Note on equatorial geodesics in circular spacetimes

TL;DR

This paper reviews equatorial geodesics in circular spacetimes with reflection symmetry, emphasizing their effective potential formulation and stability analysis, with illustrations in Kerr spacetime.

Contribution

It provides a clear exposition of geodesic equations in circular spacetimes and demonstrates their stability analysis using effective potential, with practical applications to Kerr spacetime.

Findings

Effective potential formulation simplifies geodesic analysis.

Stability criteria for equatorial geodesics are established.

Illustrations in Kerr spacetime confirm theoretical results.

Abstract

General results on equatorial geodesics are exposed in the case of circular spacetimes featuring an equatorial reflection symmetry. The way the geodesic equation equivalently rewrites in terms of an effective potential is explicitly recalled for circular and non-circular equatorial geodesics. This provides a practical tool to discuss their stability. Statements are illustrated in Kerr spacetime.