Motivated by the recent unified approach to the Smarr-like relation of anti-de Sitter (AdS) planar black holes in conjunction with the quasilocal formalism on conserved charges, we revisit the quantum statistical and thermodynamic relations of hairy AdS planar black holes. By extending the previous results, we identify the hairy contribution in the bulk and show that the holographic computation can be improved so that it is consistent with the bulk computation. We argue that the first law can be retained in its universal form and that the relation between the on-shell renormalized Euclidean action and its free energy interpretation in gravity may also be undeformed even with the hairy contribution in hairy AdS black holes.
Bibliographical noteFunding Information:
We would like to thank Byoungjoon Ahn, Jaehoon Jeong and Kyung Kiu Kim for some discussion. S.H. was supported by the National Research Foundation of Korea Grant No. NRF-2016R1D1A1A09917598. S.Y. was supported by the National Research Foundation of Korea Grant No. NRF-2015R1D1A1A09057057.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)