1305.4866 (Eoin Condron et al.)

Collapse of a cylindrically symmetric, self-similar scalar field with
non-minimal coupling    [PDF]

Eoin Condron, Brien C. Nolan

We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs. Self-similarity also gives rise to a singularity at the scaling origin. We discuss the number of degrees of freedom at an arbitrary point and prove existence and uniqueness of a 2-parameter family of solutions with a regular axis. We discuss the evolution of these solutions away from the axis toward the past null cone of the singularity, determining the maximal interval of existence in each case.

View original: http://arxiv.org/abs/1305.4866