Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue

Understand

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.