Hyperbolicity of the BSSN system of Einstein evolution equations

TL;DR

This paper analyzes the hyperbolic properties of the BSSN formulation of Einstein's equations, explaining its improved numerical stability in black hole simulations by establishing conditions under which it is hyperbolic.

Contribution

It demonstrates the equivalence of BSSN to other hyperbolic systems and clarifies the conditions for its hyperbolicity, enhancing understanding of its numerical advantages.

Findings

BSSN is equivalent to certain strongly hyperbolic systems.

Conditions for BSSN hyperbolicity are identified.

Hyperbolicity may explain BSSN's better numerical behavior.

Abstract

We discuss an equivalence between the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations, a subfamiliy of the Kidder--Scheel--Teukolsky formulation, and other strongly or symmetric hyperbolic first order systems with fixed shift and densitized lapse. This allows us to show under which conditions the BSSN system is, in a sense to be discussed, hyperbolic. This desirable property may account in part for the empirically observed better behavior of the BSSN formulation in numerical evolutions involving black holes.