Well-posed constrained evolution of3+1formulations of general relativity

Well-posed constrained evolution of 3+1 formulations of General Relativity

We present an analysis of well-posedness of constrained evolution of 3+1 formulations of GR. In this analysis we explicitly take into account the energy and momentum constraints as well as possible algebraic constraints on the evolution of high-frequency perturbations of solutions of Einstein’s equations. In this respect, our approach is principally different from standard analyses of well-pose...

Well-Posed Initial-Boundary Evolution in General Relativity

The waveform emitted in the inspiral and merger of a relativistic binary is theoretical input crucial to the success of the fledgling gravitational wave observatories. A computational approach is necessary to treat the highly nonlinear regime of a black hole or neutron star collision. Developing this computational ability has been the objective of the Binary Black Hole (BBH) Grand Challenge [1]...

Well-Posed Initial-Boundary Value Problem for Constrained Evolution

Well-posed Quasi-linear Second-order Hyperbolic Systems with Applications to Nonlinear Elastodynamics and General Relativity

General Relativity as a constrained Gauge Theory

The formulation of General Relativity presented in [1] and the Hamiltonian formulation of Gauge theories described in [2] are made to interact. The resulting scheme allows to see General Relativity as a constrained Gauge theory. Mathematics Subject Classification: 70S05, 70S15, 81T13