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

摘要

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