Homogeneous Lorentzian manifolds of a semisimple group

We describe the structure of dd-dimensional homogeneous Lorentzian GG-manifolds M=G/HM=G/H of a semisimple Lie group GG. Due to a result by N. Kowalsky, it is sufficient to consider the case when the group GG acts properly, that is the stabilizer HH is compact. Then any homogeneous space G/H̄ with a smaller group H̄⊂H admits an invariant Lorentzian metric. A homogeneous manifold G/HG/H with a connected compact stabilizer HH is called a minimal admissible manifold if it admits an invariant Lorentzian metric, but no homogeneous GG-manifold G/H̃ with a larger connected compact stabilizer H̃⊃H admits such a metric. We give a description of minimal homogeneous Lorentzian nn-dimensional GG-manifolds M=G/HM=G/H of a simple (compact or noncompact) Lie group GG. For n≤11n≤11, we obtain a list of all such manifolds MM and describe invariant Lorentzian metrics on MM.