Area, entanglement entropy and supertranslations at null infinity

Abstract

The area of a cross-sectional cut of future null infinity () 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 to the future of . Under supertranslations, the renormalized area shifts by the supertranslation charge of . In quantum gravity, we conjecture a bound relating the renormalized area to the entanglement entropy across of the outgoing quantum state on .