Area, Entanglement Entropy and Supertranslations at Null Infinity

TL;DR

This paper introduces a finite, renormalized area at null infinity in asymptotically flat spacetimes, linking it to modular energy, supertranslation charges, and conjecturing a bound with entanglement entropy in quantum gravity.

Contribution

It defines a renormalized area at null infinity, relates it to modular energy and supertranslations, and proposes a conjecture connecting it to entanglement entropy in quantum gravity.

Findings

Renormalized area depends on vacuum choice and supertranslations.

Relation established between renormalized area and modular energy including soft gravitons.

Conjecture proposed linking renormalized area to entanglement entropy.

Abstract

The area of a cross-sectional cut $\Sigma$ of future null infinity ($\mathcal{I}^+$) is infinite. We define a finite, renormalized area by subtracting the area of the same cut in any one of the infinite number of BMS-degenerate classical vacua. The renormalized area acquires an anomalous dependence on the choice of vacuum. We relate it to the modular energy, including a soft graviton contribution, of the region of $\mathcal{I}^+$ to the future of $\Sigma$. Under supertranslations, the renormalized area shifts by the supertranslation charge of $\Sigma$. In quantum gravity, we conjecture a bound relating the renormalized area to the entanglement entropy across $\Sigma$ of the outgoing quantum state on $\mathcal{I}^+$.