Self-similar spherically symmetric wave maps coupled to gravity

Abstract

We investigate spherically symmetric continuously self-similar (CSS) solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods, we provide evidence for the existence (for small coupling) of a countable family of regular CSS solutions. This fact is argued to have important implications for the ongoing studies of black hole formation in the model.

13 pages, 8 figures

References in corpus (3)

• 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

Cited by in corpus (12)

• Critical phenomena in gravitational collapse
• Critical phenomena in gravitational collapse (Physics Reports)
• On the existence of self-similar spherically symmetric wave maps coupled to gravity
• A New Transition between Discrete and Continuous Self-Similarity in Critical Gravitational Collapse
• Examples of naked singularity formation in higher-dimensional Einstein-vacuum spacetimes
• Late-time tails of wave maps coupled to gravity
• Periodic self-similar wave maps coupled to gravity
• Chaotic self-similar wave maps coupled to gravity
• Bifurcation and fine structure phenomena in critical collapse of a self-gravitating $\sigma$-field
• Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations
• Harmonic and Wave Maps Coupled with Einstein's gravitation
• Staticity, Self-Similarity and Critical Phenomena in a Self-Gravitating Nonlinear Sigma Model