Can a combination of the conformal thin-sandwich and puncture methods yield binary black hole solutions in quasi-equilibrium?

Abstract

We consider combining two important methods for constructing quasi-equilibrium initial data for binary black holes: the conformal thin-sandwich formalism and the puncture method. The former seeks to enforce stationarity in the conformal three-metric and the latter attempts to avoid internal boundaries, like minimal surfaces or apparent horizons. We show that these two methods make partially conflicting requirements on the boundary conditions that determine the time slices. In particular, it does not seem possible to construct slices that are quasi-stationary and avoid physical singularities and simultaneously are connected by an everywhere positive lapse function, a condition which must obtain if internal boundaries are to be avoided. Some relaxation of these conflicting requirements may yield a soluble system, but some of the advantages that were sought in combining these approaches will be lost.

arXiv comment8 pages, LaTeX2e, 2 postscript figures

References in corpus (14)

• Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?
• A simple construction of initial data for multiple black holes
• Conformal ``thin sandwich'' data for the initial-value problem of general relativity
• Numerical Relativity and Compact Binaries
• Binary black holes in circular orbits. II. Numerical methods and first results
• Binary black holes in circular orbits. I. A global spacetime approach
• Three-dimensional initial data for the collision of two black holes II: Quasi-circular orbits for equal-mass black holes
• The Innermost Stable Circular Orbit of Binary Black Holes
• Corotating and irrotational binary black holes in quasi-circular orbits
• A relativistic formalism to compute quasi-equilibrium configurations of non-synchronized neutron star binaries
• Innermost circular orbit of binary black holes at the third post-Newtonian approximation
• Circular orbits of corotating binary black holes: comparison between analytical and numerical results
• Comparing initial-data sets for binary black holes
• Comparing Criteria for Circular Orbits in General Relativity

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