Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole

TL;DR

This paper examines the Lyapunov bound for charged particles in Kerr-Newman-AdS black holes, revealing conditions under which the chaos bound is violated, especially in extremal and rotating black holes.

Contribution

It demonstrates that the chaos bound can be violated in Kerr-Newman-AdS black holes when angular momentum is present, particularly in extremal cases, challenging previous conjectures.

Findings

Negative cosmological constant reduces chaos

Bound more effective in AdS spacetime

Bound violation occurs with black hole rotation and extremality

Abstract

We investigate the conjectured bound on the Lyapunov exponent for a charged particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov exponent is calculated based on the effective Lagrangian. We show that the negative cosmological constant reduces the chaotic behavior of the particle, namely, it decreases the Lyapunov exponent. Hence, the bound is more effective in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the bound can be violated when the angular momenta of the black hole are turned on. Moreover, we show that in an extremal black hole, the bound is more easily violated compared to the nonextremal black hole.