Brown-York charges at null boundaries

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.

Complexity equals anything II

“…The resulting null limit action agrees with the action for a subregion with null boundaries explored in detail in, e.g., [12,[29][30][31], up to corrections related to the surface gravity of the null surfaces. In particular, we will show that the null limit of the usual Gibbons-Hawking-York (GHY) boundary term is finite, as has recently been noted in [93]. We also examine the behaviour of the Hayward term, included for codimension-two corners of the subregion, and find that it diverges in the null limit.…”

Null boundary phase space: slicings, news and memory

“…For generic D there are numerous earlier constructions, see e.g. [9,[20][21][22][23][24][25][26][27][28][29], with a varying number of BDOF.…”

Relativistic fluids, hydrodynamic frames and their Galilean versus Carrollian avatars

“…Consider now a dynamical system on a Carrollian manifold M = R × S described with an (effective) action S = dt d d x √ a ΩL, functional of a ij , Ω and b i . The associated Carrollian momenta, which replace the corresponding relativistic energy-momentum tensor (2.7) are now (see [79,90]) 58…”

“…As a first and minor remark, the term in the right-hand side of (4.36) was missing in [79,90]. 59 More importantly, it has been claimed that both vectors, the energy current Π i and the momentum P i , should vanish [74,77].…”