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Near a nondegenerate outgoing inner Cauchy horizon, a regular null coordinate behaves as $V_{-}\propto -e^{-{\kappa }_{-}v}$, where ${\kappa }_{-}>0$ is the magnitude of the inner-horizon surface gravity. Transforming stress components gives $T_{V_{-}{V}_{-}}\propto e^{2{\kappa }_{-}v}{T}_{vv}$. Even a small power-law tail can therefore cause an unbounded locally measured flux, motivating mass inflation.

Mass inflation is the growth of the interior effective mass and curvature near an inner Cauchy horizon under suitably perturbed black-hole data. It can obstruct regular spacetime extensions that exist for an exact Reissner-Nordstrom spacetime. The extension regularity matters: curvature blowup alone does not rule out every continuous-metric extension.

The inner horizon in the nonextreme Reissner-Nordstrom spacetime diagram is a Cauchy horizon. Radiation from exterior perturbations can approach it at arbitrarily late advanced time and undergo unbounded blueshift. Here its positive blueshift scale is ${\kappa }_{-}=(r_{+}^2-r_{-}^2)/r_{-}^3$. The inner-horizon blueshift coordinate behaves as $V_{-}\propto -e^{-{\kappa }_{-}v}$, soEven a decaying power-law tail can therefore generate divergent local flux. With counterstreaming radiation, backreaction produces mass inflation and curvature growth, rather than the smooth inner horizon of the exact solution.

This supports the strong cosmic censorship conjecture: a generically perturbed maximal Cauchy development is expected to lose the smooth extension across its Cauchy horizon, restoring predictability in the appropriate regularity class. The exact smooth inner horizon is unstable, not a robust failure of deterministic evolution. Curvature divergence supports an obstruction to a $C^2$ metric extension; it does not by itself exclude every continuous metric extension. The regularity class is part of the conjecture, and the blueshift argument is evidence, not a general theorem proving it.

Use the subextremal four-dimensional Reissner-Nordstrom spacetime, with $0<|Q|<M$. Its static radial function isTake the time-symmetric two-ended bridge through the outer bifurcation surface. Its initial data have $K_{ij}=0$ andon each $r\ge r_{+}$ end. The bridge is smooth: in proper radial distance $s$, $r-r_{+}=f^{\prime }(r_{+})s^2/4+O(s^4)$. 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.

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.