 Is there a spacetime which satisfies the definition? Yes. Let \(M\) be the two-dimensional plane in standard \(t,x\) coordinates. Let the metric \(g\) be such that the light cones are oriented in the \(t\) direction and open up as the absolute value of \(x\) approaches infinity. The resulting spacetime (Anti-de Sitter spacetime) is Malament-Hogarth (see Figure 2.2.2). 