Strongly hyperbolic second order Einstein's evolution equations

Details Strongly hyperbolic second order Einstein's evolution equations Strongly hyperbolic second order Einstein's evolution equations

2004-02-26

arxiv.org/abs/gr-qc/0402123v2

Phys.Rev. D70 (2004) 044012

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 16 pages, uses revtex4. Referee corections and new appendix added. English grammar improved; typos corrected

Scientific paper

10.1103/PhysRevD.70.044012

BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the conformal-traceless decomposition but keeping the three connection functions and including a densitized lapse. It is proved that a pseudo-differential first order reduction of these equations is strongly hyperbolic. In the same way, densitized Arnowitt-Deser-Misner evolution equations are found to be weakly hyperbolic. In both cases, the positive densitized lapse function and the spacelike shift vector are arbitrary given fields. This first order pseudodifferential reduction adds no extra equations to the system and so no extra constraints.

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