Entropy function from the Einstein boundary term

¹ Department of Theoretical Sciences, S.N. Bose National Centre for Basic Sciences JD Block, Sector- III, Salt Lake, Kolkata 700106, India
² Department of Physics, University of Kalyani – Kalyani 741235, India

^(a) iamanirban@bose.res.in
^(b) ashisphys18@klyuniv.ac.in
^(c) sunandan.gangopadhyay@gmail.com (corresponding author)

Received: 16 May 2021
Accepted: 21 June 2021

Abstract

We show using the entropy function formalism developed by Sen (JHEP, 09 (2005) 038) that the boundary term which arises from the Einstein‐Hilbert action is sufficient to yield the Bekenstein‐Hawking entropy of a static extremal black hole which is asymptotically flat. However, for asymptotically AdS black holes, the bulk term also plays an important role due to the presence of the cosmological constant. Further, we show that for extremal rotating black holes, both the boundary and the bulk terms contribute non‐vanishing pieces to the entropy.