Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 54 3 f Solution Created 2026-10-03 Updated 2026-10-06
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 . The inner-horizon blueshift coordinate behaves as , 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 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.