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Constrained scheme for the Einstein equations: An approach to the uniqueness issue

Uniqueness problems in the elliptic sector of constrained formulations of Einstein equations can appear in numerical models, for instance when calculating the spacetime of very compact stars or nascent black holes. The same holds for the approximation of the conformal flatness condition (CFC) which, in the last ten years, has been used in many astrophysical applications. We present here a reformulation of the elliptic sector of such formulations that has the fundamental property of overcoming the local uniqueness problems. The correct behavior of our new formulation is confirmed by means of a battery of numerical simulations in CFC.

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