Light-ring pairs from $A$-discriminantal varieties

Understand

When geodesic equations are formulated in terms of an effective potential $U$, circular orbits are characterised by $U=\partial_a U=0$.

• 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.