Strongly hyperbolic Einstein's evolution equations

NAGY, GABRIEL, ORTIZ, OMAR, AND REULA, OSCAR

PHYSICAL REVIEW D - PARTICLE AND FILDS

Año: 2004 vol. 70 p. 44012 - 44023

0556-2821

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.