Hyperbolicity of Hamiltonian formulations in General Relativity

Abstract

Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential ingredient. We develop helpful tools and classify a large class of Hamiltonian versions of Einstein's equations with live gauge conditions with respect to their hyperbolicity. Finally we find a symmetric hyperbolic Hamiltonian formulation that allows for gauge conditions which are similar to the puncture gauge.