Bound on the Lyapunov exponent in Kerr-Newman black holes via a charged particle

TL;DR

This paper examines the bounds of chaos in charged particle motion around Kerr-Newman black holes, revealing that angular momentum can cause the Lyapunov exponent to surpass previously conjectured limits.

Contribution

It demonstrates that considering angular momentum in Kerr-Newman black holes allows the Lyapunov exponent to exceed the established upper bound, challenging prior conjectures.

Findings

Lyapunov exponent can surpass the conjectured upper bound when angular momentum is included.

The maximum of the effective potential determines the Lyapunov exponent.

The extremal state of the black hole influences the location of the potential maximum.

Abstract

We investigate the conjecture on the upper bound of the Lyapunov exponent for the chaotic motion of a charged particle around a Kerr-Newman black hole. The Lyapunov exponent is closely associated with the maximum of the effective potential with respect to the particle. We show that when the angular momenta of the black hole and particle are considered, the Lyapunov exponent can exceed the conjectured upper bound. This is because the angular momenta change the effective potential and increase the magnitude of the chaotic behavior of the particle. Furthermore, the location of the maximum is also related to the value of the Lyapunov exponent and the extremal and non-extremal states of the black hole.