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 perspec- tive of gravity, which accommodates this connection, the fluctuations around the equipartition value in the area elements will lead to a minimal quantum of area Oð1ÞL2 P, which will act as a regulator for this divergence. In a particular prescription for incorporating the L2 P as zero-point-area of spacetime, this does happen and the divergence in entanglement entropy is regularized, leading to S / A=L2 P 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.