Compact binary coalescences: The subtle issue of angular momentum

Abstract

In presence of gravitational radiation, the notion of angular momentum of an isolated system acquires an infinite dimensional supertranslation ambiguity. This fact has been emphasized in the mathematical general relativity literature over several decades. We analyze the issue in the restricted context of compact binary coalescence (CBC) where the initial total angular momentum of the binary and the final black hole spin generically refer to \emph{distinct} rotation subgroups of the Bondi-Metzner-Sachs group, related by \emph{supertranslations}. We show that this ambiguity can be quantified using gravitational memory and the `black hole kick'. Our results imply that, although the ambiguity is conceptually important, under assumptions normally made in the CBC literature, it can be ignored in practice for the current and foreseeable gravitational wave detectors.

28 pages, 1 Figure. Some clarifications and a figure added at referee's suggestion

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Cited by in corpus (22)

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• Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity
• Compact binary coalescences: Constraints on waveforms
• Inferring the gravitational wave memory for binary coalescence events
• Comparing Remnant Properties from Horizon Data and Asymptotic Data in Numerical Relativity
• Null Infinity as a Weakly Isolated Horizon
• BMS charges without supertranslation ambiguity
• Unified Treatment of null and Spatial Infinity IV: Angular Momentum at Null and Spatial Infinity
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• Electromagnetic fields in compact binaries: post-Newtonian wave generation and application to double white dwarfs systems
• Unified Treatment of Null and Spatial Infinity III: Asymptotically Minkowski Space-times
• Gravitational wave cosmology I: high frequency approximation
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• ADM, BMS, and some puzzling interconnections
• On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes
• On the angular momentum of compact binary coalescence
• Supertranslation ambiguity in post-Minkowskian expansion
• Note on post-Minkowskian expansion and Bondi coordinates