We study the head-on collision of two equal mass, nonrotating black holes. We consider a range of cases from holes surrounded by a common horizon to holes initially separated by about 20M , where M is the mass of each hole. We determine the waveforms and energies radiated for both the ℓ = 2 and ℓ = 4 waves resulting from the collision. In all cases studied the normal modes of the final black hole dominate the spectrum. We also estimate analytically the total gravitational radiation emitted, taking into account the tidal heating of horizons using the membrane paradigm, and other effects. For the first time we are able to compare analytic calculations, black hole perturbation theory, and strong field, nonlinear numerical calculations for this problem, and we find excellent agreement.PACS numbers: 04.30.+x, 95.30.Sf Typeset Using REVTEX

The head-on collision of two nonrotating axisymmetric equal mass black holes is treated numerically. We take as initial data the single parameter family of time-symmetric solutions discovered by Misner which consists of two Einstein-Rosen bridges that can be placed arbitrarily distant from one another. A number of problems associated with previous attempts to evolve these data sets have been overcome. In this article, we discuss our choices for coordinate systems, gauges, and the numerical algorithms that we have developed to evolve this system. PACS numbers: 04.30.+x, 95.30.Sf