By considering the behavior of the reduced action under the scaling transformation, we present a unified derivation of the Smarr-like relation for asymptotically anti-de-Sitter planar black holes. This novel Smarr-like relation leads to useful information in the condensed matter systems through the AdS/CMT correspondence. By using our results, we provide an efficient way to obtain the holographically renormalized on-shell action without the information on the explicit forms of counter terms. We find the complete consistency of our results with those in various models discussed in the recent literatures and obtain new implications.
Bibliographical noteFunding Information:
We would like to thank Dongsu Bak and Jaehoon Jeong for helpful discussions. S.H. was supported by the National Research Foundation of Korea (NRF) grant with the Grant No. NRF-2013R1A1A2011548. This work started from a discussion in Year-End Workshop of Future-Oriented HEP Society supported by APCTP, so we appreciate it. K.K. was supported by the National Research Foundation of Korea (NRF) grant with the Grant No. NRF-2015R1D1A1A01058220. S.Y. was supported by the National Research Foundation of Korea (NRF) grant with the Grant No. NRF-2015R1D1A1A09057057.
© 2016 American Physical Society.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)