= Static patch of de Sitter spacetime
{title2=$ds^2=-(1-r^2/R^2)dt^2+dr^2/(1-r^2/R^2)+r^2d\Omega_2^2$}
This region $0\leq r<R$ of <de Sitter spacetime> is static for the central observer, with a cosmological <Killing horizon> at $r=R$. The central <proper time> fixes the normalization of $\partial_t$. Static observers have acceleration $r/(R^2\sqrt{1-r^2/R^2})$. Horizon-crossing null coordinates remove the coordinate singularity, while the global extension has compact spherical spatial slices and spacelike past/future conformal infinity.
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