Vacuum axisymmetric gravitational collapse revisited: preliminary investigation

Abstract

Validating the results of [A.M. Abrahams and C.R. Evans, Phys. Rev. Lett. 70, 2980] 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 Einstein equations for a vacuum axisymmetric spacetime with vanishing twist in spherical-polar coordinates, its linearised approximation, and identify some problems in achieving numerically stable evolution at the threshold of a black hole formation.

9 pages, 2 figures, a sign error pointeded out by a Referee in Eqs. (57,58) corrected, Eq. (56) corrected, signs in the comments below eqs. (51,56) corrected, numerous typos corrected

References in corpus (3)

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• Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum