Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field

Abstract

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 find that the sequence of solutions exhibits a Hopf-type bifurcation as the continuously self-similar solutions become unstable to perturbations away from self-similarity.

18 pages; one figure, uuencoded postscript; figure is also available at http://www.physics.ucsb.edu/people/eric_hirschmann

References in corpus (11)

• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid
• Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---
• Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse
• The Choptuik spacetime as an eigenvalue problem
• Universal Scaling and Echoing in Gravitational Collapse of a Complex Scalar Field
• Black Hole Criticality in the Brans-Dicke Model
• Continuous Self-Similarity and $S$-Duality
• Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
• Evidence for Non-perturbative String Symmetries
• S-Duality at the Black Hole Threshold in Gravitational Collapse

Cited by in corpus (32)

• Critical phenomena in gravitational collapse
• Critical phenomena in gravitational collapse (Physics Reports)
• Numerical Approaches to Spacetime Singularities
• Understanding critical collapse of a scalar field
• Phases of massive scalar field collapse
• Critical phenomena in gravitational collapse - Living Reviews
• Continuous Self-Similarity and $S$-Duality
• Charge scaling and universality in critical collapse
• Particle Creation in the Marginally Bound, Self Similar Collapse of Inhomogeneous Dust
• Black hole formation from massive scalar fields
• Critical phenomena of collapsing massless scalar wave packets
• Critical Phenomena Inside Global Monopoles
• Critical Phenomena in the Einstein-Massless-Dirac System
• Existence of naked singularities in Brans-Dicke theory of gravitation. An analytical and numerical study
• Multiply Unstable Black Hole Critical Solutions
• Renormalization group and critical behaviour in gravitational collapse
• Gravitational collapse of massless scalar field and radiation fluid
• On Perturbation Theory and Critical Exponents for Self-Similar Systems
• On Critical Exponents for Self-Similar Collapse
• Inside charged black holes I. Baryons
• On self-similar axion-dilaton configurations
• On Higher Dimensional Self-Similar Axion-Dilaton Solutions
• Analysis of Black Hole Solutions in Parabolic Class Using Neural Networks
• Nonlinear Statistical Spline Smoothers for Critical Spherical Black Hole Solutions in 4-dimension
• Wave Functions for Quantum Black Hole Formation in Scalar Field Collapse
• Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models
• Spherical Self-Similar Solutions in Einstein-Multi-Scalar Gravity
• Unveiling horizons in quantum critical collapse
• Modeling the complexity of Elliptic Black Hole Solution In 4D Using Hamiltonian Monte Carlo with Stacked Neural Networks
• Black Hole Critical Phenomena Without Black Holes
• Sequential Monte Carlo with Cross-validated Neural Networks for Complexity of Hyperbolic Black Hole Solutions in 4D
• Neural Networks Assisted Metropolis-Hastings for Bayesian Estimation of Critical Exponent on Elliptic Black Hole Solution in 4D Using Quantum Perturbation Theory