Noether current, horizon virasoro algebra, and entropy

Abstract

We provide a simple and straightforward procedure for defining a Virasoro algebra based on the diffeomorphisms near a null surface in a space-time and obtain the entropy density of the null surface from its central charge. We use the off-shell Noether current corresponding to the diffeomorphism invariance of a gravitational Lagrangian L(g_ab,R_abcd) and define the Virasoro algebra from its variation. This allows us to identify the central charge and the zero-mode eigenvalue with which we obtain the entropy density of the Killing horizon. Our approach works for all Lanczos-Lovelock models and reproduces the correct Wald entropy. The entire analysis is done off-shell without using the field equations and allows us to define an entropy density for any null surface which acts as a local Rindler horizon for a particular class of observers.