Application of Sturm's theorem to marginal stable circular orbits of a test body in spherically symmetric and static spacetimes

Abstract

In terms of Sturm's theorem, we reexamine a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a time-like geodesic in any spherically symmetric and static spacetime. MSCOs for some of the exact solutions to Einstein's equation are discussed. Sturm's theorem is explicitly applied to the Kottler (often called Schwarzschild-de Sitter) spacetime. Moreover, we analyze MSCOs for a spherically symmetric, static and vacuum solution in Weyl conformal gravity.