Brown-York charges at null boundaries

Journal Article · 09 January 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2022)029 · OSTI ID:1976424

Chandrasekaran, Venkatesa ^[1]; Flanagan, Éanna É. ^[2]; Shehzad, Ibrahim  ^[2]; Speranza, Antony J.  ^[3]

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1. University of California, Berkeley, CA (United States); Institute for Advanced Study, Princeton, NJ (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
2. Cornell University, Ithaca, NY (United States)
3. Perimeter Institute for Theoretical Physics, Waterloo (Canada); University of Illinois at Urbana-Champaign, IL (United States)

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 Tⁱ_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 hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.

• Research Organization: University of California, Oakland, CA (United States); University of California, Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); National Science foundation (NSF); Air Force Office of Scientific Research (AFOSR); Government of Canada; Simons Foundation
• Grant/Contract Number: SC0019380; AC02-05CH11231
• OSTI ID: 1976424
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English