Critical phenomena in gravitational collapse (Physics Reports)

Abstract

In general relativity black holes can be formed from regular initial data that do not contain a black hole already. The space of regular initial data for general relativity therefore splits naturally into two halves: data that form a black hole in the evolution and data that do not. The spacetimes that are evolved from initial data near the black hole threshold have many properties that are mathematically analogous to a critical phase transition in statistical mechanics. Solutions near the black hole threshold go through an intermediate attractor, called the critical solution. The critical solution is either time-independent (static) or scale-independent (self-similar). In the latter case, the final black hole mass scales as $(p-p_{\ast }{)}^{\gamma }$ along any one-parameter family of data with a regular parameter $p$ such that $p=p_{\ast }$ is the black hole threshold in that family. The critical solution and the critical exponent $\gamma$ are universal near the black hole threshold for a given type of matter. We show how the essence of these phenomena can be understood using dynamical systems theory and dimensional analysis. We then review separately the analogy with critical phase transitions in statistical mechanics, and aspects specific to general relativity, such as spacetime singularities. We examine the evidence that critical phenomena in gravitational collapse are generic, and give an overview of their rich phenomenology.

LaTex, 65 pages, 7 eps figures

References in corpus (114)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• Discrete scale invariance and complex dimensions
• The (2+1)-Dimensional Black Hole
• Near-Critical Gravitational Collapse and the Initial Mass Function of Primordial Black Holes
• Dynamics of Primordial Black Hole Formation
• 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 ---
• Late-Time Behavior of Stellar Collapse and Explosions: II. Nonlinear Evolution
• Choptuik Scaling and Quasinormal Modes in the AdS/CFT Correspondence
• Self-Similarity in General Relativity \endtitle
• Critical Behaviour in Gravitational Collapse of a Yang-Mills Field
• Understanding critical collapse of a scalar field
• Cosmological constraints on primordial black holes produced in the near-critical gravitational collapse
• Boson stars driven to the brink of black hole formation
• The spherically symmetric collapse of a massless scalar field
• Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse
• Fine Structure of Oscillons in the Spherically Symmetric ${\varphi }^4$ Klein-Gordon Model
• Choptuik scaling in null coordinates
• The Choptuik spacetime as an eigenvalue problem
• Gravitational collapse in 2+1 dimensional AdS spacetime
• Gravitational Collapse and Cosmic Censorship
• THE NUMBER OF SPHALERON INSTABILITIES OF THE BARTNIK-McKINNON SOLITONS AND NON-ABELIAN BLACK HOLES
• Phases of massive scalar field collapse
• Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour
• Final fate of the spherically symmetric collapse of a perfect fluid
• The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity
• Critical phenomena in perfect fluids
• Critical collapse and the primordial black hole initial mass function
• Convergence to a self-similar solution in general relativistic gravitational collapse
• Scaling of curvature in sub-critical gravitational collapse
• Critical Behaviour and Universality in Gravitational Collapse of a Charged Scalar Field
• Scalar field collapse in three-dimensional AdS spacetime
• A Remark on the Instability of the Bartnik-McKinnon Solutions
• Critical collapse of collisionless matter - a numerical investigation
• All nonspherical perturbations of the Choptuik spacetime decay
• Universal Scaling and Echoing in Gravitational Collapse of a Complex Scalar Field
• Gravitational Collapse of Gravitational Waves in 3D Numerical Relativity
• The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement
• Dispersion and collapse of wave maps
• Quantum Mechanics of Black Holes
• An exact solution for 2+1 dimensional critical collapse
• Rotating solitons and non-rotating, non-static black holes
• A complete classification of spherically symmetric perfect fluid similarity solutions
• Kinematic Self-Similarity
• On the linear stability of solitons and hairy black holes with a negative cosmological constant: the odd-parity sector
