Almost-stationary motions and gauge conditions in General Relativity
arXiv:gr-qc/0509015 · doi:10.1103/PhysRevD.72.124010
Abstract
An almost-stationary gauge condition is proposed with a view to Numerical Relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is derived by a variational principle, by minimizing the deviations from isometry. The corresponding almost-stationary gauge condition allows one to put the field equations in hyperbolic form, both in the free-evolution ADM and in the Z4 formalisms.
arXiv commentTalk presented at the Spanish Relativity Meeting, September 6-10 2005 Revised version
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Cited by in corpus (13)
- Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
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- A Proposal for Determining the Energy Content of Gravitational Waves by Using Approximate Symmetries of Differential Equations
- Some globally conserved currents from generalized Killing vectors and scalar test fields
- Second-Order Approximate Symmetries of the Geodesic Equations for the Reissner-Nordström Metric and Re-Scaling of Energy of a Test Particle
- Almost-Killing conserved currents: a general mass function
- Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law
- Hidden Killing Fields, Geometric Symmetries and Black Hole Mergers
- Generalized Komar currents for vector fields
- Perturbations of the almost Killing equation and their implications
- Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity
- Vector Field Dynamics: Field Equations and Energy Tensor