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arXiv · 1812.05020

Emergent geometry from stochastic dynamics, or Hawking evaporation in M(atrix) theory

Haoxing Du·Vatche Sahakian
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Abstract

We develop an microscopic model of the M-theory Schwarzschild black hole using the Banks-Fischler-Shenker-Susskind Matrix formulation of quantum gravity. The underlying dynamics is known to be chaotic, which allows us to use methods from Random Matrix Theory and non-equilibrium statistical mechanics to propose a coarse-grained bottom-up picture of the event horizon -- and the associated Hawking evaporation phenomenon. The analysis is possible due to a hierarchy between the various timescales at work. Event horizon physics is found to be non-local at the Planck scale, and we demonstrate how non-unitary physics and information loss arise from the process of averaging over the chaotic unitary dynamics. Most interestingly, we correlate the onset of non-unitarity with the emergence of spacetime geometry outside the horizon. We also write a mean field action for the evolution of qubits -- represented by polarization states of supergravity modes. This evolution is shown to have similarities to a recent toy model of black hole evaporation proposed by Osuga and Page -- a model aimed at developing a plausible no-firewall scenario.

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Haoxing Du, Vatche Sahakian. 2019-02-12. Emergent geometry from stochastic dynamics, or Hawking evaporation in M(atrix) theory. https://doi.org/10.1007/jhep03(2019)061

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