• Black Hole Criticality in the Brans-Dicke Model
• Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field
• Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry
• New Critical Behavior in Einstein-Yang-Mills Collapse
• Charge scaling and universality in critical collapse
• Continuous Self-Similarity and $S$-Duality
• Critical Collapse of Skyrmions
• Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
• Ultrarelativistic fluid dynamics
• Collapse of a Scalar Field in 2+1 Gravity
• Global structure of Choptuik's critical solution in scalar field collapse
• Numerical Renormalization Group Calculations For Similarity Solutions and Travelling Waves
• Universality and Scaling at the Onset of Quantum Black Hole Formation
• Spherical Collapse of a Mass-Less Scalar Field With Semi-Classical Corrections
• Stability of Dynamically Collapsing Gas Sphere
• Echoing and scaling in Einstein-Yang-Mills critical collapse
• Gott Time Machines, BTZ Black Hole Formation, and Choptuik Scaling
• S-Duality at the Black Hole Threshold in Gravitational Collapse
• Black-hole threshold solutions in stiff fluid collapse
• Anti-deSitter gravitational collapse
• Perturbations and Critical Behavior in the Self-Similar Gravitational Collapse of a Massless Scalar Field
• On blowup for Yang-Mills fields
• On the linear stability of solitons and hairy black holes with a negative cosmological constant: the even-parity sector
• Symmetry-seeking spacetime coordinates
• Critical gravitational collapse of a perfect fluid: nonspherical perturbations
• Renormalizing Partial Differential Equations
• Choptuik scaling in six dimensions
• Stability criterion for self-similar solutions with perfect fluids in general relativity
• Critical collapse in 2+1 dimensional AdS spacetime: quasi-CSS solutions and linear perturbations
• Spherically symmetric scalar field collapse in any dimension
• Type II Critical Collapse of a Self-Gravitating Nonlinear $\sigma$-Model
• Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system
• Critical phenomena of collapsing massless scalar wave packets
• Critical phenomena and a new class of self-similar spherically symmetric perfect-fluid solutions
• Continuous Self-Similarity Breaking in Critical Collapse
• Critical Collapse Beyond Spherical Symmetry: General Perturbations of the Roberts Solution
• Spacetime structure of self-similar spherically symmetric perfect fluid solutions
• Critical Behavior of Black Hole Formation in a Scalar Wave Collapse
• Perturbations of an exact solution for 2+1 dimensional critical collapse
• Critical Phenomena Inside Global Monopoles
• Velocity-induced collapses of stable neutron stars
• Remark on formation of colored black holes via fine tuning
• Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model
• Local and global existence theorems for the Einstein equations
• Predictability and Semiclassical Approximation at the onset of Black Hole formation
• Instability of an "Approximate Black Hole"
• Critical phenomena in Newtonian gravity
• Critical Phenomena in Nonlinear Sigma Models
• An extreme critical space-time: echoing and black-hole perturbations
• Quantum corrections to critical phenomena in gravitational collapse
• A New Transition between Discrete and Continuous Self-Similarity in Critical Gravitational Collapse
• Multiply Unstable Black Hole Critical Solutions
• Renormalization group and critical behaviour in gravitational collapse
• Self-similar spherically symmetric wave maps coupled to gravity
• On Equivalence of Critical Collapse of Non-Abelian Fields
• Angular momentum near the black hole threshold in scalar field collapse
• Critical gravitational collapse with angular momentum: from critical exponents to universal scaling functions
• Sectors of spherical homothetic collapse
• Comment on the Roberts solution for the spherically-symmetric Einstein-scalar field equations
• Analytic approximations to the spacetime of a critical gravitational collapse
• Perturbation theory for self-gravitating gauge fields I: The odd-parity sector
• Scale invariance and critical gravitational collapse
• First Order Phase Transitions in Gravitational Collapse
• Does scalar field collapse produce `zero mass' black holes?
• Critical phenomena in gravitational collapse
• Is there a connection between no-hair behavior and universality in gravitational collapse?
