an:06467203
Zbl 1317.83063
Pugliese, Daniela; Stornaiolo, Cosimo
Deformations of three-dimensional metrics
EN
Gen. Relativ. Gravitation 47, No. 3, Paper No. 20, 23 p. (2015).
0001-7701 1572-9532
2015
j
83C80 53Z05 83C57
space-time deformations; scalar fields; three-dimensional metrics; conformal methods
Summary: 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 \textit{B. Coll} et al. [Gen. Relativ. Gravitation 34, No. 2, 269--282 (2002; Zbl 1008.53039)], 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. [loc. cit.] 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.
1008.53039