The asymptopia of quasi-local mass and momentum. I. General formalism and stationary spacetimes

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Abstract
The quasi-local measures of mass and momentum introduced by Hawking, Ludvigsen and Vickers and Penrose are calculated for spheres near null infinity. Asymptotic expansion for the connection of an Einstein-Maxwell spacetime are obtained and an expansion of the 2-surface twistor equations is developed. Exact solutions are obtained for stationary spacetimes. For such spacetimes, unphysical contributions to the quasi-local mass found in the Hawking and Ludvigsen-Vickers definitions are eliminated in the twistor construction at the orders considered. In the twistor approach the total angular momentum contributes to the effective vacuum energy density and the absolutely conserved quantities associated with the Maxwell field contribute to the field momentum densities. The angular momentum twistor is found to have the required hermiticity properties with a particular choice of the twistor norm.

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