139 citations · 397 across the 21 of their papers we have counts for
21 papers
Einstein's Equations and Equivalent Hyperbolic Dynamical Systems
Arlen Anderson, Yvonne Choquet-Bruhat, James W. York
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing f…
Generalized Einstein theory with fundamental cosmological stress tensor
Arlen Anderson
Careful analysis of parametrized variational principles in mechanics and field theory leads to a generalization of Einstein theory that includes a cosmological stress tensor. This…
Fixing Einstein's equations
Arlen Anderson, James W. York
Einstein's equations for general relativity, when viewed as a dynamical system for evolving initial data, have a serious flaw: they cannot be proven to be well-posed (except in spe…
Hamiltonian Time Evolution for General Relativity
Arlen Anderson, James W. York
Hamiltonian time evolution in terms of an explicit parameter time is derived for general relativity, even when the constraints are not satisfied, from the Arnowitt-Deser-Misner-Tei…
Curvature-based Hyperbolic Systems for General Relativity
Yvonne Choquet-Bruhat, James W. York, Arlen Anderson
We review curvature-based hyperbolic forms of the evolution part of the Cauchy problem of General Relativity that we have obtained recently. We emphasize first order symmetrizable…
Curvature-based Gauge-Invariant Perturbation Theory for Gravity: A New Paradigm
Arlen Anderson, Andrew M. Abrahams, Chris Lea
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and…