Lyapunov Exponent and Charged Myers Perry Spacetimes

TL;DR

This paper analyzes the stability of circular orbits in charged Myers Perry black hole spacetimes by computing Lyapunov exponents, revealing the absence of ISCOs in higher dimensions and comparing orbital periods of different orbits.

Contribution

It introduces the calculation of Lyapunov exponents for charged Myers Perry black holes and demonstrates the non-existence of ISCOs in higher dimensions, highlighting differences in orbital periods.

Findings

No ISCOs for dimensions N ≥ 3

Timelike orbits have longer periods than null orbits

Timelike orbits are the slowest to orbit

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.