On a geometric interpretation of the 1/4 factor in black hole entropy

Abstract

The Bekenstein--Hawking entropy $S = k_B A/4\lp^2$ contains a coefficient $1/4$ that has been calculated by many approaches to quantum gravity. We show that this factor arises from the causal geometry of any null boundary in a four-dimensional Lorentzian spacetime. A heuristic accessibility argument is supported by a purely geometric derivation using the canonical symplectic structure on the cotangent bundle and the causal splitting of the space of null rays. No gravitational field equations are invoked.

Accepted for publication in CQG. 11 pages. 1 figure