Brown York charges at null boundaries

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by timelike hypersurfaces. We consider a generalization of this stress tensor to subregions bounded by null hypersurfaces. This stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle and satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the null boundary. For transformations that act covariantly on the boundary structures, the charges constructed from this Brown-York stress tensor coincide with canonical charges constructed from a version of the Wald-Zoupas procedure while for anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry. Comparing this stress tensor with the stress tensor of the celestial conformal field theory that is the putative holographic dual of quantum gravity in asymptotically flat spacetimes could provide further insights into the nature of flat space holography.