  We show generically that the dynamics of a probe particle near the event
horizon of a non-extreme black hole is described by the tachyon effective
action. The Hagedorn temperature in the action is always equal to the Hawking
temperature of the background black hole. The fact suggests that the infalling
particle should decay completely into gravitons or closed strings approaching
the event horizon. The increased area in the black hole due to absorption of a
particle should be interpreted as the entropy of degenerate states of the
closed strings that the particle decays into. With the energy match condition
between the infalling particle and the emitted closed strings on the event
horizon, we examine this variational area-entropy relation and find that it
matches in all cases if the closed string emission process from an unstable
D0-brane obeys the first law.
