Non perturbative spherical gravitational waves

TL;DR

This paper demonstrates that deviations from general relativity can produce exact vacuum spherical gravitational waves, a phenomenon absent in standard GR, highlighting a non-perturbative property of alternative gravity theories.

Contribution

It shows that spherical gravitational waves can exist in modified gravity theories like $f(R)$ gravity, unlike in general relativity, and explores their properties and energy content.

Findings

Existence of exact vacuum spherical gravitational waves in $f(R)$ gravity.

These waves have only one longitudinal polarization initially, extendable to two transverse polarizations.

Spherical gravitational waves are a non-perturbative feature of modified gravity theories.

Abstract

It is well-known that there is no spherical/topologically spherical gravitational waves in vacuum space in general relativity. We show that a deviation from general relativity leads to exact vacuum spherical gravitational waves, no matter how tiny this deviation is. We also discuss the related topics, including Vaidya-like metric in $f(R)$ gravity. We demonstrate that the existence of spherical gravitational wave is a non perturbative property for gravities. We investigate energy carried by this nonperturbative wave. We first find the wave solution from investigations of Vaidya-like metric in $f(R)$ gravity, which has only one longitude polarization. We further extend it to a metric with two transverse polarizations by directly solving the field equation.