A physical application of Kerr-Schild groups

TL;DR

This paper explores how generalized Kerr-Schild groups can be used to control and generate specific spacetime solutions in Einstein's equations, offering new methods for finding physically relevant metrics.

Contribution

It introduces the application of generalized Kerr-Schild groups to manipulate spacetime metrics and suggests new ansätze for solving Einstein's equations.

Findings

Efficient control of spacetime types via Kerr-Schild groups

Preliminary exploration of other metric transformation groups

Potential for new solutions to Einstein's equations

Abstract

The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the results show how one can control very efficiently the kind of spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through Kerr-Schild groups. Finally a preliminar study regarding other generalized groups of metric transformations is undertaken which is aimed at giving some hints in new Ans\"atze to finding useful solutions to Einstein's equations.