Generalized Symmetries of the Einstein Equations

TL;DR

This paper reformulates the symmetries of Einstein's equations in a more geometric framework, clarifying their structure and limitations, especially regarding the generalized type (c-bar) symmetries.

Contribution

It introduces a more abstract geometric formulation of Gurses' symmetries and defines a new type (c-bar) symmetry with improved algebraic properties.

Findings

Type (b) symmetry relates to manifold diffeomorphisms.

Type (c) symmetry is replaced by a more general type (c-bar).

A differential constraint limits the transformations' applicability.

Abstract

We reformulate the symmetries of Gurses [Phys. Rev. Lett. 70, 367 (1993)] in a more abstract, more geometrical manner. The type (b) transformation of \gurses\ is related to a diffeomorphism of the differentiable manifold onto itself. The type (c) symmetry is replaced by a more general type (c-bar) symmetry that has the nice property that the commutator of a type (c-bar) generator with a type (a) generator is itself of type (c-bar). We identify a differential constraint that transformations of type (c) and (c-bar) must satisfy, and which, in our opinion, may severely limit the usefulness of these transformations.