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3 Prototype Characteristic Evolution Codes

Limited computer power, as well as the instabilities arising from non-hyperbolic formulations of Einstein’s equations, necessitated that the early code development in general relativity be restricted to spacetimes with symmetry. Characteristic codes were first developed for spacetimes with spherical symmetry. The techniques for relativistic fields which propagate on null characteristics are similar to the gravitational case. Such fields are included in this section. We postpone treatment of relativistic fluids, whose characteristics are timelike, until Section 5.


 3.1 {1 + 1}-dimensional codes
  3.1.1 Adaptive mesh refinement
 3.2 {2 + 1}-dimensional codes
 3.3 The Bondi problem
  3.3.1 The conformal-null tetrad approach
  3.3.2 Axisymmetric mode coupling
  3.3.3 Twisting axisymmetry
 3.4 The Bondi mass
 3.5 3D characteristic evolution
  3.5.1 Geometrical formalism
  3.5.2 Numerical methodology
  3.5.3 Stability
  3.5.4 Accuracy
  3.5.5 First versus second differential order
  3.5.6 Nonlinear scattering off a Schwarzschild black hole
  3.5.7 Black hole in a box
 3.6 Characteristic treatment of binary black holes
 3.7 Perturbations of Schwarzschild
  3.7.1 Close approximation white hole and black hole waveforms
  3.7.2 Fissioning white hole
 3.8 Nonlinear mode coupling
 3.9 3D Einstein-Klein-Gordon system

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