= Analytic extension of a spacetime
= Analytic extensions of a spacetime
{synonym}
An analytic extension embeds a spacetime isometrically as a proper open region in a larger analytic <Lorentzian manifold> with a nondegenerate <metric tensor>. A divergence of coordinate components does not obstruct extension if a new chart makes all metric coefficients analytic and the determinant nonzero. For a static spherical metric with an analytic lapse $f$ and a positive simple horizon radius, ingoing coordinates replace $-f\,dt^2+dr^2/f$ by $-f\,dv^2+2\,dv\,dr$. This removes the <coordinate singularity> at $f=0$; transverse metric coefficients must also remain regular. An extension across such a horizon is distinct from extending through a <curvature singularity>.
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