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

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
0393-0440
265-275
Godina, Marco
35baf2fc-dd14-46ff-b0ac-098bd9770b09
Matteucci, Paolo
aa8b1ee7-e701-42c4-abae-37831e72d20f
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
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), 265-275. (doi:10.1016/S0393-0440(01)00007-9).

Record type: Article

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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More information

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
ORCID for James A. Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 10 May 2006
Last modified: 09 Jan 2022 02:33

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Contributors

Author: Marco Godina
Author: Paolo Matteucci

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