Fluxes and angular momentum

TL;DR

This paper examines the definition of angular momentum flux in gravitational radiation, addressing phase space formulation issues, and proposes improved models that better decouple radiative modes from internal degrees of freedom.

Contribution

It introduces a refined phase space framework for angular momentum flux, clarifies the degrees of freedom, and analyzes conditions for decoupling radiative modes from internal modes.

Findings

Two phase spaces are analyzed, with one better justified physically.

Both phase spaces support BMS algebra Poisson brackets.

Angular momentum flux is constrained in axisymmetric vacuum spacetimes.

Abstract

The Ashtekar-Streubel fluxes give a proposed definition of the angular momentum emitted by an isolated gravitationally radiating system. This was based on identifying a "phase space of radiative modes," independent of any internal degrees of freedom, and using the Hamiltonian functions conjugate to the action of the Bondi-Metzner-Sachs (BMS) group as the energy-momentum, supermomentum and angular momentum. However, there are some difficulties in formulating this phase space so as to get the proper degrees of freedom. I consider how to address this point, and also to identify circumstances in which the radiative modes are sufficiently decoupled that they can be assigned their own angular momentum. Two different phase spaces are considered. One, which seems to reflect what previous workers have done (it leads to the usual formulas for the Ashtekar-Streubel fluxes), is mathematically simpler, but this has unwanted degrees of freedom and is difficult to interpret physically. The second is a quotient of the first; it is better justified (at least in terms of degrees of freedom), and plausibly decouples the radiative angular momentum from internal modes (at least for systems which ultimately become stationary). The symplectic form for this quotient, and the corresponding angular momentum flux, involve highly non-local correlations. Both phase spaces are shown to have Poisson brackets implementing the BMS algebra. For both phase spaces, for axisymmetric space-times vacuum near null infinity, there can be no gravitational radiation of angular momentum about the axis of symmetry, although matter can carry off angular momentum in such cases.