Collision of boosted black holes: Second order close limit calculations - art. no. 044024

We study the head-on collision of black holes starting from unsymmetrized, Brill-Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the "close lim it approximation," in which small initial separation and momentum are assum ed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calcu lations were used for momentarily stationary initial data, and another stud y in which linearized perturbation theory was used for initially moving hol es. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbat ion theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulati ons, and will be important to subsequent applications of approximation meth ods for collisions. [S0556-2821(98)03822-3].