Abstract
We consider physical parameters of Levin and Perez-Giz’s “periodic table of orbits” around the Schwarzschild black hole, where each periodic orbit is classified according to three integers . In particular, we chart its distribution in terms of its angular momenta and energy . In the -parameter space, the set of all periodic orbits can be partitioned into domains according to their whirl number , where the limit of infinite approaches the branch of unstable circular orbits. Within each domain of a given whirl number , the infinite zoom limit converges to the common boundary with the adjacent domain of whirl number . The distribution of the periodic orbit branches can also be inferred from perturbing stable circular orbits, using the fact that every stable circular orbit is the zero-eccentricity limit of some periodic orbit, or arbitrarily close to one.
4 More- Received 16 July 2023
- Revised 25 October 2023
- Accepted 22 December 2023
DOI:https://doi.org/10.1103/PhysRevD.109.024037
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