Energy-momentum and asymptotic geometry

TL;DR

This paper demonstrates that radiative space-times are not asymptotically flat due to holonomy at null infinity caused by gravitational radiation, leading to new insights into energy-momentum exchange and wave propagation in inhomogeneous media.

Contribution

It reveals the non-flatness of radiative space-times at null infinity and introduces a measure for matter-wave energy-momentum exchange, impacting understanding of gravitational wave propagation.

Findings

Radiative space-times exhibit holonomy at null infinity.

Asymptotically covariantly constant vectors do not exist in radiative space-times.

Bulk energy-momentum exchanges can significantly affect gravitational wave propagation.

Abstract

I show that radiative space-times are not asymptotically flat; rather, the radiation field gives rise to holonomy at null infinity. (This was noted earlier, by Bramson.) This means that, when gravitational radiation is present, asymptotically covariantly constant vector fields do not exist. On the other hand, according to the Bondi-Sachs construction, a weaker class of asymptotically constant vectors does exist. Reconciling these concepts leads to a measure of the scattering of matter by gravitational waves, that is, bulk exchanges of energy-momentum between the waves and matter. Because these bulk effects are potentially larger than the tidal ones which have usually been studied, they may affect the waves' propagation more significantly, and the question of matter's transparency to gravitational radiation should be revisited. While in many cases there is reason to think the waves will be only slightly affected, some situations are identified in which the energy-momentum exchanges can be substantial enough that a closer investigation should be made. In particular, the work here suggests that gravitational waves produced when relativistic jets are formed might be substantially affected by passing through an inhomogeneous medium.