### Abstract

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 λ≤2πTBH/ which is identical to the bound recently discovered by Maldacena, Shenker, and Stanford.

Original language | English |
---|---|

Article number | 024007 |

Journal | Physical Review D |

Volume | 95 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 4 2017 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*95*(2), [024007]. https://doi.org/10.1103/PhysRevD.95.024007

**Universality in chaos of particle motion near black hole horizon.** / Hashimoto, Koji; Tanahashi, Norihiro.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 95, no. 2, 024007. https://doi.org/10.1103/PhysRevD.95.024007

}

TY - JOUR

T1 - Universality in chaos of particle motion near black hole horizon

AU - Hashimoto, Koji

AU - Tanahashi, Norihiro

PY - 2017/1/4

Y1 - 2017/1/4

N2 - 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 λ≤2πTBH/ which is identical to the bound recently discovered by Maldacena, Shenker, and Stanford.

AB - 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 λ≤2πTBH/ which is identical to the bound recently discovered by Maldacena, Shenker, and Stanford.

UR - http://www.scopus.com/inward/record.url?scp=85015040104&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015040104&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.95.024007

DO - 10.1103/PhysRevD.95.024007

M3 - Article

AN - SCOPUS:85015040104

VL - 95

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 2

M1 - 024007

ER -