Supertranslations at Timelike Infinity

Abstract

We propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. We present a detailed study of the asymptotic equations of motion and the action of supertranslations on asymptotic fields. We show that the Lee-Wald symplectic form $\Omega (g,{\delta }_{1}g,{\delta }_{2}g)$ does not get contributions from future timelike infinity with our boundary conditions. As a result, the "future charges" can be computed on any two-dimensional surface surrounding the sources at timelike infinity. We present expressions for supertranslation and Lorentz charges.

arXiv comment46 pages; v2 47 pages, refs + comments added, version to appear in JHEP

References in corpus (33)

• The Dynamics of General Relativity
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Soft Hair on Black Holes
• On BMS Invariance of Gravitational Scattering
• Aspects of the BMS/CFT correspondence
• BMS supertranslations and Weinberg's soft graviton theorem
• Asymptotic symmetries and subleading soft graviton theorem
• Superrotation Charge and Supertranslation Hair on Black Holes
• Supertranslations and Superrotations at the Black Hole Horizon
• Bondi-Sachs Formalism
• Symmetries and charges of general relativity at null boundaries
• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• Null infinity, the BMS group and infrared issues
• Asymptotic symmetries on Killing horizons
• The BMS4 algebra at spatial infinity
• Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes
• Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
• Black Hole Entropy from BMS Symmetry at the Horizon
• Relaxing the Parity Conditions of Asymptotically Flat Gravity
• Peeling or not peeling -- is that the question ?
• Asymptotics and Hamiltonians in a First order formalism
• Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity
• On the structure and applications of the Bondi-Metzner-Sachs group
• Null to time-like infinity Green's functions for asymptotic symmetries in Minkowski spacetime
• On Asymptotic Flatness and Lorentz Charges
• Celestial Holography: Lectures on Asymptotic Symmetries
• On the Stress Tensor for Asymptotically Flat Gravity
• Quantum BMS transformations in conformally flat space-times and holography
• Asymptotic symmetries and charges at spatial infinity in general relativity
• Timelike Infinity and Asymptotic Symmetry
• Supertranslations and Holographic Stress Tensor
• Generalized BMS Algebra at Timelike Infinity
• Horizon Hair from Inversion Symmetry