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We investigate the conjecture on the upper bound of the Lyapunov exponent forthe chaotic motion of a charged particle around a Kerr-Newman black hole. TheLyapunov exponent is closely associated with the maximum of the effectivepotential with respect to the particle. We show that when the angular momentaof the black hole and particle are considered, the Lyapunov exponent can exceedthe conjectured upper bound. This is because the angular momenta change theeffective potential and increase the magnitude of the chaotic behavior of theparticle. Furthermore, the location of the maximum is also related to the valueof the Lyapunov exponent and the extremal and non-extremal states of the blackhole.

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