Abstract: We consider solutions of the scalar wave equation □_gφ = 0, without symmetry, on fixed subextremal Reissner-Nordström backgrounds (M, g). Previously, it has been shown that for φ arising from sufficiently regular data on a two ended Cauchy hypersurface, the solution and its derivatives decay suitably fast on the event horizon H⁺. Using this, we show here that φ is in fact uniformly bounded, |φ| < C in the black hole interior up to and including the bifurcate Cauchy horizon CH⁺
The proof depends on novel weighted energy estimates in the black hole interior which, in combination with commutation by angular momentum operators and Sobolev embedding, yield uniform pointwise estimates.