• Phase Transition in Spherically Symmetric Gravitational Collapse of a Massless Scalar Field

Cited by in corpus (129)

• Primordial Black Holes as Dark Matter
• Primordial Black Holes as Dark Matter: Recent Developments
• Binary neutron-star mergers: a review of Einstein's richest laboratory
• The fuzzball proposal for black holes
• Critical phenomena in gravitational collapse
• String Loop Corrections to Kahler Potentials in Orientifolds
• Loop Corrections to Volume Moduli and Inflation in String Theory
• String Lessons for Higher-Spin Interactions
• Generalised constraints on the curvature perturbation from primordial black holes
• Anomalies, Anomalous U(1)'s and generalized Chern-Simons terms
• Numerical Relativity and Astrophysics
• Getting just the Supersymmetric Standard Model at Intersecting Branes on the Z6-orientifold
• Eddington-inspired Born-Infeld gravity. Phenomenology of non-linear gravity-matter coupling
• Critical Collapse of the Massless Scalar Field in Axisymmetry
• PBH dark matter from axion inflation
• Towards an S-matrix Description of Gravitational Collapse
• Inflationary theory and pulsar timing investigations of primordial black holes and gravitational waves
• Landau-Ginzburg Limit of Black Hole's Quantum Portrait: Self Similarity and Critical Exponent
• Primordial Black Holes from Multifield Inflation with Nonminimal Couplings
• Exploring New Physics Frontiers Through Numerical Relativity
• Higher-Spin Geometry and String Theory
• Novel Constraints on Mixed Dark-Matter Scenarios of Primordial Black Holes and WIMPs
• Effects of Critical Collapse on Primordial Black-Hole Mass Spectra
• Second and higher-order perturbations of a spherical spacetime
• On Choptuik's scaling in higher dimensions
• Black string solutions with negative cosmological constant
• Worldsheet Realization of the Refined Topological String
• Primordial black holes from metric preheating: mass fraction in the excursion-set approach
• Global structure of Choptuik's critical solution in scalar field collapse
• On Ellipsoidal Collapse and Primordial Black-Hole Formation
• Dynamical Singularity Resolution in Spherically Symmetric Black Hole Formation
• Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates
• Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Critical Collapse of a Complex Scalar Field with Angular Momentum
• Delayed collapses of BECs in relation to AdS gravity
• Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry
• Scaling Phenomena in Gravity from QCD
• Quantum dress for a naked singularity
• Critical Phenomena in Head-on Collisions of Neutron Stars
• New Features of Gravitational Collapse in Anti-de Sitter Spacetimes
• Genericity aspects in gravitational collapse to black holes and naked singularities
• Some Phenomenology of Intersecting D-Brane Models
• Critical gravitational collapse: towards a holographic understanding of the Regge region
• Critical collapse of rotating radiation fluids
• Geons with spin and charge
• 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
• Critical bubbles and implications for critical black strings
• Induced gravity in Z_N orientifold models
• Black Hole Formation from the Collision of Plane-Fronted Gravitational Waves
• Critical phenomena in the aspherical gravitational collapse of radiation fluids
• Choptuik's Critical Phenomenon in Einstein-Gauss-Bonnet Gravity
• Choptuik Scaling and The Merger Transition
• Border of Spacetime
• Gravitational collapse of quantum matter
• Collapse of Charged Scalar Field in Dilaton Gravity
• Type II critical phenomena of neutron star collapse
• Moving Closer to the Collapse of a Massless Scalar Field in Spherically Symmetric Anti-de Sitter Spacetimes
• Numerical Study of Cosmic Censorship in String Theory
• Almost-stationary motions and gauge conditions in General Relativity
• Collapsing shells, critical phenomena and black hole formation
• Ricci flows and infinite dimensional algebras
• Two worlds collide: Interacting shells in AdS spacetime and chaos
• Critical Collapse in the Axion-Dilaton System in Diverse Dimensions
• Primordial Black Holes with QCD Color Charge
• Hamiltonian Formulation of Scalar Field Collapse in Einstein Gauss Bonnet Gravity
• Approximately self-similar critical collapse in 2+1 dimensions
• More On Critical Collapse of Axion-Dilaton System in Dimension Four
• Critical behavior in Ricci flow
• Is general relativity `essentially understood' ?
