Brown-York charges at null boundaries

• Published in: arXiv.org 2022-04
• Main Authors: Chandrasekaran, Venkatesa, Flanagan, Eanna E, Ibrahim, Shehzad, Speranza, Antony J
• Format: Article
• Language: English
• Subjects: Conservation equations; Dirichlet problem; Hyperspaces; Mathematical analysis; Relativity; Rigging; Stress tensors; Tensors; Transformations (mathematics)
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2109.11567

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.