Penrose limits of homogeneous spaces
arXiv:math/0405506 · doi:10.1016/j.geomphys.2005.08.002
Abstract
We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sharp and conclude with a remark about the existence of null homogeneous geodesics.
16 pages, many changes particularly to sections 6 and 7
References in corpus (7)
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- Solvable model of strings in a time-dependent plane-wave background
- Solvable models of strings in homogeneous plane wave backgrounds
- Penrose Limits and Spacetime Singularities
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Cited by in corpus (10)
- Homogeneous geodesics in homogeneous Finsler spaces
- Locally homogeneous pp-waves
- Exact Parallel Waves in General Relativity
- Symmetric M-Theory Backgrounds
- Homogeneous geodesics of left invariant Finsler metrics
- The existence of light-like homogeneous geodesics in homogeneous Lorentzian manifolds
- Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
- Homogeneous Geodesics in Generalized Wallach Spaces
- On the Geometric Orbit Property for Lorentz Manifolds
- Pseudo-Riemannian Weakly Symmetric Manifolds