The angular momentum of the gravitational field and the Poincare group

Abstract

We redefine the gravitational angular momentum in the framework of the teleparallel equivalent of general relativity. In similarity to the gravitational energy-momentum, the new definition for the gravitational angular momentum is coordinate independent. By considering the Poisson brackets in the phase space of the theory, we find that the gravitational energy-momentum and angular momentum correspond to a representation of the Poincaré group. This result allows us to define Casimir type invariants for the gravitational field.

arXiv comment20 pages, no figures, accepted by Class. Quantum Gravity

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• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
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• Energy and Angular Momentum Densities in a Godel-Type Universe in the Teleparallel Geometry
• Energy Contents of Some Well-Known Solutions in Teleparallel Gravity
• On the gravitational angular momentum of rotating sources
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• The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass
• On Teleparallel Quantum Gravity in Schwarzschild Space-Time
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• The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes
• The angular momentum of plane-fronted gravitational waves in the teleparallel equivalent of general relativity
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• Teleparallel formalism of galilean gravity
• On Quantum Cosmology in Teleparallel Gravity
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