Gauged motion in general relativity and in Kaluza-Klein theories

TL;DR

This paper extends the concept of gauged motion, a generalized symmetry for stationary spacetimes, to general spacetimes and Kaluza-Klein theories, providing a broader framework for understanding physical symmetries.

Contribution

It introduces a new definition of gauged motion applicable to general spacetimes and Kaluza-Klein theories, expanding the scope of symmetry analysis in general relativity.

Findings

Gauged motion is defined for general spacetimes using gauged Lie derivatives.

The concept is extended to Kaluza-Klein theories, unifying symmetry descriptions.

Provides a detailed study of gauged motion in stationary spacetimes.

Abstract

In a recent paper [1] a new generalization of the Killing motion, the {\it gauged motion}, has been introduced for stationary spacetimes where it was shown that the physical symmetries of such spacetimes are well described through this new symmetry. In this article after a more detailed study in the stationary case we present the definition of gauged motion for general spacetimes. The definition is based on the gauged Lie derivative induced by a threading family of observers and the relevant reparametrization invariance. We also extend the gauged motion to the case of Kaluza-Klein theories.