Area, Entanglement Entropy and Supertranslations at Null Infinity

TL;DR

The paper introduces a finite renormalized area for cuts of null infinity by subtracting areas in fiducial BMS vacua, revealing an anomalous vacuum dependence tied to the vacuum data. It links this renormalized area to the modular energy, including soft graviton contributions, and shows how it transforms under BMS supertranslations. By generalizing the subtraction to allow an arbitrary fiducial vacuum, it argues that the full modular energy (hard plus soft) governs the transformation, and it conjectures a bound relating the renormalized area to the entanglement entropy across the cut, suggesting a second-law-like statement for information flow at null infinity with potential implications for the black hole information paradox.

Abstract

The area of a cross-sectional cut $Σ$ 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 $Σ$. Under supertranslations, the renormalized area shifts by the supertranslation charge of $Σ$. In quantum gravity, we conjecture a bound relating the renormalized area to the entanglement entropy across $Σ$ of the outgoing quantum state on $\mathcal{I}^+$.