Energy Level Diagrams for Black Hole Orbits

Details Energy Level Diagrams for Black Hole Orbits Energy Level Diagrams for Black Hole Orbits

2009-07-29

arxiv.org/abs/0907.5195v2

Class.Quant.Grav.26:235010,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages

Scientific paper

10.1088/0264-9381/26/23/235010

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 to 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.

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