Understanding critical collapse of a scalar field

Abstract

I construct a spherically symmetric solution for a massless real scalar field minimally coupled to general relativity which is discretely self-similar (DSS) and regular. This solution coincides with the intermediate attractor found by Choptuik in critical gravitational collapse. The echoing period is Delta = 3.4453 +/- 0.0005. The solution is continued to the future self-similarity horizon, which is also the future light cone of a naked singularity. The scalar field and metric are C1 but not C2 at this Cauchy horizon. The curvature is finite nevertheless, and the horizon carries regular null data. These are very nearly flat. The solution has exactly one growing perturbation mode, thus confirming the standard explanation for universality. The growth of this mode corresponds to a critical exponent of gamma = 0.374 +/- 0.001, in agreement with the best experimental value. I predict that in critical collapse dominated by a DSS critical solution, the scaling of the black hole mass shows a periodic wiggle, which like gamma is universal. My results carry over to the free complex scalar field. Connections with previous investigations of self-similar scalar field solutions are discussed, as well as an interpretation of Delta and gamma as anomalous dimensions.

RevTex, 26 galley or 53 preprint pages, 3 EPS figures, 2 tables

References in corpus (15)

• 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 ---
• Critical Behaviour in Gravitational Collapse of a Yang-Mills Field
• The spherically symmetric collapse of a massless scalar field
• Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse
• Choptuik scaling in null coordinates
• The Choptuik spacetime as an eigenvalue problem
• Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour
• Universal Scaling and Echoing in Gravitational Collapse of a Complex Scalar Field
• Black Hole Criticality in the Brans-Dicke Model
• Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field
• Continuous Self-Similarity and $S$-Duality
• Charge scaling and universality in critical collapse
• Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
• S-Duality at the Black Hole Threshold in Gravitational Collapse

Cited by in corpus (95)

• Critical phenomena in gravitational collapse
• Self-Similarity in General Relativity \endtitle
• Critical phenomena in gravitational collapse (Physics Reports)
• Numerical Approaches to Spacetime Singularities
• Kadath: a spectral solver for theoretical physics
• Phases of massive scalar field collapse
• Simulation of primordial black hole formation using pseudo-spectral methods
• Critical phenomena in gravitational collapse - Living Reviews
• Scaling of curvature in sub-critical gravitational collapse
• Critical Behaviour and Universality in Gravitational Collapse of a Charged Scalar Field
• Nonuniform black strings in various dimensions
• All nonspherical perturbations of the Choptuik spacetime decay
• On Choptuik's scaling in higher dimensions
• Charge scaling and universality in critical collapse
• News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes
• Critical Phenomena in Neutron Stars II: Head-on Collisions
• Global structure of Choptuik's critical solution in scalar field collapse
• Echoing and scaling in Einstein-Yang-Mills critical collapse
• Particle Creation in the Marginally Bound, Self Similar Collapse of Inhomogeneous Dust
• Domain wall interacting with a black hole: A new example of critical phenomena
• Black-hole threshold solutions in stiff fluid collapse
• Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity
• Soap Bubbles in Outer Space: Interaction of a Domain Wall with a Black Hole
• Critical Collapse of a Complex Scalar Field with Angular Momentum
• Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry
• On critical collapse of gravitational waves
• Critical gravitational collapse of a perfect fluid: nonspherical perturbations
• Scaling Phenomena in Gravity from QCD
• Modified general relativity as a model for quantum gravitational collapse
• Type II Critical Collapse of a Self-Gravitating Nonlinear $\sigma$-Model
• Critical phenomena of collapsing massless scalar wave packets
• Black hole critical behaviour with the generalized BSSN formulation
• Continuous Self-Similarity Breaking in Critical Collapse
• Self-similarity in Einstein-Maxwell-dilaton theories and critical collapse
• Aspherical deformations of the Choptuik spacetime
• Critical phenomena in the gravitational collapse of electromagnetic waves
• Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution
• Spherically Symmetric Black Hole Formation in Painlevé-Gullstrand Coordinates
• Dimensional Dependence of Black Hole Formation in Self-Similar Collapse of Scalar Field
• Critical phenomena in the collapse of gravitational waves
• Critical Collapse in Einstein-Gauss-Bonnet Gravity in Five and Six Dimensions
• Choptuik Scaling and The Merger Transition
• Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models
• Choptuik's critical spacetime exists
• The affine-null formulation of the gravitational equations: spherical case
• Moving Closer to the Collapse of a Massless Scalar Field in Spherically Symmetric Anti-de Sitter Spacetimes
• Black Tsunamis and Naked Singularities in AdS
• Evolution of Brill waves with an adaptive pseudospectral method
• Critical behavior in 3-d gravitational collapse of massless scalar fields
• Critical phenomena in gravitational collapse with two competing massless matter fields
• Critical collapse of a massive vector field
• Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves
• An extreme critical space-time: echoing and black-hole perturbations
• Quantum corrections to critical phenomena in gravitational collapse
• Critical phenomena in the gravitational collapse of electromagnetic dipole and quadrupole waves
• A New Transition between Discrete and Continuous Self-Similarity in Critical Gravitational Collapse
• Black Hole Formation in AdS Einstein-Gauss-Bonnet Gravity
• Renormalization group and critical behaviour in gravitational collapse
• Twist-free axisymmetric critical collapse of a complex scalar field
• Self-similar spherically symmetric wave maps coupled to gravity
• Angular momentum near the black hole threshold in scalar field collapse
• Examples of naked singularity formation in higher-dimensional Einstein-vacuum spacetimes
• Simulations of gravitational collapse in null coordinates: II. Critical collapse of an axisymmetric scalar field
• Formulation Improvements for Critical Collapse Simulations
• Gravitational collapse of quantum fields and Choptuik scaling
• A semi-linear wave model for critical collapse
• Gravitational collapse of massless scalar field and radiation fluid
• Critical Phenomena in Non-spherically Symmetric Scalar Bubble Collapse
• Dynamics of critical collapse
• Critical gravitational collapse of a non-minimally coupled scalar field
• Strength of the naked singularity in critical collapse
• Holographic Signatures of Critical Collapse
• Scale invariance and critical gravitational collapse
• Kinematics of discretely self-similar spherically symmetric spacetimes
• Higher Dimensional Choptuik Scaling in Painleve Gullstrand Coordinates
• Type II critical behavior of gravitating magnetic monopoles
• Critical behavior of spherically symmetric domain wall collapse
• Type II critical collapse on a single fixed grid: a gauge-driven ingoing boundary method
• Bifurcation and fine structure phenomena in critical collapse of a self-gravitating $\sigma$-field
• On the critical behaviour of gapped gravitational collapse in confined spacetime
• Multidomain Galerkin-Collocation method: characteristic spherical collapse of scalar fields
• Unveiling horizons in quantum critical collapse
• Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions
• Self-similar solutions and critical behavior in Einstein-Maxwell-dilaton theory sourced by charged null fluids
• Quantum Critical Collapse Abhors a Naked Singularity
• Investigation into Length Scale Dominance in Critical Black Hole Formation
• Galerkin Method in the Gravitational Collapse: a Dynamical System Approach
• Gravitational collapse of a spherical scalar field
• Critical spacetime crystals in continuous dimensions
• A No-Boundary Method for Numerical Relativity
• New results on the dynamics of critical collapse
• Black Hole Formation in Lovelock Gravity
• Boundary dynamics in competing critical black hole formation
• Comparison of linear Brill and Teukolsky waves
• Global versus Local Aspects of Critical Collapse