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 gravitational waves (Brill waves). A gaugeinvariant 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 quasinormal 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 find excellent agreement between the theoretically predicted $\ell =2\mathrm{}$ and $\ell =4\mathrm{}$ wave forms and the wave forms 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.

• Received 20 December 1991

DOI:https://doi.org/10.1103/PhysRevD.45.3544