Improved Reall-Santos method for AdS black holes in general higher derivative gravities

Peng-Ju Hu, Liang Ma, H. Lu, Yi Pang

Published 2023-12-18Version 1

For asymptotically flat black holes, Reall-Santos method is a powerful tool to compute leading higher derivative corrections to the thermodynamic variables without actually solving the modified field equations. However, its generalization to asymptotically AdS black holes with general higher derivative corrections is a highly nontrivial task. Using the example of Einstein-Gauss-Bonnet gravity, we show that a direct application of the method fails to produce the correct on-shell action. To resolve this problem, we first derive the conditions under which field redefinitions do not affect thermodynamic variables of AdS black holes with general 4-derivative corrections. We then show that Reall-Santos method does apply to a particular 4-derivative gravity model, known as the Einstein-Weyl gravity. We thus propose that to compute the thermodynamic quantities of AdS black holes in a model with general 4-derivative interactions, one simply needs to transform it to a Einstein-Weyl gravity with identical thermodynamic variables by appropriate field redefinitions. We explicitly verify this proposal with spherically-symmetric and static charged black holes in Einstein-Maxwell theory extended with generic 4-derivative interactions.