Space-time deformations as extended conformal transformations

TL;DR

This paper introduces a framework where space-time metric deformations are viewed as extended conformal transformations, linking them to gravitational wave perturbations and approximate symmetries, with potential physical applications.

Contribution

It defines space-time metric deformations as extended conformal transformations and relates them to gravitational waves and approximate symmetries.

Findings

Deformations can be interpreted as extended conformal transformations.

Gravitational waves are described as small metric deformations.

Deformations relate to approximate Killing vectors and symmetries.

Abstract

A definition of space-time metric deformations on an $n$-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation theory giving a natural picture by which gravitational waves are described by small deformations of the metric. As further result, deformations can be related to approximate Killing vectors (approximate symmetries) by which it is possible to parameterize the deformed region of a given manifold. The perspectives and some possible physical applications of such an approach are discussed.