Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-09-13
Phys.Rev.D79:024017,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, 5 figures. Minor changes to be consistent with published version
Scientific paper
10.1103/PhysRevD.79.024017
Uniqueness problems in the elliptic sector of constrained formulations of Einstein equations have a dramatic effect on the physical validity of some numerical solutions, for instance when calculating the spacetime of very compact stars or nascent black holes. The fully constrained formulation (FCF) proposed by Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak is one of these formulations. It contains, as a particular case, the approximation of the conformal flatness condition (CFC) which, in the last ten years, has been used in many astrophysical applications. The elliptic part of the FCF basically shares the same differential operators as the elliptic equations in CFC scheme. We present here a reformulation of the elliptic sector of CFC 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. Finally, we extend these ideas to FCF, complementing the mathematical analysis carried out in previous studies.
Cerdá-Durán Pablo
Cordero-Carrión Isabel
Dimmelmeier Harald
Gourgoulhon Eric
Jaramillo Jose Luis
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