First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

Details First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

2003-03-26

arxiv.org/abs/gr-qc/0303104v2

Phys.Rev.D68:084013,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

revtex4, 7 pages, text and references added, typos corrected, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.68.084013

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.

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