Near-horizon chaos beyond Einstein gravity
arxiv(2024)
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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