Construction of initial data for 3+1 numerical relativity

Abstract

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 technique, introduced by Lichnerowicz and enhanced by York, is presented. Two standard methods, the conformal transverse-traceless one and the conformal thin sandwich, are discussed and illustrated by some simple examples. Finally a short review regarding initial data for binary systems (black holes and neutron stars) is given.

Minor modifications, updated references, 28 pages, 5 figures, contribution to the Proceedings of the VII Mexican School on Gravitation and Mathematical Physics, held in Playa del Carmen, Mexico (Nov. 26 - Dec. 2, 2006), Journal of Physics: Conference Series, in press

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• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes
• Numerical evolution of multiple black holes with accurate initial data
• Extremal black holes in the Hořava-Lifshitz gravity
• Binary Neutron Stars in Quasi-equilibrium
• Multipole Analysis of Kicks in Collision of Binary Black Holes
• Self-Interacting Gravitational Atoms in the Strong-Gravity Regime
• Boson star head-on collisions with constraint-violating and constraint-satisfying initial data
• NRPyElliptic: A Fast Hyperbolic Relaxation Elliptic Solver for Numerical Relativity, I: Conformally Flat, Binary Puncture Initial Data
• A spectral method algorithm for numerical simulations of gravitational fields
• Galerkin-Collocation domain decomposition method for arbitrary binary black holes
• The Algebraic-Hyperbolic Approach to the Linearized Gravitational Constraints on a Minkowski Background
• Modifications for numerical stability of black hole evolution
• Black hole initial data by numerical integration of the parabolic-hyperbolic form of the constraints
• Shells around black holes: the effect of freely specifiable quantities in Einstein's constraint equations
• Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild
• The inverse spatial Laplacian of spherically symmetric spacetimes
• A spectral approach to numerical simulations of the ADM equations