Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations
arXiv:gr-qc/0509092 · doi:10.1103/PhysRevD.72.104009
Abstract
We study the implications of adopting hyperbolic driver coordinate conditions motivated by geometrical considerations. In particular, conditions that minimize the rate of change of the metric variables. We analyze the properties of the resulting system of equations and their effect when implementing excision techniques. We find that commonly used coordinate conditions lead to a characteristic structure at the excision surface where some modes are not of outflow-type with respect to any excision boundary chosen inside the horizon. Thus, boundary conditions are required for these modes. Unfortunately, the specification of these conditions is a delicate issue as the outflow modes involve both gauge and main variables. As an alternative to these driver equations, we examine conditions derived from extremizing a scalar constructed from Killing's equation and present specific numerical examples.
9 figures
References in corpus (18)
- Evolution of Binary Black Hole Spacetimes
- Gauge conditions for long-term numerical black hole evolutions without excision
- Global existence for the Einstein vacuum equations in wave coordinates
- A multidomain spectral method for solving elliptic equations
- Numerical Relativity: A review
- General-covariant evolution formalism for Numerical Relativity
- Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries
- Toward standard testbeds for numerical relativity
- Critical Collapse of the Massless Scalar Field in Axisymmetry
- Strongly hyperbolic second order Einstein's evolution equations
- A symmetry-breaking mechanism for the Z4 general-covariant evolution system
- On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations
- Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein's equations
- Dynamical shift conditions for the Z4 and BSSN hyperbolic formalisms
- Symmetry-seeking spacetime coordinates
- On the existence of initial data containing isolated black holes
- Dynamical Gauge Conditions for the Einstein Evolution Equations
- A new geometric invariant on initial data for Einstein equations
Cited by in corpus (13)
- Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
- Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
- Conformal and covariant Z4 formulation of the Einstein equations: strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- Kinetic screening in nonlinear stellar oscillations and gravitational collapse
- UV completions, fixing the equations and nonlinearities in -essence
- K-dynamics: well-posed 1+1 evolutions in K-essence
- A minimization problem for the lapse and the initial-boundary value problem for Einstein's field equations
- Lattice Boltzmann Model for Numerical Relativity
- Well-posed constrained evolution of 3+1 formulations of General Relativity
- Dynamical Chameleon Neutron Stars: stability, radial oscillations and scalar radiation in spherical symmetry
- Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity
- Flux-Vector-Splitting (FVS) method for Z4 formalism and its numerical analysis