Colliding plane wave solution in F(R)=R^{N} gravity

TL;DR

This paper explores colliding plane wave solutions within F(R)=R^{N} gravity, revealing how the theory's parameters influence wave interactions and extending Einstein's plane wave collision models to modified gravity.

Contribution

It demonstrates the existence of isometric regions in F(R)=R^{N} gravity analogous to Einstein's colliding plane waves, introducing N as a measure of source strength and analyzing wave behavior in modified gravity.

Findings

Identifies isometric regions in F(R)=R^{N} gravity corresponding to colliding plane waves.

Shows N > 1 acts as a source strength parameter analogous to charge.

Recovers Einstein's plane wave solutions when N=1.

Abstract

We identify a region of F(R)=R^{N} gravity without external sources which is isometric to the spacetime of colliding plane waves (CPW). From the derived curvature sources, N (N>1) measures the strength (i.e. the charge) of the source. The analogy renders construction and collision of plane waves in F(R)=R^{N} gravity possible, as in the Einstein-Maxwell (EM) theory, simply because R=0. A plane wave in this type of gravity is equivalent to a Weyl curvature plus an electromagnetic energy-momentum-like term (i.e. 'source without source'). For N=1 we recover naturally the plane waves (and their collision) in Einstein's theory. Our aim is to find the effect of an expanding universe by virtue of F(R)=R^{N} on the colliding gravitational plane waves of Einstein.