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An extendible spacetime admits a spacetime extension in the specified regularity class. A coordinate horizon need not obstruct an extension: the exterior Schwarzschild chart extends through its horizon in regular null coordinates. Maximality refers to extensions of the given spacetime, not to the mere absence of a singularity in one coordinate chart.

A maximal analytic extension of an analytic spacetime is an analytic spacetime extension admitting no further proper analytic extension as a regular spacetime of the same dimension. It is different from a maximal Cauchy development, which can end at a smooth Cauchy horizon. Additional global choices or quotients can affect uniqueness. The simply connected extension of positive-mass Schwarzschild spacetime through both horizons is the Kruskal spacetime; its curvature singularities remain boundaries.

A spacetime extension is an isometric embedding of a spacetime as a proper open subset of a larger connected spacetime with a nondegenerate Lorentzian metric. The allowed differentiability class must be specified: analytic, smooth and low-regularity extensions are different questions. Divergent curvature can obstruct a regular extension even when an incomplete geodesic has finite affine length.