Initial Data for Numerical Relativity

Abstract

Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy initial data in the 3+1 decomposition of Einstein's equations. We will then explore how these formalisms have been used in constructing initial data for spacetimes containing black holes and neutron stars. In the topics discussed, emphasis is placed on those issues that are important for obtaining astrophysically realistic initial data for compact binary coalescence.

50 pages, LaTeX(livrev.cls), Review article for "Living Reviews in Relativity" (http://www.livingreviews.org/), July 2000

References in corpus (12)

• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests
• Regular coordinate systems for Schwarzschild and other spherical spacetimes
• A new form of the Kerr solution
• The Innermost Stable Circular Orbit of Binary Black Holes
• Nonexistence of conformally flat slices of the Kerr spacetime
• A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity
• Quasi-circular Orbits for Spinning Binary Black Holes
• Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits : Polytropic equations of state
• Irrotational binary neutron stars in quasiequilibrium
• Revised Relativistic Hydrodynamical Model for Neutron-Star Binaries
• A multi-domain spectral method for scalar and vectorial Poisson equations with non-compact sources

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