Abstract
We review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to current 3D black hole codes that run forever. A prime application of characteristic evolution is Cauchy-characteristic matching, which is also reviewed.
Highlights
We are entering an era in which Einstein’s equations can effectively be considered solved at the local level
There is no single code in existence today which purports to be capable of computing the waveform of gravitational radiation emanating from the inspiral and merger of two black holes, the premier problem in classical relativity
Most work in numerical relativity is based upon the Cauchy “3 + 1” formalism [108], with the gravitational radiation extracted by perturbative Cauchy methods which introduce an artificial Schwarzschild background [1, 3, 2, 5]
Summary
We are entering an era in which Einstein’s equations can effectively be considered solved at the local level. At least in the near future, the computational application of characteristic evolution is likely to be restricted to some mixed form, in which boundary conditions are set on a non-singular but incomplete initial null hypersurface and on a second nonsingular hypersurface (or perhaps several), which together with the initial null hypersurface present a nontrivial domain of dependence. This second hypersurface may itself be either (i) null, (ii) timelike or (iii) spacelike. We trace the development of CCM from early feasibility studies through current attempts to treat the binary black hole problem
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