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

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, epsilon(S) = S/M-ADM(2), is a superposition with relative weights of Lambda = 0.783 for conformal Kerr and (1 - Lambda) = 0.217 for Bowen-York. In addition, we measure the spin relative to the initial horizon mass M-H0, and find that the quantity chi = S/M-H0(2) reaches a maximum of chi(max) = 0.9856 for Lambda = 0.753. After equilibration, the final black-hole spin should lie in the interval 0.9324 < chi(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 chi(max)(final) = 0.935 when Lambda = 0.783. We also study the evolution of the apparent horizon structure of this maximal black hole in detail.