José Luis Jaramillo — Page 3

arXiv2009

Isolated Horizon structures in quasiequilibrium black hole initial data

Isolated horizon conditions enforce the time invariance of both the intrinsic and the extrinsic geometry of a (quasilocal) black hole horizon. Nonexpanding horizons, only requiring the invariance of the intrinsic geometry, have been successfully employed in the (excision) initial data of black holes in instantaneous equilibrium. Here we propose the use of the full isolated horizon structure when solving the elliptic system resulting from the complete set of conformal 3+1 Einstein equations under a quasiequilibrium ansatz prescription. We argue that a set of geometric inner boundary conditions for this extended elliptic system then follows, determining the shape of the excision surface.

gr-qc↗

arXiv2009

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

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, Grandclément, 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.

gr-qc↗