Lyapunov exponent ISCO and Kolmogorov Senai entropy for Kerr Kiselev black hole

TL;DR

This paper investigates the stability and chaos of geodesic motion around Kerr-Kiselev black holes by calculating Lyapunov exponents and Kolmogorov-Senai entropy, revealing properties of circular orbits and their implications for black hole dynamics.

Contribution

It introduces a novel analysis of Lyapunov exponents and KS entropy for Kerr-Kiselev black holes, linking these measures to ISCO and marginally bound orbits, and compares null and time-like geodesics.

Findings

Null circular geodesics have higher angular frequency than time-like geodesics.

Null circular geodesics have the shortest orbital period among all circular orbits.

Lyapunov exponent and KS entropy relate to the stability of geodesics and ISCO.

Abstract

Geodesic motion has significant characteristics of space-time. We calculate the principle Lyapunov exponent (LE), which is the inverse of the instability timescale associated with this geodesics and Kolmogorov-Senai (KS) entropy for our rotating Kerr-Kiselev (KK) black hole. We have investigate the existence of stable/unstable equatorial circular orbits via LE and KS entropy for time-like and null circular geodesics. We have shown that both LE and KS entropy can be written in terms of the radial equation of innermost stable circular orbit (ISCO) for time-like circular orbit. Also, we computed the equation marginally bound circular orbit, which gives the radius (smallest real root) of marginally bound circular orbit (MBCO). We found that the null circular geodesics has larger angular frequency than time-like circular geodesics ($Q_o > Q_{\sigma}$). Thus, null-circular geodesics provides the fastest way to circulate KK black holes. Further, it is also to be noted that null circular geodesics has shortest orbital period $(T_{photon}< T_{ISCO})$ among the all possible circular geodesics. Even null circular geodesics traverses fastest than any stable time-like circular geodesics other than the ISCO.