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.

我们一般性地证明，非极端黑洞事件视界附近的探测粒子的动力学是由快子有效作用来描述的。作用中的哈格多恩温度始终等于背景黑洞的霍金温度。这一事实表明，落入的粒子应该完全衰变成接近事件视界的引力子或闭合弦。黑洞中由于吸收粒子而增加的面积应解释为粒子衰变成的闭合弦的简并态的熵。根据事件视界上落入粒子和发射的闭合弦之间的能量匹配条件，我们检查了这种变分面积熵关系，并发现如果不稳定 D0 膜的闭合弦发射过程遵循第一个，那么它在所有情况下都匹配法律。