  We construct a large class of vacuum solutions of the Einstein equations
without any symmetries and with controlled asymptotics near a timelike
singularity. The solutions are obtained by a Fuchs analysis of the equations
which evolve the metric in a spacelike direction.
  We further observe that the changes of signs of some of the terms (walls) in
the associated Hamiltonian invalidate the "cosmological billards" heuristic
arguments for existence of singularities of mixmaster type in the current
context.
