Bound on Lyapunov exponents with spinning particles in Kerr–Newman spacetimes

Abstract

In this work, we investigate the Lyapunov exponents associated with the chaotic dynamics of spinning charged particles in the Kerr–Newman spacetime, focusing on whether these exponents can exceed the MSS scale. The black hole charge is held fixed, and two distinct configurations are analyzed: the black hole rotation aligned and anti-aligned with the z -axis. In the aligned case, an exceedance occurs exclusively when the black hole angular momentum surpasses a critical threshold; notably, for a fixed angular momentum of 0.20,  no exceedance is observed irrespective of variations in the particle’s spin, charge, or total angular momentum. In the anti-aligned configuration, by contrast, exceedances emerge once the black hole angular momentum, or the particle’s spin, charge, or total angular momentum exceeds its respective threshold. Furthermore, an increase in the particle’s negative charge suppresses chaotic motion, whereas an increase in positive charge enhances it. In the extremal limit, the black hole reduces to a zero-temperature system, wherein the exponents remain strictly positive for all spin configurations. These results show that these exponents associated with chaotic dynamics can be larger than the MSS scale.