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.
Highlights
The instability of an orbit can be identified by a positive value of Lyapunov exponent [13,14]
In this paper we have clarify some aspect about principle Lyapunov exponent, KS entropy and unstable null-circular geodesics
We have presented that the principle Lyapunov exponent and KS entropy can be express in terms of the equation of innermost stable circular orbit (ISCO)
Summary
The instability of an orbit can be identified by a positive value of Lyapunov exponent [13,14]. It is well-known that maximal Lyapunov exponents (MLE) can distinguish a chaotic dynamics from others, which may initiate unstable/homoclinic orbits by a perturbation. For a spinning black hole the number of unstable orbits increase very rapidly and crowded into the corresponding phase [15,16,17]. Panis et al [22] discussed about Keplerian disk orbiting a Schwarzschild black hole embedded in an asymptotically uniform magnetic field where they have found three possible scenarios i.e. Panis et al [22] discussed about Keplerian disk orbiting a Schwarzschild black hole embedded in an asymptotically uniform magnetic field where they have found three possible scenarios i.e. (1) regular
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