On the Architecture of Spacetime Geometry

Abstract

We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein-Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity and loop quantum gravity, as well as the AdS/CFT correspondence.

Figures (1)

• Figure 1: (Colour Online) Consider a region $A$ on a Cauchy slice of some smooth background geometry. The density matrix $\rho_{ A}$ controls the physics throughout the causal domain $\cal D$. This geometry varies only on some large distance scales $L_{\text{geom}}$. We consider a spacetime region $\Gamma$ of size $L_{\text{reg}}\ll L_{\text{geom}}$ near the entangling surface $\Sigma$. Within this region, the spacetime looks like flat space and the light sheets defining $\partial\cal D$ look like Rindler horizons.