On Useful Conformal Tranformations In General Relativity

TL;DR

This paper explores new aspects of local conformal transformations in general relativity, demonstrating their utility in deriving Einstein equations and reducing topological invariants across dimensions.

Contribution

It introduces novel applications of conformal transformations for deriving Einstein equations and dimensional reduction of topological invariants in gravitational theories.

Findings

Derived Einstein equations for cosmological and Schwarzschild metrics using conformal transformations.

Applied conformal transformations for dimensional reduction of the Gauss-Bonnet invariant.

Highlighted new features of conformal transformations in gravitational applications.

Abstract

Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.