3+1 formalism and bases of numerical relativity - LUTh ...
3+1 formalism and bases of numerical relativity - LUTh ...
3+1 formalism and bases of numerical relativity - LUTh ...
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foliation, 40<br />
free evolution scheme, 176<br />
fully constrained scheme, 175<br />
future, 16<br />
Gamma freezing, 168<br />
Gauss relation, 35<br />
Gaussian curvature, 22<br />
Gaussian normal coordinates, 62<br />
geodesic slicing, 62, 152<br />
globally hyperbolic, 39<br />
Hamiltonian constraint, 54<br />
Hamiltonian constraint violation, 176<br />
harmonic, 159<br />
harmonic decomposition<br />
generalized, 186<br />
harmonic slicing, 159<br />
helical Killing vector, 146<br />
helical symmetry, 146<br />
hole, 115<br />
hyperbolic Gamma driver, 171<br />
hypersurface, 19<br />
induced metric on Σ, 21<br />
intrinsic curvature, 22<br />
inverse conformal metric, 87<br />
Isenberg-Wilson-Mathews approximation, 100<br />
isolated bodies, 103<br />
IWM, 100<br />
Killing vector, 116<br />
Komar angular momentum, 121<br />
Komar mass, 116<br />
Komar mass <strong>of</strong> the hole, 118<br />
KST formulation, 181<br />
lapse function, 41<br />
leaf, 40<br />
Levi-Civita connection, 22<br />
Lichnerowicz equation, 98<br />
Lie derivative, 190<br />
Lie dragged, 42<br />
locally nonrotating observers, 43<br />
longitudinal part, 127<br />
INDEX 219<br />
Lorentz factor, 76<br />
matter energy density, 52<br />
matter momentum density, 52<br />
matter stress tensor, 52<br />
maximal slicing, 153<br />
maximal slicings, 100<br />
mean curvature, 24<br />
minimal distortion, 165<br />
minimal surface, 133<br />
momentarily static, 132<br />
momentum constraint, 54<br />
momentum constraint violation, 177<br />
non-exp<strong>and</strong>ing horizon, 148<br />
normal coordinates, 163<br />
normal evolution vector, 42<br />
null, 21<br />
orthogonal projector onto Σ, 29<br />
parabolic Gamma driver, 170<br />
partially constrained scheme, 175<br />
past, 16<br />
perfect fluid, 75<br />
Plateau problem, 155<br />
Poincaré transformations, 105<br />
polar slicing, 158<br />
positive Yamabe class, 130<br />
principal curvatures, 24<br />
principal directions, 24<br />
principal part, 62<br />
principal symbol, 195<br />
proper baryon number density, 78<br />
proper internal energy, 80<br />
proper rest-mass energy density, 80<br />
pseudo-minimal distortion, 167<br />
pull-back mapping, 20<br />
puncture, 136<br />
push-forward mapping, 20<br />
quasi-isotropic gauge, 114<br />
quasi-linear, 63<br />
radiation gauge, 166<br />
Ricci equation, 48