Null and timelike circular orbits from equivalent 2D metrics

Abstract The motion of particles on spherical 1 + 3 dimensional spacetimes can, under some assumptions, be described by the curves a two-dimensional manifold, optical and Jacobi manifolds for null timelike curves, respectively. In this paper we resort to auxiliary metrics study circular geodesics generic static, spherically symmetric, asymptotically flat spacetimes, whose functions are at least C 2 smooth. This is done studying Gaussian curvature bidimensional equivalent manifold as well geodesic paths these. considers both geodesics. through retrieves known result number light rings spacetime outside black hole with horizonless compact objects. With an procedure can formulate similar theorem marginally stable orbits given satisfying previously mentioned assumptions.