Abstract. A spinning black hole with a much smaller black hole companion forms a fundamental gravitational system, like a colossal classical analog to an atom. In an appealing if imperfect analogy with atomic physics, this gravitational atom can be understood through a discrete spectrum of periodic orbits. Exploiting a correspondence between the set of periodic orbits and the set of rational numbers, we are able to construct periodic tables of orbits and energy level diagrams of the accessible states around black holes. We also present a closed-form expression for the rational q, thereby quantifying zoom-whirl behavior in terms of spin, energy and angular momentum. The black hole atom is not just a theoretical construct, but corresponds to extant astrophysical systems detectable by future gravitational wave observatories.

PACS numbers: 97.60.Lf, 04.70.−s, 95.30.Sf

Print publication: Issue 23 (7 December 2009)
Received 30 July 2009, in final form 12 October 2009
Published 6 November 2009