Journal of High Energy Physics

, 2018:125 | Cite as

Symmetries and charges of general relativity at null boundaries

  • Venkatesa Chandrasekaran
  • Éanna É. Flanagan
  • Kartik Prabhu
Open Access
Regular Article - Theoretical Physics


We study general relativity at a null boundary using the covariant phase space formalism. We define a covariant phase space and compute the algebra of symmetries at the null boundary by considering the boundary-preserving diffeomorphisms that preserve this phase space. This algebra is the semi-direct sum of diffeomorphisms on the two sphere and a nonabelian algebra of supertranslations that has some similarities to supertranslations at null infinity. By using the general prescription developed by Wald and Zoupas, we derive the localized charges of this algebra at cross sections of the null surface as well as the associated fluxes. Our analysis is covariant and applies to general non-stationary null surfaces. We also derive the global charges that generate the symmetries for event horizons, and show that these obey the same algebra as the linearized diffeomorphisms, without any central extension. Our results show that supertranslations play an important role not just at null infinity but at all null boundaries, including non-stationary event horizons. They should facilitate further investigations of whether horizon symmetries and conservation laws in black hole spacetimes play a role in the information loss problem, as suggested by Hawking, Perry, and Strominger.


Black Holes Classical Theories of Gravity Space-Time Symmetries 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Venkatesa Chandrasekaran
    • 1
  • Éanna É. Flanagan
    • 2
    • 3
  • Kartik Prabhu
    • 3
  1. 1.Center for Theoretical Physics and Department of PhysicsUniversity of CaliforniaBerkeleyU.S.A.
  2. 2.Department of PhysicsCornell UniversityIthacaU.S.A.
  3. 3.Cornell Laboratory for Accelerator-based Sciences and Education (CLASSE)Cornell UniversityIthacaU.S.A.

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