Radiative multipole moments of integer-spin fields in curved spacetime

TL;DR

This paper calculates radiative multipole moments of various fields in Schwarzschild spacetime up to third order in velocity, revealing universal wave-propagation corrections due to spacetime curvature that are independent of multipole order and field type.

Contribution

It provides a detailed third-order velocity expansion of radiative moments, highlighting universal wave-propagation corrections caused by spacetime curvature in curved spacetime.

Findings

Wave-propagation corrections are universal and independent of multipole order.

Corrections depend on spacetime curvature, with equal contributions from temporal and spatial parts.

Third-order calculations clarify the influence of curvature on radiation in Schwarzschild spacetime.

Abstract

Radiative multipole moments of scalar, electromagnetic, and linearized gravitational fields in Schwarzschild spacetime are computed to third order in v in a weak-field, slow-motion approximation, where v is a characteristic velocity associated with the motion of the source. To zeroth order in v, a radiative moment of order l is given by the corresponding source moment differentiated l times with respect to retarded time. At second order in v, additional terms appear inside the spatial integrals. These are near-zone corrections which depend on the detailed behavior of the source. At third order in v, the correction terms occur outside the spatial integrals, so that they do not depend on the detailed behavior of the source. These are wave-propagation corrections which are heuristically understood as arising from the scattering of the radiation by the spacetime curvature surrounding the source. Our calculations show that the wave-propagation corrections take a universal form which is independent of multipole order and field type. We also show that in general relativity, temporal and spatial curvatures contribute equally to the wave-propagation corrections.