Deformations of three-dimensional metrics

Abstract

We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar fields. We describe by this approach to deformation the results obtained by Coll et al. in [1], 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 [1] 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.

arXiv comment22 pages, 6 Tables

References in corpus (18)

• The Black Hole in Three Dimensional Space Time
• Extended Theories of Gravity
• Geometry of the 2+1 Black Hole
• Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
• A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies
• Kerr-Schild Symmetries
• Three-dimensional metrics as deformations of a constant curvature metric
• A review about Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry
• Space-time deformations as extended conformal transformations
• The extended Conformal Einstein field equations with matter: the Einstein-Maxwell field
• Flat deformation theorem and symmetries in spacetime
• Reference frames and rigid motions in relativity
• Two-step spacetime deformation induced dynamical torsion
• On the degrees of freedom of a semi-Riemannian metric
• A class of conformal curves in the Reissner-Nordström spacetime
• Small deformations of extreme Kerr black hole initial data
• Reference frames and rigid motions in relativity: Applications
• Flat deformation of a spacetime admitting two Killing fields