  We present spherically symmetric solutions to Einstein's equations which are
equivalent to canonical Schwarzschild and Reissner-Nordstrom black holes on the
exterior, but with singular (Planck-density) shells at their respective event
and inner horizons. The locally measured mass of the shell and the singularity
are much larger than the asymptotic ADM mass. The area of the shell is equal to
that of the corresponding canonical black hole, but the physical distance from
the shell to the singularity is a Planck length, suggesting a natural
explanation for the scaling of the black hole entropy with area. The existence
of such singular shells enables solutions to the black hole information problem
of Schwarzschild black holes and the Cauchy horizon problem of
Reissner-Nordstrom black holes. While we cannot rigorously address the
formation of these solutions, we suggest plausibility arguments for how normal
black hole solutions may evolve into such states. We also comment on the
possibility of negative mass Schwarzschild solutions that could be constructed
using our methods. Requirements for the non-existence of negative-mass
solutions may put restrictions on the types of singularities allowed in an
ultraviolet theory of gravity.
