Jacobi stability of circular orbits around conformally invariant Weyl gravity black holes

TL;DR

This paper analyzes the stability of circular orbits around Weyl conformal gravity black holes, providing new insights into their stability properties and the influence of solution parameters.

Contribution

It investigates the Jacobi and Lyapunov stability of timelike circular geodesics in Weyl black holes, a topic with renewed interest since 1989.

Findings

Identifies conditions for stability of circular orbits.

Shows how free parameters affect black hole stability.

Provides a detailed analysis of geodesic stability in Weyl gravity.

Abstract

Weyl conformal gravity was originally proposed in the early twentieth century as an attempt to unify gravitation and electromagnetism. Since 1989, renewed interest in this fourth-order theory of gravity has emerged following the discovery of several exact black hole solutions. In this work, we investigate the timelike circular geodesics of a spherically symmetric Weyl black hole. The effective potential, the circular geodesics and their Jacobi and Lyapunov stability are discussed. Our analysis provides new insights into the stability properties of Weyl black holes and the role of the free parameters appearing in their solutions.