Perturbations of classical fields by gravitational shockwaves

• Published in: arXiv.org 2024-11
• Main Authors: Fursaev, D V, Davydov, E A, Pirozhenko, I G, Tainov, V A
• Format: Article
• Language: English
• Subjects: Cauchy problems; Gravitational effects; Gravitational waves; Hyperspaces; Perturbation; Scalars; Shock waves; Spherical waves; Wave fronts
• ISSN: 2331-8422

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.