Strongly Hyperbolic Extensions of the ADM Hamiltonian

Understand

The ADM Hamiltonian formulation of general relativity with prescribed lapse and shift is a weakly hyperbolic system of partial differential equations.

• In general weakly hyperbolic systems are not mathematically well posed.
• For well posedness, the theory should be reformulated so that the complete system, evolution equations plus gauge conditions, is (at least) strongly hyperbolic.
• Traditionally, reformulation has been carried out at the level of equations of motion.