In the auxiliary variables
the wave equation becomes a first-order system, In spherical symmetry there are four algebraically independent components of the Einstein equations. Of these, one is a linear combination of derivatives of the other and can be disregarded. The other three contain only first derivatives of the metric, namely , , and , and are Because of spherical symmetry, the only dynamics is in the scalar field equations (22, 23). The metric can be found by integrating the ODEs (24) and (25) for a and at any fixed t, given and . Equation (26) can be ignored in this “fully constrained” evolution scheme.http://www.livingreviews.org/lrr-2007-5 |
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