https://doi.org/10.1140/epjc/s10052-015-3744-7
Regular Article - Theoretical Physics
Entropy function from the gravitational surface action for an extremal near horizon black hole
Department of Physics, Indian Institute of Technology, Guwahati, 781039, Assam, India
* e-mail: bibhas.majhi@iitg.ernet.in
Received:
7
August
2015
Accepted:
19
October
2015
Published online:
2
November
2015
It is often argued that all the information of a gravitational theory is encoded in the surface term of the action; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. the derivation of the Einstein’s equations, the surface term calculated on the horizon leads to the entropy, etc. Here I investigate the role of it in the context of the entropy function and the entropy of extremal near horizon black holes. Considering only the Gibbons–Hawking–York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such a function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that the gravitational action is of a “holographic” nature – the surface term contains information of the bulk.
© SIF and Springer-Verlag Berlin Heidelberg, 2015
