoliubov–Goldstone degrees of freedom of a quantum-critical state of N soft gravitons describing the black hole quantum portrait. They can be viewed as the Goldstone modes of a broken symmetry acting on the graviton condensate
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
Summary
It has been appreciated that Goldstone interpretation of these modes, with the number of broken generators as well as the spontaneous breaking order parameter scaling as N, automatically accounts for the right 1/N scaling behavior both of the energy gap as well as of the coupling of Goldstone-qubits This picture naturally accounts for various timescales of information-processing, such as, gener√ating chaos and scrambling information within the time tscr ∼ N L P ln(N) [8], as well as, generating large entanglement at the quantum critical point [4,5,6,7]. Black hole hair manifests itself in 1/N-corrections to the probe particle scattering at the critical graviton condensate [9] These corrections measure the 1/N quantum deviation from the classical metric motion. In order to answer this question, we shall first make the connection to the limiting case of Minkowski space, describing it as a coherent state of gravitons
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