On Spacetime Entanglement

TL;DR

This paper explores how holographic entanglement entropy in braneworld models aligns with the Bekenstein-Hawking area law, highlighting the role of curvature and extrinsic geometry in quantum gravity.

Contribution

It demonstrates the realization of finite entanglement entropy consistent with the area law in Randall-Sundrum II models and extends the analysis to include curvature-squared interactions.

Findings

Entanglement entropy matches the Wald entropy for large regions.

Extrinsic curvature terms appear in entanglement entropy but not in Wald entropy.

Limitations on the applicability of these results are discussed.

Abstract

We examine the idea that in quantum gravity, the entanglement entropy of a general region should be finite and the leading contribution is given by the Bekenstein-Hawking area law. Using holographic entanglement entropy calculations, we show that this idea is realized in the Randall-Sundrum II braneworld for sufficiently large regions in smoothly curved backgrounds. Extending the induced gravity action on the brane to include the curvature-squared interactions, we show that the Wald entropy closely matches the expression describing the entanglement entropy. The difference is that for a general region, the latter includes terms involving the extrinsic curvature of the entangling surface, which do not appear in the Wald entropy. We also consider various limitations on the validity of these results.