Nonlinear instability of the Reissner-Nordström Cauchy horizon under spherical perturbations

Consider smooth, spherically symmetric initial data with two asymptotically flat ends for the Einstein-Maxwell-scalar field equation, and suppose the data are globally close to Reissner-Nordström data. Nonlinear Cauchy-horizon instability conjecture. Generic such initial data give rise to solutions that are not in $W^{1,2}_{loc}$ near the Cauchy horizon. This is the nonlinear analogue of the paper's linear instability theorem. At the time of the source, it was not known whether a sufficiently regular solution with data close to Reissner-Nordström could become singular near the Cauchy horizon.