Appropriate choice of coordinates is evidently important. However, for binary systems, rather few results have been obtained using the natural choice of bispherical coordinates. So far, variations of such coordinates have only been used by Ansorg and collaborators and only in the context of initial data [8, 6, 7]. We believe that applying these coordinates, or similar coordinates, to evolutionary codes could lead to interesting results, in terms of both speed and accuracy.
The application of spectral methods to theories more complicated than general relativity is also imaginable. One of the possible fields of application is the study of branes, where there is an additional dimension to spacetime. The fact that spectral methods are accurate with relatively few degrees of freedom makes them a good candidate for simulating systems with extra dimensions. The addition of gauge fields is also something that could be studied with spectral methods, to investigate the possibility of “hairy” black holes, for instance. Of course, these are just a few ideas of what the future applications of spectral methods to the field of relativity might be.
Living Rev. Relativity 12, (2009), 1
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