Hyperbolic formulations and numerical relativity: Experiments using Ashtekar's connection variables (Q2703408)

The paper discusses several formulations of general relativity aiming at the best numerical estimates. The authors compare especially the ADM (Arnowitt-Deser-Misner) formalism as a standard tool in canonical and numerical gravity, with the Ashtekar formalism, with partly used additional gauge conditions. The gauge conditions ensure that the systems are weakly, strongly or symmetric hyperbolic. The numerical laboratory working with the gravitational wave propagation in plane symmetric spacetimes, the violation of the constraint equations are the numerical control parameters showing the accuracy of the simulation. The time integration uses two different methods, the Crank-Nicholson method and the Brailovskaya method. In the considered case both methods give nearly identical evolutions, but the Brailovskaya method requires less computational time. NEWLINENEWLINENEWLINEIt is shown that the violation of the constraints for the ADM- and Ashtekar (it is perhaps the first use of this formulation in numerical relativity) evolution are similar. Furthermore the comparison between the weakly hyperbolic and the strongly hyperbolic and symmetric hyperbolic systems shows that the last two have better properties. The differences between the strongly and symmetric hyperbolic systems are small.