Well-posed initial-boundary evolution in general relativity

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 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 Value Problem for a Constrained Evolution System and Radiation-controlling Constraint-preserving Boundary Conditions

A well-posed initial-boundary value problem is formulated for the model problem of vector wave equation subject to the divergence-free constraint. Existence, uniqueness, and stability of the solution is proved by reduction to a system evolving the constraint quantity trivially, namely, the second time derivative of the constraint quantity is zero. A new set of radiationcontrolling constraint-pr...

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