Metric-affine gravity and the Nester-Witten 2-form
Metric-affine gravity and the Nester-Witten 2-form
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.
Hilbert–Einstein Lagrangian, spinors, gauge-natural, superpotential
265-275
Godina, Marco
35baf2fc-dd14-46ff-b0ac-098bd9770b09
Matteucci, Paolo
aa8b1ee7-e701-42c4-abae-37831e72d20f
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
2001
Godina, Marco
35baf2fc-dd14-46ff-b0ac-098bd9770b09
Matteucci, Paolo
aa8b1ee7-e701-42c4-abae-37831e72d20f
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
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), .
(doi:10.1016/S0393-0440(01)00007-9).
Abstract
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
Identifiers
Local EPrints ID: 29334
URI: http://eprints.soton.ac.uk/id/eprint/29334
ISSN: 0393-0440
PURE UUID: b005c20e-2047-4a22-8ff5-87061bb3bba8
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Date deposited: 10 May 2006
Last modified: 16 Mar 2024 02:34
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Contributors
Author:
Marco Godina
Author:
Paolo Matteucci
Author:
James A. Vickers
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