Conformal cylinder of two-dimensional de Sitter spacetime
= Conformal cylinder of two-dimensional de Sitter spacetime
{title2=$ds^2=\sec^2T(dT^2-d\chi^2),\quad -\pi/2<T<\pi/2$}
The <conformal time> $T=2\arctan(e^t)-\pi/2$ satisfies $\sin T=\tanh t$ and $\cos T=\operatorname{sech}t$. Multiplying the physical metric by $\cos^2T$ gives a finite <conformal compactification> with periodic spatial coordinate. Its past and future conformal boundaries are spacelike circles. <Null geodesics> have slopes $d\chi/dT=\pm1$.