Noether current of the surface term of Einstein-Hilbert action, Virasoro algebra and entropy

TL;DR

This paper derives the Noether current from the surface term of Einstein-Hilbert action, relates it to black hole entropy via Virasoro algebra, and simplifies previous approaches to understanding gravitational entropy.

Contribution

It presents a new derivation of the Noether current from the surface term and links it to black hole entropy using a simplified Virasoro algebra approach.

Findings

Charge on the horizon relates to Bekenstein-Hawking entropy

Entropy can be derived from Virasoro algebra and Cardy formula

Simplifies previous methods and discusses physical implications

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 (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.