Bounds for Lyapunov exponent of circular light orbits in black holes
Year: 2025
Type: article
Abstract: Chaotic systems near black holes satisfy a universal bound, $$\lambda \le \kappa _H$$ λ ≤ κ H linking the Lyapunov coefficient $$\lambda $$ λ associated with unstable orbits to surface gravity $$\kappa _H$$ 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.
Source: The European Physical Journal C
Authors: Emanuel Gallo, Thomas Mädler
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408424043