Affine generalization of the Komar complex of general relativity

Mathematics – Logic

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Quantum Gravity

Scientific paper

On the basis of the ``on shell'' Noether identities of the metric-affine gauge approach of gravity, an affine superpotential is derived which comprises the energy- and angular-momentum content of exact solutions. In the special case of general relativity (GR) or its teleparallel equivalent, the Komar or Freud complex, respectively, are recovered. Applying this to the spontaneously broken anti-de Sitter gauge model of McDowell and Mansouri with an induced Euler term automatically yields the correct mass and spin of the Kerr-AdS solution of GR with a (induced) cosmological constant without the factor two discrepancy of the Komar formula.

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