Dynamical analysis of null geodesics in brane-world spacetimes

TL;DR

This paper conducts a detailed dynamical analysis of null geodesics in brane-world black hole and wormhole spacetimes, revealing stability properties, photon spheres, and bifurcations that deepen understanding of their geometric and physical features.

Contribution

It provides the first comprehensive dynamical systems analysis of null geodesics in CFM brane-world spacetimes, including stability and bifurcation characterizations.

Findings

Identification of semistable photon spheres

Lyapunov and Jacobi stability criteria agree

Detection of a degenerated Bogdanov-Takens bifurcation

Abstract

In this work, we present an extensive dynamical analysis of the null geodesics in the spacetimes proposed by Casadio, Fabbri, and Mazzacurati (CFM), which model black holes and wormholes in a Randall-Sundrum brane. Geodesic stability is evaluated by Lyapunov and Jacobi criteria, with coinciding results. Semistable photon spheres are found in the geometries of interest. Bifurcations associated with the dynamical system are also investigated, characterizing a degenerated Bogdanov-Takens bifurcation. Our results suggest deep connections between the geometric characteristics of the CFM spacetimes and the dynamics of null geodesics in these backgrounds.