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

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.

New relation between entanglement and geometry from M(atrix) theory

“…we may not assume that the background is on shell as we have done so. If object 1 were to be a black hole, we expect that the chaotic nature of Matrix theory admits a metastable spherical configuration that is long-lived as it evaporates away slowly via Hawking radiation [4]. It has been shown that this stochastic short timescale dynamics can be effectively modeled by adding by hand a quadratic mass term to the action.…”

“…(49) 4 One can also consider the probe to be a graviton. As a result, α 2 → 0 and we must keep the ε 2 2 term from (38).…”