A longstanding open problem in mathematical physics has been that of finding an action principle for the Einstein–Weyl (EW) equations. In this paper, we present for the first time such an action principle in three dimensions in which the Weyl vector is not exact. More precisely, our model contains, in addition to the Weyl nonmetricity, a traceless part. If the latter is (consistently) set to zero, the equations of motion boil down to the EW equations. In particular, we consider a metric affine f(R) gravity action plus additional terms involving Lagrange multipliers and gravitational Chern–Simons contributions. In our framework, the metric and the connection are considered as independent objects, and no a priori assumptions on the nonmetricity and the torsion of the connection are made. The dynamics of the Weyl vector turns out to be governed by a special case of the generalized monopole equation, which represents a conformal self-duality condition in three dimensions.

An action principle for the Einstein–Weyl equations / S. Klemm, L. Ravera. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 158(2020 Dec), pp. 103958.1-103958.9. [10.1016/j.geomphys.2020.103958]

An action principle for the Einstein–Weyl equations

S. Klemm
;
2020

Abstract

A longstanding open problem in mathematical physics has been that of finding an action principle for the Einstein–Weyl (EW) equations. In this paper, we present for the first time such an action principle in three dimensions in which the Weyl vector is not exact. More precisely, our model contains, in addition to the Weyl nonmetricity, a traceless part. If the latter is (consistently) set to zero, the equations of motion boil down to the EW equations. In particular, we consider a metric affine f(R) gravity action plus additional terms involving Lagrange multipliers and gravitational Chern–Simons contributions. In our framework, the metric and the connection are considered as independent objects, and no a priori assumptions on the nonmetricity and the torsion of the connection are made. The dynamics of the Weyl vector turns out to be governed by a special case of the generalized monopole equation, which represents a conformal self-duality condition in three dimensions.
Chern–Simons actions; Einstein–Weyl equations; metric affine theories of gravity; modified theories of gravity; self-duality in odd dimensions; Weyl connection; high energy physics - theory; general relativity and quantum cosmology; mathematical physics; mathematics - differential geometry; mathematics - mathematical physics
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
http://arxiv.org/abs/2006.15890v1
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/828675
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