4 More Spherical Symmetry

The pioneering work of Choptuik on the spherical massless scalar field has been followed by a plethora of further investigations. These could be organised under many different criteria. We have chosen the following rough categories:

Some of these examples were constructed because they may have intrinsic physical relevance (semiclassical gravity, primordial black holes), others as toy models for 3+1-dimensional gravity, and others mostly out of a purely mathematical interest. Table 1 gives an overview of these models.

 4.1 Matter obeying wave equations
  4.1.1 2-dimensional nonlinear σ model
  4.1.2 Spherical Einstein–SU(2) sigma model
  4.1.3 Einstein–Yang–Mills
  4.1.4 Vacuum 4+1
  4.1.5 Scalar field collapse in 2+1
  4.1.6 Scalar field collapse in higher dimensions
  4.1.7 Other systems obeying wave equations
 4.2 Perfect fluid matter
  4.2.1 Spherical symmetry
  4.2.2 Nonspherical perturbations
  4.2.3 Cosmological applications
 4.3 Collisionless matter
 4.4 Criticality in singularity formation without gravitational collapse
 4.5 Analytic studies and toy models
  4.5.1 Exact solutions of Einstein–Klein–Gordon
  4.5.2 Toy models
 4.6 Quantum effects

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