Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-03-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Some clarification added and typos corrected. Final version to appear in Classical and Quantum Gravity
Scientific paper
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain.
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