# Gravitational fields with a non-Abelian, bidimensional Lie algebra of symmetries

@article{Sparano2001GravitationalFW, title={Gravitational fields with a non-Abelian, bidimensional Lie algebra of symmetries}, author={Giovanni Sparano and Gaetano Vilasi and Alexandre M. Vinogradov}, journal={Physics Letters B}, year={2001}, volume={513}, pages={142-146} }

## 23 Citations

### Einstein Metrics with Two-Dimensional Killing Leaves and Their Applications in Physics

- Mathematics
- 2011

Solutions of vacuum Einstein’s field equations, for the class of pseudo-Riemannian four-metrics admitting a non Abelian two dimensional Lie algebra of Killing fields, are explicitly described. When…

### Geometric and physical properties of Einstein metrics with 2-dimensional Killing leaves ∗

- Physics
- 2006

Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of a sub-class of these gravitational fields…

### Gravitational Fields with 2-Dimensional Killing Leaves and the Gravitational Interaction of Light

- Physics
- 2010

Gravitational fields invariant for a non Abelian Lie algebra generating a 2-dimensional distribution, are explicitly described. When the orthogonal distribution is integrable and the metric is not…

### Spin-1 gravitational waves. Theoretical and experimental aspects

- Physics
- 2005

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their…

### Gravitational waves as exact solutions of Einstein field equations

- Physics, Mathematics
- 2007

Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. A sub-class of these gravitational fields have a wave-like…

### ON THE POLARIZATION OF GRAVITATIONAL WAVES

- Physics
- 2013

Physical properties of gravitational waves, belonging to the larger class of exact solutions of Einstein field equations which are invariant for a non-Abelian two-dimensional Lie algebra of Killing…

### Ricci Flat 4-Metrics with Bidimensional Null Orbits

- Mathematics, Physics
- 2006

Pseudo-Riemannian \(4\)-metrics with bidimensional null Killing orbits are studied. Both Lorentzian and Kleinian (or neutral) cases, are treated simultaneously. Under the assumption that the…

### Ricci Flat 4-Metrics with Bidimensional Null Orbits

- Mathematics, Physics
- 2006

Pseudo-Riemannian $4$-metrics with bidimensional null Killing orbits are studied. Both Lorentzian and Kleinian (or neutral) cases, are treated simultaneously. Under the assumption that the…

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A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex…

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