Vacuum axisymmetric gravitational collapse revisited: Preliminary investigation

Validating the results of Abrahams and Evans [Phys. Rev. Lett. 70, 2980--2983 (1993)] poses a numerical challenge and has been inspiring a lot of research. We join these efforts and present our first steps to achieve this goal: we discuss a formulation of the Einstein equations for a vacuum axisymmetric spacetime with a vanishing twist in spherical-polar coordinates and its linearized approximation, and identify some problems in achieving numerically stable evolution at the threshold of a black hole formation.