On the Architecture of Spacetime Geometry

TL;DR

This paper suggests that entanglement entropy can be used to understand the structure of spacetime in quantum gravity, showing it follows an area law consistent with the Bekenstein-Hawking formula across various models.

Contribution

It introduces entanglement entropy as a universal probe of spacetime architecture, supported by evidence from multiple approaches in quantum gravity.

Findings

Entanglement entropy obeys an area law in smooth spacetimes.

The entropy aligns with the Bekenstein-Hawking formula.

Support from perturbative quantum gravity, loop quantum gravity, and AdS/CFT.

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.