Two-dimensional de Sitter spacetime
= Two-dimensional de Sitter spacetime
{title2=$ds^2=dt^2-\cosh^2t\,d\chi^2$}
Unit-radius <two-dimensional de Sitter spacetime> is the <hyperboloid> $(X^0)^2-(X^1)^2-(X^2)^2=-1$ in three-dimensional <Minkowski spacetime>. Its closed coordinates are $X^0=\sinh t$, $X^1=\cosh t\cos\chi$, $X^2=\cosh t\sin\chi$, with $t\in\mathbb R$ and $\chi$ periodic modulo $2\pi$. Unwrapping $\chi$ gives its universal covering spacetime instead.