Finite entanglement entropy from the zero-point-area of spacetime

TL;DR

This paper proposes that the divergence in entanglement entropy near horizons is regularized by a minimal quantum of area, leading to finite entropy proportional to horizon area over Planck length squared, linking quantum spacetime structure to gravity.

Contribution

It introduces a zero-point-area concept as a regulator for entanglement entropy divergence, connecting horizon thermodynamics with emergent gravity and microscopic degrees of freedom.

Findings

Entanglement entropy is proportional to horizon area divided by Planck length squared.

Regularization via zero-point-area yields finite entropy matching Wald entropy in general gravity models.

Divergence in entanglement entropy indicates deep links between quantum spacetime and gravitational dynamics.

Abstract

The calculation of entanglement entropy S of quantum fields in spacetimes with horizon shows that, quite generically, S (a) is proportional to the area A of the horizon and (b) is divergent. I argue that this divergence, which arises even in the case of Rindler horizon in flat spacetime, is yet another indication of a deep connection between horizon thermodynamics and gravitational dynamics. In an emergent perspective of gravity, which accommodates this connection, the fluctuations around the equipartition value in the area elements will lead to a minimal quantum of area, of the order of L_P^2, which will act as a regulator for this divergence. In a particular prescription for incorporating L_P^2 as zero-point-area of spacetime, this does happen and the divergence in entanglement entropy is regularized, leading to S proportional to (A/L_P^2) in Einstein gravity. In more general models of gravity, the surface density of microscopic degrees of freedom is different which leads to a modified regularisation procedure and the possibility that the entanglement entropy - when appropriately regularised - matches the Wald entropy.