Marginally stable circular orbits in stationary axisymmetric spacetimes

Understand

We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also addressed.

• Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics.
• The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions.
• MSCOs are explicitly calculated for concrete examples of physical interest.