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), 265-275. (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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0393-0440(01)00007-9
ISSNs: 0393-0440 (print)
Related URLs:
Keywords: Hilbert–Einstein Lagrangian, spinors; gauge-natural, superpotential
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 29334
Accepted Date and Publication Date:
Date Deposited: 10 May 2006
Last Modified: 31 Mar 2016 11:54

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