2022/07/29 by Pedro V. P. Cunha, Carlos A. R. Herdeiro, Cunha, Pedro V. P. +4 · 5 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.2207.14506
7 pages + Appendices
arxiv created 2022/07/29 · openalex publication_date 2022/07/29 · arxiv updated 2022/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The motion of particles on spherical 1 + 3 dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this paper we resort to auxiliary 2-dimensional metrics to study circular geodesics of generic static, spherically symmetric, and asymptotically flat 1 + 3 dimensional spacetimes, whose functions are at least C2 smooth. This is done by studying the Gaussian curvature of the bidimensional equivalent manifold as well as the geodesic curvature of circular paths on these. This study considers both null and timelike circular geodesics. The study of null geodesics through the optical manifold retrieves the known result of the number of light rings (LRs) on the spacetime outside a black hole and on spacetimes with horizonless compact objects. With an equivalent procedure we can formulate a similar theorem on the number of marginally stable timelike circular orbits (TCOs) of a given spacetime satisfying the previously mentioned assumption