  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.
