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arXiv · 2412.10328

Bounds for Lyapunov exponent of circular light orbits in black holes

Emanuel Gallo·Thomas Mädler
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Abstract

Chaotic systems near black holes satisfy a universal bound, $λ\leq κ_H$ linking the Lyapunov coefficient $λ$ associated with unstable orbits to surface gravity $κ_H$ of the event horizon. A natural question is whether this bound is satisfied by unstable circular null geodesics in the vicinity of black holes. However, there are known cases where this bound is violated. It is intriguing to ask whether there exists an alternative universal bound that is valid in such situations. We show that for any spherically symmetric, static black hole that satisfies Einstein's equations and the dominant energy condition, there exist other universal bounds relating the Lyapunov coefficient to a generalized notion of surface gravity at the photon sphere. As applications, we show how these bounds also constrain the imaginary part of quasinormal modes in the eikonal regime and how the Lyapunov coefficient relates to the shadow size and the entropy of the horizon.

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Emanuel Gallo, Thomas Mädler. 2025-03-10. Bounds for Lyapunov exponent of circular light orbits in black holes. https://doi.org/10.1140/epjc%2Fs10052-025-14046-8

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