Stability analysis of circular orbits around a charged BTZ black hole spacetime in a nonlinear electrodynamics model via Lyapunov exponents

TL;DR

This paper analyzes the stability of circular orbits around a charged BTZ black hole in a nonlinear electrodynamics framework using Lyapunov exponents, revealing conditions for chaos and orbit stability.

Contribution

It introduces a stability analysis of timelike and null circular orbits in a (2+1)D charged BTZ black hole with nonlinear Maxwell gravity, employing Lyapunov exponents to assess chaos.

Findings

Proper time Lyapunov exponent varies with orbit radius and charge.

Null orbits analyzed via coordinate time Lyapunov exponent and instability ratio.

Behavior of stability ratios depends on charge and cosmological constant parameters.

Abstract

We investigate the existence and stability of both the timelike and null circular orbits for a (2+1) dimensional charged BTZ black hole in Einstein-nonlinear Maxwell gravity with a negative cosmological constant. The stability analysis of orbits are performed to study the possibility of chaos in geodesic motion for a special case of black hole so-called conformally invariant Maxwell spacetime. The computations of both proper time Lyapunov exponent ($\lambda_{p}$) and coordinate time Lyapunov exponent ($\lambda_{c}$) are useful to determine the stability of these circular orbits. We observe the behavior of the ratio $(\lambda_{p}/\lambda_{c})$ as a function of radius of circular orbits for the timelike case in view of different values of charge parameter. However, for the null case, we calculate only the coordinate time Lyapunov exponent ($\lambda_{c}$) as there is no proper time for massless test particles. More specifically, we further analyze the behavior of the ratio of $\lambda_{Null}$ to angular frequency ($\Omega_{c}$), so-called instability exponent as a function of charge ($q$) and parameter related to cosmological constant ($l$) for the particular values of other parameters.