LAUSR

When geodesic equations are formulated in terms of an effective potential U , circular orbits are characterised by U = ∂aU = 0. In this paper we consider the case where U is an algebraic function. Then the condition for circular orbits defines an A-discriminantal variety. A theorem by Rojas and Rusek, suitably interpreted in the context of effective potentials, gives a precise criteria for certain types of spacetimes to contain at most two branches of light rings (null circular orbits), where one is stable and the other one unstable. We identify a few classes of static, spherically symmetric spacetimes for which these two branches occur.