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Study of conformally flat initial data for highly spinning black holes and their early evolutions

Carlos O. Lousto, Hiroyuki Nakano, Yosef Zlochower, Bruno C. Mundim, and Manuela Campanelli

Center for Computational Relativity and Gravitation, and School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA

Phys. Rev. D 85, 124013 – Published 7 June, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.124013

Abstract

We study conformally flat initial data for an arbitrary number of spinning black holes with exact analytic solutions to the momentum constraints constructed from a linear combination of the classical Bowen-York and conformal Kerr extrinsic curvatures. The solution leading to the largest intrinsic spin, relative to the Arnowitt-Deser-Misner (ADM) mass of the spacetime, $ϵ_{S} = S / M_{ADM}^{2}$ , is a superposition with relative weights of $Λ = 0.783$ for conformal Kerr and $(1 - Λ) = 0.217$ for Bowen-York. In addition, we measure the spin relative to the initial horizon mass $M_{H_{0}}$ , and find that the quantity $χ = S / M_{H_{0}}^{2}$ reaches a maximum of $χ^{\max } = 0.9856$ for $Λ = 0.753$ . After equilibration, the final black-hole spin should lie in the interval $0.9324 < χ_{final} < 0.9856$ . We perform full numerical evolutions to compute the energy radiated and the final horizon mass and spin. We find that the black hole settles to a final spin of $χ_{final}^{\max } = 0.935$ when $Λ = 0.783$ . We also study the evolution of the apparent horizon structure of this maximal black hole in detail.

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Study of conformally flat initial data for highly spinning black holes and their early evolutions

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