Towards a general description of the interior structure of rotating
  black holes
  The purpose of this paper is to present a number of proposals about the
interior structure of a rotating black hole that is accreting slowly, but in an
arbitrary time- and space-dependent fashion. The proposals could potentially be
tested with numerical simulations. Outgoing and ingoing particles free-falling
in the parent Kerr geometry become highly focused along the principal outgoing
and ingoing null directions as they approach the inner horizon, triggering the
mass inflation instability. The original arguments of Barrabes, Israel &
Poisson (1990) regarding inflation in rotating black holes are reviewed, and
shown to be based on Raychauduri's equation applied along the outgoing and
ingoing null directions. It is argued that gravitational waves should behave in
the geometric optics limit, and consequently that the spacetime should be
almost shear-free. A full set of shear-free equations is derived. A specific
line-element is proposed, which is argued should provide a satisfactory
approximation during early inflation. Finally, it is argued that
super-Planckian collisions between outgoing and ingoing particles will lead to
entropy production, bringing inflation to an end, and precipitating collapse.
