Numerically generated black-hole spacetimes: Interaction with gravitational waves.

In this paper we present results from a new two-dimensional numerical relativity code used to study the interaction of gravitational waves with a black hole. The initial data correspond to a single black hole superimposed with time-symmetric gravita-tional waves (Brill waves). A gauge invariant method is presented for extracting the gravitational waves from the numerically generated spacetime. We show that the interaction between the gravitational wave and the black hole excites the quasinor-mal modes of the black hole. An extensive comparison of these results is made to black hole perturbation theory. For low amplitude initial gravitational waves, we nd excellent agreement between the theoretically predicted`= 2 and`= 4 waveforms and the waveforms generated by the code. Additionally, a code test is performed wherein the propagation of the wave on the black hole background is compared to the evolution predicted by perturbation theory.