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We prove that a large class of smooth solutions $\psi$ to the linear waveequation $\Box_g\psi=0$ on subextremal rotating Kerr spacetimes which areregular and decaying along the event horizon become singular at the Cauchyhorizon. More precisely, we show that assuming appropriate upper and lowerbounds on the energy along the event horizon, the solution has infinite(non-degenerate) energy on any spacelike hypersurfaces intersecting the Cauchyhorizon transversally. Extrapolating from known results in theReissner--Nordstr\"om case, the assumed upper and lower bounds required for ourtheorem are conjectured to hold for solutions arising from generic smooth andcompactly supported initial data on a Cauchy hypersurface. This result ismotivated by the strong cosmic censorship conjecture in general relativity.

Instability results for the wave equation in the interior of Kerr black holes