Stability analysis of geodesics in dynamical Chern-Simons black holes: a geometrical perspective

TL;DR

This paper uses geometric methods to analyze the stability of geodesics around rotating black holes in dynamical Chern-Simons gravity, highlighting advantages over traditional stability approaches.

Contribution

It applies Kosambi-Cartan-Chern theory to compare Jacobi and Liapunov stability of black hole geodesics in a modified gravity context.

Findings

Jacobi stability offers a more geometrical insight than Liapunov stability.

The study provides a detailed stability analysis specific to dynamical Chern-Simons black holes.

Abstract

We apply the Kosambi-Cartan-Chern theory to perform an extensive examination of Jacobi stability of geodesics around rotating black hole solutions to dynamical Chern-Simons gravity, a theory that introduces modifications to General Relativity via a scalar field non-minimally coupled to curvature scalars. We present a comparative study between Jacobi and Liapunov stability, pointing out the advantages of the more geometrical method over the usual Liapunov approach.