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Deformations of three-dimensional metrics

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Abstract

We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar field. We describe by this approach to deformation the results obtained by Coll et al. (Gen. Relativ. Gravit. 34:269, 2002), where it is stated that any three-dimensional metric was locally obtained as a deformation of a constant curvature metric parameterized by a 2-form. To this aim, we construct the corresponding deforming matrices and provide their classification according to the properties of the scalar \(\sigma \) and of the vector \(\mathbf {s}\) used in Coll et al. (Gen Relativ Gravit 34:269, 2002) to deform the initial metric. The resulting causal structure of the deformed geometries is examined, too. Finally we apply our results to a spherically symmetric three geometry and to a space sector of Kerr metric.

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Notes

  1. Capital latin letters \(A\) are tensorial indices while Latin letter \(a\) denote the tensorial character of each object i.e. they are spacetime indices.

  2. In units of \(c=G=1.\)

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Acknowledgments

D.P. gratefully acknowledges support from the Blanceflor Boncompagni-Ludovisi, née Bildt and wishes to thank the Angelo Della Riccia Foundation and thanks the institutional support of the Faculty of Philosophy and Science of the Silesian University of Opava. This work is partially supported by the INFN Iniziativa Specifica QGSKY “Quantum Universe”.

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Authors and Affiliations

  1. Faculty of Philosophy and Science, Institute of Physics, Silesian University in Opava, Bezručovo náměstí 13, 74601, Opava, Czech Republic

    Daniela Pugliese

  2. INFN, Sez. di Napoli, Complesso Universitario MSA via Cintia, 80126, Naples, Italy

    Cosimo Stornaiolo

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  1. Daniela Pugliese
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  2. Cosimo Stornaiolo
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Correspondence to Daniela Pugliese.

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Pugliese, D., Stornaiolo, C. Deformations of three-dimensional metrics. Gen Relativ Gravit 47, 20 (2015). https://doi.org/10.1007/s10714-015-1864-x

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