Godina, Marco, Matteucci, Paolo and Vickers, James A.
Metric-affine gravity and the Nester-Witten 2-form
Journal of Geometry and Physics, 39, (4), . (doi:10.1016/S0393-0440(01)00007-9).
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In this paper we redefine the well-known metric-affine Hilbert Lagrangian in terms of a spin connection and a spin-tetrad. On applying the Poincaré–Cartan method and using the geometry of gauge-natural bundles, a global gravitational superpotential is derived. On specializing to the case of the Kosmann lift, we recover the result originally found by Kijowski [Gen. Rel. Gravity 9 (1978) (10) 857] for the metric (natural) Hilbert Lagrangian. On choosing a different, suitable lift, we can also recover the Nester–Witten 2-form, which plays an important role in the energy positivity proof and in many quasi-local definitions of mass.
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