The wave equation on black hole interiors

Abstract

We consider solutions of the massless scalar wave equation, without symmetry, on fixed subextremal Reissner-Nordstrom backgrounds with nonvanishing charge. Previously, it has been shown that for solutions arising from sufficiently regular data on a two ended Cauchy hypersurface, the solution and its derivatives decay suitably fast on the event horizon . Using this, we show here that the solutions are in fact uniformly bounded in the black hole interior up to and including the bifurcate Cauchy horizon . The proof depends on novel weighted energy estimates in the black hole interior which, in combination with commutation by angular momentum operators and application of Sobolev embedding, yield uniform pointwise estimates. This problem is related to the Strong Cosmic Censorship Conjecture.