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

✍ Scribed by Marco Godina; Paolo Matteucci; James A. Vickers

Book ID
104343013
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
105 KB
Volume
39
Category
Article
ISSN
0393-0440

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✦ Synopsis

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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