Symmetries and charges of general relativity at null boundaries

Abstract

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.

v3: minor error in Sec. 5.3 corrected; v2: added appendices on trivial diffeomorphisms and relation to 1810.01847; v1: 59 pages + appendices, 2 figures

References in corpus (11)

• Gravitational action with null boundaries
• Surface charge algebra in gauge theories and thermodynamic integrability
• New symmetries for the Gravitational S-matrix
• Null Conservation Laws for Gravity
• Gravitational Memory in Higher Dimensions
• Fock representation of gravitational boundary modes and the discreteness of the area spectrum
• A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
• On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries
• Conservation of asymptotic charges from past to future null infinity: Maxwell fields
• Horizon supertranslation and degenerate black hole solutions
• Supertranslations and Holography near the Horizon of Schwarzschild Black Holes

Cited by in corpus (92)

• Carrollian Physics at the Black Hole Horizon
• Carroll Structures, Null Geometry and Conformal Isometries
• Bridging Carrollian and Celestial Holography
• Covariant phase space with boundaries
• Spacetime structure near generic horizons and soft hair
• Black Hole Entropy and Soft Hair
• The $\Lambda$-BMS${}_4$ Charge Algebra
• The Weyl BMS group and Einstein's equations
• Extended corner symmetry, charge bracket and Einstein's equations
• Generalized BMS charge algebra
• Null boundary phase space: slicings, news and memory
• Isolated Surfaces and Symmetries of Gravity
• Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Black hole memory effect
• Gravitational Edge Modes, Coadjoint Orbits, and Hydrodynamics
• Persistent gravitational wave observables: general framework
• Brown-York charges at null boundaries
• Gravity from symmetry: Duality and impulsive waves
• A general framework for gravitational charges and holographic renormalization
• T-Witts from the horizon
• Conservation and Integrability in Lower-Dimensional Gravity
• Carrollian hydrodynamics from symmetries
• Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity
• Null Surface Thermodynamics
• BMS-like symmetries in cosmology
• Charges and Fluxes on (Perturbed) Non-expanding Horizons
• The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity
• Generalized Black Hole Entropy is von Neumann Entropy
• Black Hole Memory
• Null infinity as an open Hamiltonian system
• Non-Expanding horizons: Multipoles and the Symmetry Group
• Wald-Zoupas prescription with (soft) anomalies
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Persistent gravitational wave observables: Nonlinear plane wave spacetimes
• Symmetries, charges and conservation laws at causal diamonds in general relativity
• Ambiguity resolution for integrable gravitational charges
• Asymptotics with a positive cosmological constant: IV. The `no-incoming radiation' condition
• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
• Affine-null metric formulation of General Relativity at two intersecting null hypersurfaces
• Quantum Null Geometry and Gravity
• "Conserved charges" of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory
• Renormalization of conformal infinity as a stretched horizon
• Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves
• Null Infinity as a Weakly Isolated Horizon
• Horizons and Null Infinity: A Fugue in 4 voices
• On Symplectic Form for Null Boundary Phase Space
• Virasoro hair and entropy for axisymmetric Killing horizons
• Angular momentum at null infinity in Einstein-Maxwell theory
• Null Infinity and Horizons: A New Approach to Fluxes and Charges
• Generating functional for gravitational null initial data
• Can we detect a supertranslated black hole?
• Covariant canonical formulations of classical field theories
• Memory effect and BMS symmetries for extreme black holes
• Gravitational memory: new results from post-Newtonian and self-force theory
• Cosmic branes and asymptotic structure
• Corner symmetry and quantum geometry
• Displacement memory effect near the horizon of black holes
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• Infrared Effects in the Late Stages of Black Hole Evaporation
• A generalization of the quadruple formula for the energy of gravitational radiation in de Sitter spacetime
• Supertranslations at Timelike Infinity
• Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• Horizon Hair from Inversion Symmetry
• Quantum Area Fluctuations from Gravitational Phase Space
• Asymptotic Limit of Null Hypersurfaces
• Gravitational-wave energy and other fluxes in ghost-free bigravity
• One-loop partition function of gravity with leaky boundary conditions
• Apparent Horizons Associated with Dynamical Black Hole Entropy
• On black hole supertranslations and hydrodynamic enstrophy
• On Super-Translation transition between Quasi-local Black holes
• Null Surface Thermodynamics in Topologically Massive Gravity
• On the Charge Algebra of Causal Diamonds in Three Dimensional Gravity
• Can the Near-Horizon Black Hole Memory be detected through Binary Inspirals?
• Constants of motion in gravitational self-force theory
• A twistorial description of BMS symmetries at null infinity
• Weakly Isolated Horizons: $3+1$ decomposition and canonical formulations in self-dual variables
• Supertranslations at Spatial and Timelike Infinities in the First-Order Formalism
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Null infinity as a Killing horizon
• Using thermodynamics to learn gravitational wave physics
• Barnich-Troessaert Bracket as a Dirac Bracket on the Covariant Phase Space
• Dynamical horizons and Super-Translation transitions of the horizon
• Covariant phase space with null boundaries
• Hamiltonian BRST formalism for gauge fields on black hole spacetimes
• All near-horizon symmetries of the Schwarzschild black hole in linearised gravity
• News tensor on null hypersurfaces
• Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics
• Superrotations are Linkages
• The integrability of Virasoro charges for axisymmetric Killing horizons