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 Tij 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 hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.
Highlights
The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface
This paper has presented a novel expression for a Brown-York stress tensor associated with null hypersurfaces in general relativity and has established its two key features: covariant
For the field space considered in CFP, which imposes boundary conditions fixing ni and k, this happens to agree with the Dirichlet variational principle adopted in the present paper
Summary
Latin letters from the beginning of the alphabet a, b, c, . . . are used to denote spacetime tensor indices, while those from the middle of the alphabet i, j, k, . . . are used for tensors defined on a timelike or null bounding hypersurface. Are used for tensors defined on a timelike or null bounding hypersurface. Are used to denote spacetime tensor indices, while those from the middle of the alphabet i, j, k, . Differential forms such as the spacetime volume form or hypersurface volume form η are often written with indices suppressed. When denoting a contraction on one or more indices, we will use the shorthand a to indicate the indices which are contracted, while continuing to suppress the remaining indices. We use the notation iV for contraction with a vector V a into a differential form
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