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arXiv · 2301.02016

Comment on "A comment on metric vs metric-affine gravity"

Gonzalo J. Olmo·P. J. Porfírio
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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].

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Gonzalo J. Olmo, P. J. Porfírio. 2023-01-05. Comment on "A comment on metric vs metric-affine gravity". https://doi.org/10.1016/j.nuclphysb.2023.116074

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