Living Reviews in Relativity

"Critical Phenomena in Gravitational Collapse"
Carsten Gundlach and José M. Martín-García  

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1 Introduction
1.1 Overview of the subject
1.2 Plan of this review
2 Theory
2.1 Universality
2.2 Self-similarity
2.3 Mass scaling
2.4 Type I
2.5 Coordinate choices for the dynamical systems picture
2.6 Approximate self-similarity and universality classes
2.7 The analogy with critical phase transitions
3 The Scalar Field
3.1 Field equations in spherical symmetry
3.2 The black hole threshold
3.3 Global structure of the critical solution
3.4 Near-critical spacetimes and naked singularities
3.5 Electric charge
3.6 Self-interaction potential
3.7 Nonspherical perturbations: Stability and angular momentum
4 More Spherical Symmetry
4.1 Matter obeying wave equations
4.2 Perfect fluid matter
4.3 Collisionless matter
4.4 Criticality in singularity formation without gravitational collapse
4.5 Analytic studies and toy models
4.6 Quantum effects
5 Beyond Spherical Symmetry
5.1 Perturbative approach to angular momentum
5.2 Axisymmetric vacuum gravity
5.3 Scalar field
5.4 Neutron star collision in axisymmetry
5.5 Black hole collisions
6 Acknowledgements
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