All symmetry groups of pp-waves in teleparallel gravity

TL;DR

This paper develops a method to identify all symmetry groups of pp-wave spacetimes in teleparallel gravity, revealing two previously overlooked solutions in both teleparallel gravity and General Relativity.

Contribution

It extends the symmetry analysis of pp-wave spacetimes to teleparallel gravity using the Cartan-Karlhede algorithm, discovering new solutions.

Findings

Identified all symmetry groups of pp-waves in teleparallel gravity.

Discovered two new solutions permitted in both teleparallel gravity and GR.

Abstract

We elaborate on and further develop an approach to determining the teleparallel analogue of spacetimes in General Relativity (GR) by studying the Teleparallel analogue of pp-Wave (TppW) spacetimes. This relies on using the fact that these solutions belong to the Vanishing Scalar Invariant (VSI) subclass for which the explicit forms of the frame and spin-connection are known. By identifying the pp-wave (ppW) metric within this class, we are able to use frame based symmetry methods and the Cartan-Karlhede (CK) algorithm to determine the necessary form for the frame. Through this analysis we find two overlooked solutions that are permitted in teleparallel gravity (TPG) and in GR.