$BM{S}_4$ Surface-Charge Algebra via Hamiltonian Framework

Abstract

Surface-charge algebra associated with BMS${}_4$ symmetry on the null infinity of asymptotically flat spacetime is studied via the Hamiltonian framework. A coordinate system, where boundaries of constant-time hypersurfaces cross the null infinity, is adopted. The equation itself which determines the variation of the surface charges turns out the same as that previously obtained via the covariant framework by Barnich and Troessaert, and is non-integrable for general radiation field $C_{AB}$. However, if $C_{AB}$ is independent of retarded time $u$, the variation equation is integrable and the conserved surface charges generate BMS${}_4$ algebra without central extension.

19 pages; ver2: a footnote and a reference added

References in corpus (8)

• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Aspects of the BMS/CFT correspondence
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• BMS charge algebra
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Comments on holographic current algebras and asymptotically flat four dimensional spacetimes at null infinity
• Brown-Henneaux's Canonical Approach to Topologically Massive Gravity

Cited by in corpus (3)

• Conserved charges of the extended Bondi-Metzner-Sachs algebra
• BMS Particles in Three Dimensions
• The Holographic Nature of Null Infinity