  The maximal analytic Schwarzschild spacetime is manifestly inextendible as a
Lorentzian manifold with a twice continuously differentiable metric. In this
paper, we prove the stronger statement that it is even inextendible as a
Lorentzian manifold with a continuous metric. To capture the obstruction to
continuous extensions through the curvature singularity, we introduce the
notion of the spacelike diameter of a globally hyperbolic region of a
Lorentzian manifold with a merely continuous metric and give a sufficient
condition for the spacelike diameter to be finite. The investigation of
low-regularity inextendibility criteria is motivated by the strong cosmic
censorship conjecture.
