Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy

Abstract

A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument:diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012)) (arXiv:1204.1422) obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.