A Simplified Mathematical Model for the Formation of Null Singularities   Inside Black Holes II
  We study a simple system of two hyperbolic semi-linear equations, inspired by the Einstein equations. The system, which was introduced in gr-qc/0612136, is a model for singularity formation inside black holes. We show for a particular case of the equations that the system demonstrates a finite time blowup. The singularity that is formed is a null singularity. Then we show that in this particular case the singularity has features that are analogous to known features of models of black-hole interiors - which describe the inner-horizon instability. Our simple system may provide insight into the formation of null singularities inside spinning or charged black holes. 
Dan Gorbonos, Gershon Wolansky