Compact binary coalescences: The subtle issue of angular momentum

TL;DR

This paper investigates the ambiguity in defining angular momentum in gravitational wave sources, showing that while conceptually significant, it can generally be neglected in current gravitational wave observations due to practical considerations.

Contribution

The paper clarifies the supertranslation ambiguity in angular momentum for binary coalescences and demonstrates its practical insignificance for current gravitational wave detectors.

Findings

Supertranslation ambiguity affects angular momentum in gravitational radiation.

Memory effects and black hole kicks quantify the ambiguity.

In practice, the ambiguity can be ignored with current detectors.

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.