Causal Boundary Entropy From Horizon Conformal Field Theory

Abstract

The quantum theory of near horizon regions of spacetimes with classical spatially flat, homogeneous and isotropic Friedman-Robertson-Walker geometry can be approximately described by a two dimensional conformal field theory. The central charge of this theory and expectation value of its Hamiltonian are both proportional to the horizon area in units of Newton's constant. The statistical entropy of horizon states, which can be calculated using two dimensional state counting methods, is proportional to the horizon area and depends on a numerical constant of order unity which is determined by Planck scale physics. This constant can be fixed such that the entropy is equal to a quarter of the horizon area in units of Newton's constant, in agreement with thermodynamic considerations.