Universality in chaos of particle motion near black hole horizon

The motion of a particle near a horizon of a spherically symmetric static black hole is shown to possess a universal Lyapunov exponent of chaos bounded by its surface gravity. To probe the horizon, we introduce an electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be to the surface gravity of the black hole. This value is independent of the external forces, the particle mass and background geometry, and in this sense this Lyapunov exponent is universal. Unless there are other sources of chaos, the Lyapunov exponent is subject to an inequality $\ensuremath{\lambda}\ensuremath{\le}2\ensuremath{\pi}{T}_{\mathrm{BH}}/\ensuremath{\hbar}$, which is identical to the bound recently discovered by Maldacena, Shenker, and Stanford.

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