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The Initial Data Problem

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3+1 Formalism in General Relativity

Part of the book series: Lecture Notes in Physics ((LNP,volume 846))

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Abstract

The problem of solving the constraint equations to get valid initial data for the time evolution is discussed. We focus on two methods based on the conformal decomposition introduced in Chap. 7: the conformal transverse-traceless method and the conformal thin sandwich method. Both methods are illustrated by initial data in Schwarzschild spacetime. Finally, we give a survey of the construction of initial for binary compact objects, which are of major interest in numerical relativity.

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Notes

  1. 1.

    Although it is \( \hbox{\it{quasi-linear}}\) in the technical sense, i.e. linear with respect to the highest-order derivatives.

  2. 2.

    See however Ref. [80] for some attempt to circumvent this.

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    Éric Gourgoulhon

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Gourgoulhon, É. (2012). The Initial Data Problem. In: 3+1 Formalism in General Relativity. Lecture Notes in Physics, vol 846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24525-1_9

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