• No black holes from light
• Gravitational Collapse of Baryonic and Dark matter
• On Perturbation Theory and Critical Exponents for Self-Similar Systems
• Final Fate of Subcritical Evolutions of Boson Stars
• Critical collapse of ultra-relativistic fluids: damping or growth of aspherical deformations
• Arithmetical Chaos and Quantum Cosmology
• The naked singularity in the global structure of critical collapse spacetimes
• Semiclassical Instability of the Cauchy Horizon in Self-Similar Collapse
• The 5-D Choptuik critical exponent and holography
• Inside charged black holes I. Baryons
• On Critical Exponents for Self-Similar Collapse
• On self-similar axion-dilaton configurations
• A Numerical Study of Boson Star Binaries
• A Toy Model for Topology Change Transitions: Role of Curvature Corrections
• Driven neutron star collapse: Type~I critical phenomena and the initial black hole mass distribution
• On Higher Dimensional Self-Similar Axion-Dilaton Solutions
• The Spherically Symmetric Standard Model with Gravity
• Kinematics of discretely self-similar spherically symmetric spacetimes
• Exact solutions and critical chaos in dilaton gravity with a boundary
• Geon black holes and quantum field theory
• Nonlinear Statistical Spline Smoothers for Critical Spherical Black Hole Solutions in 4-dimension
• Higher Dimensional Choptuik Scaling in Painleve Gullstrand Coordinates
• On the chaos of D-brane phase transitions
• A Rotating, Inhomogeneous Dust Interior for the BTZ Black Hole
• Type II critical behavior of gravitating magnetic monopoles
• Weak cosmic censorship conjecture in BTZ black holes with scalar fields
• Analytical solutions for black-hole critical behaviour
• Gravitational Collapse of Phantom Fluid in (2+1)-Dimensions
• On the critical behaviour of gapped gravitational collapse in confined spacetime
• Fractal Threshold Behavior in Vacuum Gravitational Collapse
• Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models
• On Susy Standard-like models from orbifolds of D=6 Gepner orientifolds
• Unveiling horizons in quantum critical collapse
• Chaotic self-similar wave maps coupled to gravity
• Quantum group symmetry and discrete scale invariance: Spectral aspects
• Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions
• Investigation into Length Scale Dominance in Critical Black Hole Formation
• Stability and Critical Behavior of Gravitational Monopoles
• Gravitational collapse of a spherical scalar field
• Asymptotics of Solutions of a Perfect Fluid Coupled with a Cosmological Constant in Four-Dimensional Spacetime with Toroidal Symmetry
• Homothetic Self-Similar Solutions of the Three-Dimensional Brans-Dicke Gravity
• Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations
• A scenario for critical scalar field collapse in $Ad{S}_3$
• Critical spacetime crystals in continuous dimensions
• Kink Stability of Self-Similar Solutions of Scalar Field in 2+1 Gravity
• Boundary dynamics in competing critical black hole formation
• Power-laws from critical gravitational collapse: The mass distribution of subsolar objects
• Numerical Relativity with Arbitrary Precision Arithmetic: Applications to Gravitational Collapse
• Cosmic Censorship of Trans-Planckian Field Ranges in Gravitational Collapse
• Perturbation theory of spherically symmetric self-similar black holes
• Critical behavior of collapsing surfaces
• Neural Networks Assisted Metropolis-Hastings for Bayesian Estimation of Critical Exponent on Elliptic Black Hole Solution in 4D Using Quantum Perturbation Theory
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Universality of the subsolar mass distribution from critical gravitational collapse
• Comparison of linear Brill and Teukolsky waves
• Critical collapse of a massive scalar field in semi-classical loop quantum gravity