Malament-Hogarth
Malament-Hogarth spacetimes are spacetimes defined by causal properties, usually in the context of the studies of supertasks (performing an infinite number of tasks in a finite time). They're defined by the presence of a timelike half-curve $\gamma_1$ and a timelike curve $\gamma_2$ going from a point $q$ to a point $p$ such that \begin{eqnarray} \int_{\gamma_1} d\tau &=& \infty\nonumber\\ \int_{\gamma_2} d\tau &<& \infty\nonumber \end{eqnarray} And $\gamma_1 \subset I^-(p)$.
1. History
2. Topology
3. Metrics and coordinates
4. Tensor quantities
5. Symmetries
6. Stress-energy tensor
7. Curves
8. Equations
9. Causal structure
By a theorem of X, Malament-Hogarth spacetimes cannot be globally hyperbolic, although they may be stably causal (Anti de Sitter space is an example of a M-H spacetime).