  The BKL conjecture, stated in the 60s and early 70s by Belinski, Khalatnikov
and Lifshitz, proposes a detailed description of the generic asymptotic
dynamics of spacetimes as they approach a spacelike singularity. It predicts
complicated chaotic behaviour in the generic case, but simpler non-chaotic one
in cases with symmetry assumptions or certain kinds of matter fields.
  Here we construct a new class of four-dimensional vacuum spacetimes
containing spacelike singularities which show non-chaotic behaviour. In
contrast with previous constructions, no symmetry assumptions are made. Rather,
the metric is decomposed in Iwasawa variables and conditions on the asymptotic
evolution of some of them are imposed. The constructed solutions contain five
free functions of all space coordinates, two of which are constrained by
inequalities. We investigate continuous and discrete isometries and compare the
solutions to previous constructions. Finally, we give the asymptotic behaviour
of the metric components and curvature.
