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.