Lyapunov exponent and charged Myers–Perry spacetimes

Abstract

We compute the proper time Lyapunov exponent for charged Myers Perry black hole spacetime and investigate the instability of the equatorial circular geodesics (both timelike and null) via this exponent. We also show that for more than four spacetime dimensions $(N \geq 3)$, there are \emph{no} Innermost Stable Circular Orbits (ISCOs) in charged Myers Perry black hole spacetime. We further show that among all possible circular orbits, timelike circular orbits have \emph{longer} orbital periods than null circular orbits (photon spheres) as measured by asymptotic observers. Thus, timelike circular orbits provide the \emph{slowest way} to orbit around the charged Myers Perry black hole.