Black hole thermalization, D0 brane dynamics, and emergent spacetime

Abstract

When matter falls past the horizon of a large black hole, the expectation from string theory is that the configuration thermalizes and the information in the probe is rather quickly scrambled away. The traditional view of a classical unique spacetime near a black hole horizon conflicts with this picture. The question then arises as to what spacetime does the probe actually see as it crosses a horizon, and how does the background geometry imprint its signature onto the thermal properties of the probe. In this work, we explore these questions through an extensive series of numerical simulations of D0 branes. We determine that the D0 branes quickly settle into an incompressible symmetric state -thermalized within a few oscillations through a process driven entirely by internal non-linear dynamics. Surprisingly, thermal background fluctuations play no role in this mechanism. Signatures of the background fields in this thermal state arise either through fluxes, i.e. black hole hair; or if the probe expands to the size of the horizon -which we see evidence of. We determine simple scaling relations for the D0 branes' equilibrium size, time to thermalize, lifetime, and temperature in terms of their number, initial energy, and the background fields. Our results are consistent with the conjecture that black holes are the fastest scramblers as seen by Matrix theory.

Scrambling with matrix black holes

“…5 A similar situation was numerically analyzed in Matrix theory in Ref. [20] where both probe and bath resided in the bosonic sector of On the left, we have the nearest-neighbor case; in the middle and the right, the Matrix or BMN case. In the graphs on the left and in the middle, black denotes a link between corresponding qubits, while white denotes no link.…”

“…The latter is a Lagrange multiplier whose equations of motion immediately yield the N 2 Gauss-law constraints, X j;m X j 0 ;m 0 f jm;j 0 m 0 ;j 00 m 00 c j m c j 0 m 0 ¼ 0; (20) with the conventional gauge choice a j m ¼ 0 (corresponding to A ¼ 0). Tracing over the matrix structure entirely, the Hamiltonian splits into several pieces which we write as…”

“…In that work, it was found that the scrambling time scale-to the crude extent scrambling could be defined classicallyscaled as 1=T, with no dependence on the entropy. Reference [20] proposed that this was a pathology of the classical treatment, and that a quantum-mechanical analysis is probably needed to reveal the ln S=T dependence, if present.…”

“…Other attempts of understanding scrambling dynamics in Matrix and Matrix-like theories can be found in Refs. [17][18][19][20].…”

Warm p -soup and near extremal black holes

“…However, this was not understood in terms of elementary branes, but from a gauge theory per-1 These theories have also been explored in a high temperature regime using numerical methods [16][17][18][19], where the theory is not dual to black holes, but qualitatively similar behaviour has been observed. The issue of the IR instability was analytically studied in the high temperature regime [20,21].…”