The nature of gravitational singularities, long mysterious, 
has become more clear in recent years due to a combination 
of mathematical and numerical methods.  These indicate that 
as the singularity is approached spatial derivative terms in 
the equations of motion become unimportant compared to time 
derivative terms.  This reduces the equations to the well 
studied equations of homogeneous spacetimes, with their 
corresponding (generally) oscillatory dynamics.  The general 
singularity is thus spacelike, local and oscillatory.