Stress Tensor on Null Boundaries

TL;DR

This work extends the Brown-York quasilocal stress-tensor framework to null boundaries by employing a general double-foliation formalism, enabling a well-posed variational principle and a BY-like stress tensor on null surfaces. The null-boundary stress tensor yields quasilocal energy and angular momentum densities defined through the scalar momentum $\Xi$ and related geometric data, with explicit results for Minkowski, Schwarzschild, AdS-Schwarzschild, and slow-rotating spacetimes, and reproduces the Bondi mass in the asymptotically flat case. A reference term $\mathcal{S}_0$ and a proposed null-boundary counterterm allow finite energies without embedding difficulties, offering a parallel to the AdS counterterm method in flat space. The approach suggests potential connections to flat-space holography and gravity in the light-front, and provides a practical tool for analyzing quasilocal gravitational observables on null boundaries.

Abstract

Using the Brown-York prescription for the definition of quasilocal gravitational energy-momentum tensor on a boundary and also complete canonical structure on a null boundary which has been found recently \cite{Aghapour:2018icu}, we propose a similar stress tensor on the null boundary. Then we exploit this stress tensor to compute the quasi-local energy and angular momentum for some well-known gravitational solutions. We have found that in addition to reference spacetime method for regularizing total energy, in the case of null boundary we can add a possible counterterm so avoiding embedding difficulties.

Figures (3)

• Figure 1: Space time region with timelike and spacelike boundaries
• Figure 2: Non-orthogonal boundaries.
• Figure 3: Space-Time region with a null and space-like boundaries