Jonathan Luk: Linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations

It has long been suggested that solutions to linear scalar
wave equation on a fixed subextremal Reissner-Nordström spacetime with
non-vanishing charge are generically singular at the Cauchy horizon. We
prove that generic smooth and compactly supported initial data on a
Cauchy hypersurface indeed give rise to solutions with infinite
nondegenerate energy near the Cauchy horizon in the interior of the
black hole. This instability is related to the celebrated blue shift
effect in the interior of the black hole. The problem is motivated by
the strong cosmic censorship conjecture and it is expected that for the
full nonlinear Einstein-Maxwell system, this instability leads to a
singular Cauchy horizon for generic small perturbations of
Reissner-Nordström spacetime. Moreover, in addition to the instability
result, we also show as a consequence of the proof that Price’s law
decay is generically sharp along the event horizon. This is a joint work
with S.-J. Oh.