= Solution
Use the subextremal four-dimensional <Reissner-Nordstrom spacetime>, with $0<|Q|<M$. Its static radial function is
$$
f(r)=1-\frac{2M}{r}+\frac{Q^2}{r^2},\qquad r_\pm=M\pm\sqrt{M^2-Q^2}.
$$
Take the time-symmetric two-ended bridge through the outer <bifurcation surface>. Its <initial data> have $K_{ij}=0$ and
$$
h=f^{-1}dr^2+r^2d\Omega^2
$$
on each $r\ge r_+$ end. The bridge is smooth: in proper radial distance $s$, $r-r_+=f'(r_+)s^2/4+O(s^4)$. Each asymptotically flat end is an infinite <Riemannian distance> away. Hence the spatial <Riemannian manifold> is complete and admits no proper same-dimensional smooth <isometric extension> as a connected spatial manifold.
Its <maximal Cauchy development> includes the two exteriors and the adjacent future and past regions between $r_+$ and $r_-$. It ends at inner <Cauchy horizons>, not at a <curvature singularity>. Since the simple root at $r_-$ is removable in horizon-penetrating coordinates and all curvature invariants are finite there, the exact solution extends across these <Cauchy horizons>. The extension is no longer globally determined by the given <initial data>.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-311-cauchy-development.png]
{title=The maximal Cauchy development of a complete Reissner-Nordstrom bridge ends at extendible inner Cauchy horizons}
{height=500}
The shaded region is the <maximal Cauchy development>; dashed upper and lower null edges are inner <Cauchy horizons>. The displayed neighboring diamonds illustrate smooth continuation, rather than the entire infinite extension.
The <strong cosmic censorship conjecture> concerns generic admissible <initial data>, in a specified extension regularity. Exact charged spherical data are exceptional. Perturbations can produce <mass inflation> at the inner <Cauchy horizon>, obstructing suitably regular extensions; the precise conjecture depends on the matter model and whether extensions are required to be $C^0$, $C^2$, or another regularity. Thus this exact extendible example does not refute a generic <strong cosmic censorship conjecture>.
For an Einstein-Maxwell example the gravitational triple $(\Sigma,h,K)$ must be accompanied by electromagnetic <initial data>. One may take zero magnetic field and the smooth radial electric flux $Q/r^2$ through the bridge. The charges at the two ends have opposite signs when measured with outward normals. This is an example in the electrovacuum theory, not vacuum <initial data>.
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