Brown-York charges at null boundaries

TL;DR

This paper extends the Brown-York stress tensor to null hypersurfaces in general relativity, providing a simple, covariantly conserved expression that aligns with known charges and has applications in asymptotic symmetries and holography.

Contribution

It introduces a novel null hypersurface Brown-York stress tensor derived from the on-shell action, which is independent of auxiliary null vectors and compatible with covariant conservation.

Findings

The null Brown-York tensor has a simple, auxiliary-vector-independent form.

Charges derived match canonical charges for covariant transformations.

Differences in charges for anomalous transformations are explicitly characterized.

Abstract

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor $T{}^i{}_j$ takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hypersurfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.