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Journal of High Energy Physics

, 2019:229 | Cite as

Symmetries, charges and conservation laws at causal diamonds in general relativity

  • Venkatesa Chandrasekaran
  • Kartik PrabhuEmail author
Open Access
gular Article - Theoretical Physics
  • 13 Downloads

Abstract

We study the covariant phase space of vacuum general relativity at the null boundary of causal diamonds. The past and future components of such a null boundary each have an infinite-dimensional symmetry algebra consisting of diffeomorphisms of the 2-sphere and boost supertranslations corresponding to angle-dependent rescalings of affine parameter along the null generators. Associated to these symmetries are charges and fluxes obtained from the covariant phase space formalism using the prescription of Wald and Zoupas. By analyzing the behavior of the spacetime metric near the corners of the causal diamond, we show that the fluxes are also Hamiltonian generators of the symmetries on phase space. In particular, the supertranslation fluxes yield an infinite family of boost Hamiltonians acting on the gravitational data of causal diamonds. We show that the smoothness of the vector fields representing such symmetries at the bifurcation edge of the causal diamond implies suitable matching conditions between the symmetries on the past and future components of the null boundary. Similarly, the smoothness of the spacetime metric implies that the fluxes of all such symmetries are conserved between the past and future components of the null boundary. This establishes an infinite set of conservation laws for finite subregions in gravity analogous to those at null infinity. We also show that the symmetry algebra at the causal diamond has a non-trivial center corresponding to constant boosts. The central charges associated to these constant boosts are proportional to the area of the bifurcation edge, for any causal diamond, in analogy with the Wald entropy formula.

Keywords

Classical Theories of Gravity Space-Time Symmetries 

Notes

Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Theoretical Physics and Department of PhysicsUniversity of CaliforniaBerkeleyU.S.A.
  2. 2.Cornell Laboratory for Accelerator-based Sciences and Education (CLASSE)Cornell UniversityIthacaU.S.A.

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