Energy Level Diagrams for Black Hole Orbits

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 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.

8 pages

References in corpus (10)

• Gravitational waves from scattering of stellar-mass black holes in galactic nuclei
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Gravitational wave snapshots of generic extreme mass ratio inspirals
• A Periodic Table for Black Hole Orbits
• Zoom-Whirl Orbits in Black Hole Binaries
• Detection Rate Estimates of Gravity-waves Emitted During Parabolic Encounters of Stellar Black Holes in Globular Clusters
• Computing inspirals in Kerr in the adiabatic regime. I. The scalar case
• Dynamics of Black Hole Pairs I: Periodic Tables
• Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
• Verifying black hole orbits with gravitational spectroscopy

Cited by in corpus (29)

• Timelike geodesics in Naked Singularity and Black Hole Spacetimes
• Orbital mechanics and quasiperiodic oscillation resonances of black holes in Einstein-Æther theory
• Periodic orbits around a spherically symmetric naked singularity
• Rational Orbits around Charged Black Holes
• Periodic orbits and their gravitational wave radiations in a polymer black hole in loop quantum gravity
• The harmonic structure of generic Kerr orbits
• The Transient Gravitational-Wave Sky
• Geodesics and periodic orbits in Kehagias-Sfetsos black holes in deformed Hourava-Lifshitz gravity
• Periodic orbits around Kerr Sen black holes
• Precession of timelike bound orbits in Kerr spacetime
• Towards an observational test of black hole versus naked singularity at the galactic center
• Precessing and periodic timelike orbits and their potential applications in Einsteinian cubic gravity
• Timelike bound orbits and pericenter precession around black hole with conformally coupled scalar hair
• Periodic orbits and gravitational wave radiation in short hair black hole spacetimes for an extreme mass ratio system
• Periodic orbits and their gravitational wave radiations around the Schwarzschild-MOG black hole
• Periodical orbits and waveforms with spontaneous Lorentz symmetry-breaking in Kalb-Ramond gravity
• Periodic orbits and their gravitational wave radiations in black hole with dark matter halo
• Equatorial periodic orbits and gravitational waveforms in a black hole free of Cauchy horizon
• Energies and angular momenta of periodic Schwarzschild geodesics
• Gravitational radiations from periodic orbits around Einstein-Æther black holes
• Periodic orbits of neutral test particles in Reissner-Nordström naked singularities
• Gravitational wave radiation from periodic orbits and quasi-periodic oscillations in Einstein non-linear Maxwell-Yukawa black hole
• Periodic equatorial orbits in a black bounce scenario
• Gravitational Wave Signatures from Periodic Orbits around a non-commutative inspired black hole surrounded by quintessence
• Periodic orbits and their gravitational wave radiations in $\gamma$-metric
• Taxonomy of periodic orbits and gravitational waves in a non-rotating Destounis-Suvorov-Kokkotas black hole spacetime
• Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity
• Gravitational waveforms from periodic orbits around a novel regular black hole
• Equatorial periodic orbits and gravitational wave signatures in Euler-Heisenberg black holes surrounded by perfect fluid dark matter