Ehlers symmetry at the next derivative order

TL;DR

This paper demonstrates that Ehlers' SL(2,R) symmetry in four-dimensional gravity persists even when curvature squared corrections are included, due to modified transformation laws that maintain symmetry during reduction.

Contribution

It reveals how Ehlers' symmetry is preserved at the next derivative order through corrected transformation laws in gravity with curvature squared terms.

Findings

Ehlers' symmetry remains intact with curvature squared corrections.

Modified SL(2,R) transformation laws resolve scaling issues.

Symmetry preservation extends to higher derivative gravity theories.

Abstract

We analyse four-dimensional gravity in the presence of general curvature squared corrections and show that Ehlers' SL(2,R) symmetry, which appears in the reduction of standard gravity to three dimensions, is preserved by the correction terms. The mechanism allowing this is a correction of the SL(2,R) transformation laws which resolves problems with the different scaling behaviour of various terms occurring in the reduction.