Momentum Flow in Black Hole Binaries: I. Post-Newtonian Analysis of the Inspiral and Spin-Induced Bobbing

Abstract

A brief overview is presented of a new Caltech/Cornell research program that is exploring the nonlinear dynamics of curved spacetime in binary black hole collisions and mergers, and of an initial project in this program aimed at elucidating the flow of linear momentum in black-hole binaries (BBHs). The "gauge-dependence" (arbitrariness) in the localization of linear momentum in BBHs is discussed, along with the hope that the qualitative behavior of linear momentum will be gauge-independent. Harmonic coordinates are suggested as a possibly preferred foundation for fixing the gauge associated with linear momentum. For a BBH or other compact binary, the Landau-Lifshitz formalism is used to define the momenta of the binary's individual bodies in terms of integrals over the bodies' surfaces or interiors, and define the momentum of the gravitational field (spacetime curvature) outside the bodies as a volume integral over the field's momentum density. These definitions will be used in subsequent papers that explore the internal nonlinear dynamics of BBHs via numerical relativity. This formalism is then used, in the 1.5PN approximation, to explore momentum flow between a binary's bodies and its gravitational field during the binary's orbital inspiral. Special attention is paid to momentum flow and conservation associated with synchronous spin-induced bobbing of the black holes, in the so-called "extreme-kick configuration" (where two identical black holes have their spins lying in their orbital plane and antialigned).

15 pages, 5 figures and 1 table

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• Bobbing and Kicks in Electromagnetism and Gravity
• Motion in classical field theories and the foundations of the self-force problem
• Superkicks in ultrarelativistic encounters of spinning black holes
• Post-Newtonian Approximation in Maxwell-Like Form
• Compact Binary Waveform Center-of-Mass Corrections
• First frequency-domain phenomenological model of the multipole asymmetry in gravitational-wave signals from binary-black-hole coalescence
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• Universal features of gravitational waves emitted by superkick binary black hole systems
• KETJU -- resolving small-scale supermassive black hole dynamics in GADGET-4
• The Status of Black-Hole Binary Merger Simulations with Numerical Relativity
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• Event Horizon Deformations in Extreme Mass-Ratio Black Hole Mergers
• Incorporation of model accuracy in gravitational wave Bayesian inference
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• Relativistic gas accretion onto supermassive black Hole binaries from inspiral through merger
• Unveiling the electrodynamic nature of spacetime collisions
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