Comment on "A comment on metric vs metric-affine gravity"
Abstract
It has been recently claimed in [arXiv:2211.12327] that an action of the Einstein-Palatini form plus a torsionless Pontryagin term (multiplied by a constant) represents a counterexample to the conclusions of [arXiv:0705.1879], namely, that Lovelock gravity is the only case in which the metric and metric-affine formulations of gravity are equivalent. However, given that the Pontryagin term (multiplied by a constant) can be written as a total D-divergence, it is a textbook matter to realise that the addition of such (or any other) D-divergence only affects at the boundary, leaving invariant the field equations and its solutions, which are those of GR \`{a} la Palatini. We thus conclude that the example provided in [arXiv:2211.12327] is not a valid counterexample of [arXiv:0705.1879].
Keywords
Cite
@article{arxiv.2301.02016,
title = {Comment on "A comment on metric vs metric-affine gravity"},
author = {Gonzalo J. Olmo and P. J. Porfírio},
journal= {arXiv preprint arXiv:2301.02016},
year = {2023}
}
Comments
3 pages, version accepted to NPB