On black hole thermalization, D0 brane dynamics, and emergent spacetime

TL;DR

This paper uses numerical simulations of D0 branes to investigate how black hole horizons influence the thermalization process and emergent spacetime, revealing rapid internal thermalization driven by non-linear dynamics independent of background fluctuations.

Contribution

It demonstrates that D0 branes thermalize quickly through internal non-linear dynamics and establishes scaling relations linking their properties to background fields and initial conditions.

Findings

D0 branes rapidly reach an incompressible thermalized state

Thermalization occurs independently of background fluctuations

Scaling relations connect D0 brane properties to initial energy and background fields

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.