Collision of two slowly rotating, initially nonboosted, black holes in the close limit

We study the collision of two slowly rotating, initially nonboosted, black holes in the close limit. A "punctures" modification of the Bowen-York method is used to construct conformally flat initial data appropriate to the problem. We keep only the lowest nontrivial orders capable of giving rise to radiation of both gravitational energy and angular momentum. We show that even with these simplifications, an extension to higher orders of the linear Regge-Wheeler-Zerilli black hole perturbation theory is required to deal with the evolution equations of the leading contributing multipoles. This extension is derived, together with appropriate extensions of the Regge-Wheeler and Zerilli equations. The data are numerically evolved using these equations to obtain the asymptotic gravitational waveforms and amplitudes. Expressions for the radiated gravitational energy and angular momentum are derived and used together with the results of the numerical evolution to provide quantitative expressions for the relative contribution of different terms, and their significance is analyzed.