Mathematical issues in a fully constrained formulation of the Einstein equations

Isabel Cordero-Carrión, José María Ibáñez, Eric Gourgoulhon, José Luis Jaramillo, and Jérôme Novak
Phys. Rev. D 77, 084007 – Published 7 April 2008

Abstract

Bonazzola, Gourgoulhon, Grandclément, and Novak [Phys. Rev. D 70, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic system. We have carried out a preliminary analysis of the mathematical structure of that system, in particular, focusing on the equations governing the evolution for the deviation of a conformal metric from a flat fiducial one. The choice of a Dirac gauge for the spatial coordinates guarantees the mathematical characterization of that system as a (strongly) hyperbolic system of conservation laws. In the presence of boundaries, this characterization also depends on the boundary conditions for the shift vector in the elliptic subsystem. This interplay between the hyperbolic and elliptic parts of the complete evolution system is used to assess the prescription of inner boundary conditions for the hyperbolic part when using an excision approach to black hole space-time evolutions.

  • Received 28 January 2008

DOI:https://doi.org/10.1103/PhysRevD.77.084007

©2008 American Physical Society

Authors & Affiliations

Isabel Cordero-Carrión1,*, José María Ibáñez1,†, Eric Gourgoulhon2,‡, José Luis Jaramillo2,3,§, and Jérôme Novak2,∥

  • 1Departamento de Astronomía y Astrofísica, Universidad de Valencia, Valencia, Spain
  • 2Laboratoire Univers et Théories (LUTH), Observatoire de Paris, CNRS, Université Paris Diderot, Place Jules Janssen, 92190 Meudon, France
  • 3Instituto de Astrofísica de Andalucía, CSIC, Apartado Postal 3004, Granada 18080, Spain

  • *Isabel.Cordero@uv.es
  • Jose.M.Ibanez@uv.es
  • eric.gourgoulhon@obspm.fr
  • §jarama@iaa.es
  • Jerome.Novak@obspm.fr

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 77, Iss. 8 — 15 April 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×