Stability of circular geodesics in equatorial plane of Kerr spacetime
Pradeep Singh, Hemwati Nandan, Lokesh Kumar Joshi, Nidhi Handa and, Shobhit Giri
TL;DR
This paper investigates the stability of circular geodesics in Kerr black hole spacetime using Lyapunov and Jacobi stability analyses, comparing different methods and visualizing results through phase portraits.
Contribution
It provides a comprehensive comparison of Lyapunov and KCC stability methods for geodesics in Kerr spacetime, including phase portrait verification.
Findings
Lyapunov analysis confirms stability regions for geodesics.
KCC theory offers an alternative perspective on geodesic stability.
Phase portraits visually support stability results.
Abstract
We analyze the stability of circular geodesics for timelike as well as null geodesics of the Kerr BH spacetime with rotation parameter on the equatorial plane by Lyapunov stability analysis. Also, we verify the results of stability by presenting the phase portrait for both timelike and null geodesics. Further, by reviewing the Kosambi-Cartan-Chern (KCC) theory, we analyze the Jacobi stability for Kerr spacetime and present a comparative study of the methods used for stability analysis of geodesics.
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