Marginally stable circular orbit of a test body in spherically symmetric and static spacetimes

TL;DR

This paper analyzes the properties of marginally stable circular orbits in spherically symmetric, static spacetimes, revealing that certain metric components do not influence these orbits, which has implications for gravity testing.

Contribution

It demonstrates that the metric component g_{rr} does not affect MSCOs and shows that ISCO measurements can serve as tests of gravity similar to gravitational redshift experiments.

Findings

Metric components are separable from constants of motion.

g_{rr} does not influence MSCOs.

ISCO measurements can test gravity like gravitational redshift.

Abstract

We study a marginally stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. It turns out that the metric components are separable from the constants of motion along geodesics. We show also that a metric component $g_{rr}$ with a radial coordinate $r$ does not affect MSCOs. This suggests that, as a test of gravity, any ISCO measurement may be put into the same category as gravitational redshift experiments. MSCOs for exact solutions to the Einstein's equation are also mentioned.