Spacetimes with continuous local isotropies
Abstract
General relativistic spacetimes in which at every point p in some neighbourhood W the tangent space Tp is invariant under the same continuous subgroup g of the Lorentz group are considered. Some previously open problems for such spacetimes are discussed and solved, and a comprehensive survey of such spacetimes is provided. For most cases, invariance of the curvature and its first covariant derivative under g imply the existence of an isometry group in W containing g as an isotropy group. In the remaining cases, invariance of second and third derivatives may be required for this implication, and in particular, the necessity of invariance of the third derivative is proved for the locally rotationally symmetric spacetimes discussed by Ellis and by Stewart and Ellis.
| You currently do not have access to the full text article. |
|---|
