= Universal cover of two-dimensional de Sitter spacetime
{title2=$ds^2=\sec^2\eta(-d\eta^2+d\xi^2),\quad\xi\in\mathbb R$}
The unrestricted spatial coordinate unwraps the spatial circle of <two-dimensional de Sitter spacetime>. The <conformal time> $\eta=\arcsin(\tanh t)$ lies in $(-\pi/2,\pi/2)$, and <null geodesics> have slopes $d\xi/d\eta=\pm1$. Constant-$\eta$ lines are <Cauchy hypersurfaces>: along any causal curve $|d\xi/d\eta|\leq1$, so a curve cannot escape to spatial infinity in a bounded conformal-time interval. The covering spacetime is therefore <globally hyperbolic>, despite its observer-dependent cosmological horizons. Identifying $\xi$ modulo $2\pi$ gives the de Sitter cylinder, also globally hyperbolic.
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