Energies and angular momenta of periodic Schwarzschild geodesics
arxiv(2024)
摘要
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 (z,w,v). In particular, we chart its
distribution in terms of its angular momenta L and energy E. In the
(L,E)-parameter space, the set of all periodic orbits can be partitioned into
domains according to their whirl number w, where the limit of infinite w
approaches the branch of unstable circular orbits. Within each domain of a
given whirl number w, the infinite zoom limit
lim_z→∞(z,w,v) converges to the common boundary with the
adjacent domain of whirl number w-1. 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.
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