Strongly hyperbolic second order Einstein's evolution equations

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 prov...

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Bibliographic Details
Published inarXiv.org
Main Authors Nagy, Gabriel, Ortiz, Omar E, Reula, Oscar A
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.08.2004
Subjects
Differential equations
Euclidean space
Evolution
Mathematical analysis
Model reduction
Quantum theory
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0402123