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Near-horizon chaos beyond Einstein gravity

Surajit Das,Surojit Dalui, Rickmoy Samanta

arxiv(2024)

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Abstract
We investigate chaos in the dynamics of outgoing massless particles near the horizon of static spherically symmetric (SSS) black holes in two well-motivated models of f(R) gravity. In both these models, we probe chaos in the particle trajectories (under suitable harmonic confinement) in the vicinity of the black hole horizons, for a set of initial conditions. The particle trajectories, associated Poincaré sections, and Lyapunov exponents clearly illustrate the role played by the black hole horizon in the growth of chaos within a specific energy range. We demonstrate how this energy range is controlled by the parameters of the modified gravity theory under consideration. The growth of chaos in such a classical setting is known to respect a surface gravity bound arising from universal aspects of particle dynamics close to the black hole horizon [K. Hashimoto and N. Tanahashi, Phys. Rev. D 95, 024007 (2017)], analogous to the quantum MSS bound [J. Maldacena, S.H. Shenker and D. Stanford, JHEP 08 (2016) 106]. Interestingly, both models studied in our work respect the bound, in contrast to some of the other models of f(R) gravity in the existing literature. The work serves as a motivation to use chaos as an additional tool to probe Einstein gravity in the strong gravity regime in the vicinity of black hole horizons.
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