Singularities in rotating black holes coupled to a massless scalar field.

We employ a late-time expansion to study the interior of rotating black holes coupled to a massless scalar field in asymptotically flat spacetime. We find that decaying fluxes of scalar radiation into the black hole necessitate the existence of a null singularity at the Cauchy horizon and a central spacelike singularity at radius $r = 0$. In particular, the decaying influxes source a localized cloud of scalar radiation near $r=0$ whose amplitude grows unboundedly large as advanced time $v \to \infty$. The scalar cloud inevitably results in a central spacelike singularity at late times $v$, with the curvature near $r = 0$ diverging like $r^{-\alpha v}$, where $\alpha > 0$ is a constant.