NSF-ITP-95-154 gr-qc/95mmnnn Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field

We examine the gravitational collapse of a non-linear sigma model in spherical symmetry. There exists a family of continuously self-similar solutions parameterized by the coupling constant of the theory. These solutions are calculated together with the critical exponents for black hole formation of these collapse models. We also nd that the sequence of solutions exhibits a Hopf-type bifurcation as the continuously self-similar solutions become unstable to perturbations away from self-similarity. Typeset using REVTEX Electronic address: [email protected] Electronic address: [email protected]