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The maximal analytic Schwarzschild spacetime is manifestly inextendible as aLorentzian manifold with a twice continuously differentiable metric. In thispaper, we prove the stronger statement that it is even inextendible as aLorentzian manifold with a continuous metric. To capture the obstruction tocontinuous extensions through the curvature singularity, we introduce thenotion of the spacelike diameter of a globally hyperbolic region of aLorentzian manifold with a merely continuous metric and give a sufficientcondition for the spacelike diameter to be finite. The investigation oflow-regularity inextendibility criteria is motivated by the strong cosmiccensorship conjecture.

The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian Geometry