Dynamic black hole spacetimes are studied by examining the evolution of apparent horizons surrounding the holes. We performed numerical evolutions of three different initial data sets: nonrotating black holes distorted by time symmetric (Brill) gravitational waves, distorted rotating black holes, and the time symmetric two black hole Misner data. Although the initial data sets represent different physical problems, the results for these systems are strikingly similar. At early times in the evolution, the apparent horizons may be very distorted and nonspherical (or disjoint in the case of two black holes, but the systems quickly settle down to a nearly spherical or oblate (in the case of rotating holes) configuration and the horizons are then seen to oscillate at the quasinormal frequency of the final black hole. In the case of two black holes with disjoint horizons, we see the appearance of a larger horizon surrounding both holes as they collide. From this point the horizon dynamics is very similar to the single distorted black hole systems. The wavelength and damping time of the quasinormal modes and the rotation parameter in the rotating cases can be read off directly from oscillations in the geometry of the black hole horizons. The apparent horizon is thus shown to be a powerful tool in the study of black hole spacetimes.

• Received 30 March 1994

DOI:https://doi.org/10.1103/PhysRevD.50.3801