Perturbations of classical fields by gravitational shockwaves

TL;DR

This paper develops a linearized framework to analyze how classical fields, modeled by scalar fields, are perturbed by gravitational shockwaves, revealing effects like radiation conversion and shockwave interactions with sources.

Contribution

It introduces a general method to study classical field perturbations caused by gravitational shockwaves, including effects on pointlike sources and supertranslation-induced initial data.

Findings

Perturbations propagate above the shockwave front as solutions to a characteristic Cauchy problem.

Gravitational shockwaves induce scalar shockwaves and convert non-stationary perturbations into outgoing radiation.

The approach applies to a broad class of shockwave geometries, including null particles and branes.

Abstract

Gravitational shockwaves are geometries where components of the transverse curvature have abrupt behaviour across null hypersurfaces, which are fronts of the waves. We develop a general approach to describe classical field theories on such geometries in a linearized approximation, by using free scalar fields as a model. Perturbations caused by shockwaves exist above the wave front and are solutions to a characteristic Cauchy problem with initial data on the wave front determined by a supertranslation of ingoing fields. A special attention is paid to perturbations of fields of pointlike sources generated by plane-fronted gravitational shockwaves. One has three effects: conversion of non-stationary perturbations into an outgoing radiation, a spherical scalar shockwave which appears when the gravitational wave hits the source, and a plane scalar shockwave accompanying the initial gravitational wave. Our analysis is applicable to gravitational shockwaves of a general class including geometries sourced by null particles and null branes.