Collision of two black holes: Theoretical framework

Abstract

Highly nonspherical time-dependent collisions between black holes may be powerful sources of gravitational radiation. We consider various attempts at estimating the efficiency of the generation of radiation by such collisions. To determine the actual efficiency as well as to understand the details of the dynamical coalescence of black-hole event horizons, we have developed a numerical method for solving the Einstein gravitational field equations in these high-velocity strong-field regions. The head-on collision of two nonrotating vacuum black holes is chosen as an example of our technique. We use the geometrodynamical model of a black hole as an Einstein-Rosen bridge. The initial data to be evolved are the time-symmetric conformally flat data discovered by Misner. A new set of spatial coordinates for these data is derived. Then the general space plus time decomposition of Einstein's equations is presented and specialized to the axisymmetric nonrotating case. Details of the evolution will be given in later papers.