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

Abstract

The calculation of entanglement entropy S of quantum fields in spacetimes with horizon shows that, quite generically, S is (a) proportional to the area A of the horizon and (b) 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 O(1)L_P², which will act as a regulator for this divergence. In a particular prescription for incorporating the L_P² as zero-point-area of spacetime, this does happen and the divergence in entanglement entropy is regularized, leading to S A/L_P² in Einstein gravity. In more general models of gravity, the surface density of microscopic degrees of freedom is different which leads to a modified regularization procedure and the possibility that the entanglement entropy - when appropriately regularized - matches the Wald entropy.