Asymptotic Limit of Null Hypersurfaces

TL;DR

This paper investigates the asymptotic behavior of null hypersurfaces in asymptotically flat spacetimes, revealing connections between the null Raychaudhuri equation, Bondi mass-loss, and Carrollian stress tensors at null infinity.

Contribution

It establishes the asymptotic limits of null hypersurfaces, linking finite-distance null physics to null infinity and connecting the Raychaudhuri constraint with the Bondi mass-loss formula.

Findings

Null Raychaudhuri constraint asymptotes to Bondi mass-loss formula.

Null Brown-York tensor yields Carrollian stress tensor at null infinity.

Finite-distance null phase space approaches Ashtekar-Streubel phase space.

Abstract

We study null hypersurfaces approaching null infinity in asymptotically flat spacetimes within the Bondi-Sachs gauge. The null Raychaudhuri constraint is shown to asymptote to the Bondi mass-loss formula, interpreted as a stress tensor conservation law. This stress tensor, the null Brown-York tensor, yields a Carrollian stress tensor at null infinity from the bulk. Furthermore, we establish that the canonical phase space on finite-distance null hypersurfaces asymptotes to the Ashtekar-Streubel phase space. This connection between finite-distance null physics and null infinity unveils promising insights.