Conformal hyperbolic formulation of the Einstein equations - art. no. 064017

We propose a reformulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the nonconformal degrees of freedom with the latter satisfying a first order strongly hyperbolic syste m. The conformal degrees of freedom are taken to be determined by the choic e of slicing and the initial data, and an regarded as given functions (alon g with the lapse and the shift) in the hyperbolic part of the evolution. We find that there is a two parameter family of hyperbolic systems for the no nconformal degrees of freedom for a given set of trace free variables. The two parameters are uniquely fixed if we require the system to be "consisten tly trace-free," i.e., the time derivatives of the trace free variables rem ain trace-free to the principal part, even in the presence of constraint vi olations due to numerical truncation error. We show that by forming linear combinations of the trace free variables a conformal hyperbolic system with only physical characteristic speeds can also be constructed. [S0556-2821(9 9)05516-2].