231 citations · 787 across the 12 of their papers we have counts for
14 papers · 1 filter
Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
I. Cordero-Carrión, J. M. Ibáñez, E. Gourgoulhon +2
Bonazzola, Gourgoulhon, Grandclément, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according…
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
J. L. Jaramillo, J. A. Valiente Kroon, E. Gourgoulhon
This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a…
Shells around black holes: the effect of freely specifiable quantities in Einstein's constraint equations
Keith Matera, Thomas W. Baumgarte, Eric Gourgoulhon
We solve Einstein's constraint equations in the conformal thin-sandwich decomposition to model thin shells of non-interacting particles in circular orbit about a non-rotating black…
Trapping Horizons as inner boundary conditions for black hole spacetimes
J. L. Jaramillo, E. Gourgoulhon, I. Cordero-Carrion +1
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision…
Construction of initial data for 3+1 numerical relativity
Eric Gourgoulhon
This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal…
3+1 Formalism and Bases of Numerical Relativity
Eric Gourgoulhon
These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-conta…