Marginally stable circular orbits in stationary axisymmetric spacetimes

TL;DR

This paper derives a geometric condition for the existence of marginally stable circular orbits in stationary axisymmetric spacetimes with reflection symmetry, providing an algorithmic method to find these orbits and calculating them for specific examples.

Contribution

It introduces a geometric characterization of marginally stable circular orbits and an algorithmic approach for their determination in a broad class of spacetimes.

Findings

Derived a necessary condition for MSCO existence.

Decoupled energy and angular momentum from metric quantities.

Explicitly calculated MSCOs for specific spacetimes.

Abstract

We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs are explicitly calculated for concrete examples of physical interest.