Conformal-thin-sandwich initial data for a single boosted or spinning black hole puncture

Abstract

Sequences of initial-data sets representing binary black holes in quasi-circular orbits have been used to calculate what may be interpreted as the innermost stable circular orbit. These sequences have been computed with two approaches. One method is based on the traditional conformal-transverse-traceless decomposition and locates quasi-circular orbits from the turning points in an effective potential. The second method uses a conformal-thin-sandwich decomposition and determines quasi-circular orbits by requiring the existence of an approximate helical Killing vector. Although the parameters defining the innermost stable circular orbit obtained from these two methods differ significantly, both approaches yield approximately the same initial data, as the separation of the binary system increases. To help understanding this agreement between data sets, we consider the case of initial data representing a single boosted or spinning black hole puncture of the Bowen-York type and show that the conformal-transverse-traceless and conformal-thin-sandwich methods yield identical data, both satisfying the conditions for the existence of an approximate Killing vector.

13 pages, 2 figures

References in corpus (5)

• Hydrodynamic Simulations in 3+1 General Relativity
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• On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes
• Can a combination of the conformal thin-sandwich and puncture methods yield binary black hole solutions in quasi-equilibrium?
• Comparing Criteria for Circular Orbits in General Relativity

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• Construction of initial data for 3+1 numerical relativity
• Approximate initial data for binary black holes
• Perturbational Treatment of the Gravitational Potential Effect on Binary Black Hole Evolution
• Conformal thin-sandwich puncture initial data for boosted black holes
• Puncture black hole initial data in the conformal thin-sandwich formalism
• Analytical Tendex and Vortex Fields for Perturbative Black Hole Initial Data