Dynamics of Black Hole Pairs I: Periodic Tables

Abstract

Although the orbits of comparable mass, spinning black holes seem to defy simple decoding, we find a means to decipher all such orbits. The dynamics is complicated by extreme perihelion precession compounded by spin-induced precession. We are able to quantitatively define and describe the fully three dimensional motion of comparable mass binaries with one black hole spinning and expose an underlying simplicity. To do so, we untangle the dynamics by capturing the motion in the orbital plane. Our results are twofold: (1) We derive highly simplified equations of motion in a non-orthogonal orbital basis, and (2) we define a complete taxonomy for fully three-dimensional orbits. More than just a naming system, the taxonomy provides unambiguous and quantitative descriptions of the orbits, including a determination of the zoom-whirliness of any given orbit. Through a correspondence with the rationals, we are able to show that zoom-whirl behavior is prevalent in comparable mass binaries in the strong-field regime. A first significant conclusion that can be drawn from this analysis is that all generic orbits in the final stages of inspiral under gravitational radiation losses are characterized by precessing clovers with few leaves and that no orbit will behave like the tightly precessing ellipse of Mercury. The gravitational waveform produced by these low-leaf clovers will reflect the natural harmonics of the orbital basis -- harmonics that, importantly, depend only on radius. The significance for gravitational wave astronomy will depend on the number of windings the pair executes in the strong-field regime and could be more conspicuous for intermediate mass pairs than for stellar mass pairs.

19 pages, lots of figures

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• Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
• Gravitational waveforms from periodic orbits around a quantum-corrected black hole
• A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
• Inspiral of Generic Black Hole Binaries: Spin, Precession, and Eccentricity
• Periodic orbits and their gravitational wave radiations in black hole with dark matter halo
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• Spinning compact binary inspiral II: Conservative angular dynamics
• 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
• Gravitational Wave Signatures from Periodic Orbits around a non-commutative inspired black hole surrounded by quintessence
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• Periodic orbits and their gravitational wave radiations in $\gamma$-metric
• Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity
• Algorithms and radiation dynamics for the vicinity of black holes I. Methods and codes
• Equatorial periodic orbits and gravitational wave signatures in Euler-Heisenberg black holes surrounded by perfect fluid dark matter