Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity

Understand

Two new formulations of general relativity are introduced.

• The first one is a parabolization of the Arnowitt, Deser, Misner (ADM) formulation and is derived by addition of combinations of the constraints and their derivatives to the right-hand-side of the ADM evolution equations.
• The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed.
• This system may be classified as mixed hyperbolic - second-order parabolic.