Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 39, Issue 22, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-6382/ac987e
Keywords
black holes; light rings; marginally stable circular orbits
Categories
Funding
- Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia) [UIDB/04106/2020, UIDP/04106/2020]
- FCT [57/2016, 57/2017, UIDB/00099/2020, 2021.06539.BD]
- European Union [FunFiCO-777740]
- [PTDC/FIS-OUT/28407/2017]
- [CERN/FIS-PAR/0027/2019]
- [PTDC/FIS-AST/3041/2020]
- [CERN/FIS-PAR/0024/2021]
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This paper investigates the motion of particles on spherical 1 + 3 dimensional spacetimes under certain assumptions. It explores the curves on a two-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves respectively. The study uses auxiliary two-dimensional metrics to analyze circular geodesics and considers both null and timelike circular geodesics.
The motion of particles on spherical 1 + 3 dimensional spacetimes can, under some assumptions, be described by the curves on a two-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this paper we resort to auxiliary two-dimensional metrics to study circular geodesics of generic static, spherically symmetric, and asymptotically flat 1 + 3 dimensional spacetimes, whose functions are at least C-2 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 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 of a given spacetime satisfying the previously mentioned assumptions.
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