A New Transition between Discrete and Continuous Self-Similarity in Critical Gravitational Collapse

Abstract

We analyze a bifurcation phenomenon associated with critical gravitational collapse in a family of self-gravitating SU(2) $\sigma$-models. As the dimensionless coupling constant decreases, the critical solution changes from discretely self-similar (DSS) to continuously self-similar (CSS). Numerical results provide evidence for a bifurcation which is analogous to a heteroclinic loop bifurcation in dynamical systems, where two fixed points (CSS) collide with a limit cycle (DSS) in phase space as the coupling constant tends to a critical value.

4 pages, 5 figures, uses REVTeX

References in corpus (6)

• Dispersion and collapse of wave maps
• Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere
• Type II Critical Collapse of a Self-Gravitating Nonlinear $\sigma$-Model
• Critical Phenomena Inside Global Monopoles
• Critical Phenomena in Nonlinear Sigma Models
• Self-similar spherically symmetric wave maps coupled to gravity

Cited by in corpus (9)

• Critical phenomena in gravitational collapse
• Critical phenomena in gravitational collapse (Physics Reports)
• News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes
• Black-hole threshold solutions in stiff fluid collapse
• Bifurcation and pattern changing with two real scalar fields
• Late-time tails of wave maps coupled to gravity
• Bifurcation and fine structure phenomena in critical collapse of a self-gravitating $\sigma$-field
• Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions
• Global versus Local Aspects of Critical Collapse