Lorentzian Homogeneous Ricci-Flat Metrics on Almost Abelian Lie Groups
Lorentzian Homogeneous Ricci-Flat Metrics on Almost Abelian Lie Groups
We study Lorentzian left-invariant metrics on almost abelian Lie groups of dimensions larger than three. An almost abelian Lie group is a Lie group whose Lie algebra has a codimension one abelian ideal. Ricci-flat and non-flat conditions on the Lie algebra are derived. In particular, we generalize the four-dimensional Petrov solution to arbitrarily higher dimensions.
15 pages, no figures
Mathematics - Differential Geometry, High Energy Physics - Theory, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), FOS: Mathematics, FOS: Physical sciences, Primary 53B30, Secondary 53C30, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology
Mathematics - Differential Geometry, High Energy Physics - Theory, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), FOS: Mathematics, FOS: Physical sciences, Primary 53B30, Secondary 53C30, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology
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