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Metric-affine gravity and the Nester-Witten 2-form

Godina, Marco, Matteucci, Paolo and Vickers, James A. (2001) Metric-affine gravity and the Nester-Witten 2-form Journal of Geometry and Physics, 39, (4), pp. 265-275. (doi:10.1016/S0393-0440(01)00007-9).

Record type: Article


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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Published date: 2001
Keywords: Hilbert–Einstein Lagrangian, spinors, gauge-natural, superpotential


Local EPrints ID: 29334
ISSN: 0393-0440
PURE UUID: b005c20e-2047-4a22-8ff5-87061bb3bba8

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Date deposited: 10 May 2006
Last modified: 17 Jul 2017 15:58

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Author: Marco Godina
Author: Paolo Matteucci

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