Numerical study of cosmic no-hair conjecture. II. Analysis of initial data

We investigate the initial data for localized gravitational waves in space-time with a cosmological constant. Using a conformal transformation, we find that the Hamiltonian and momentum constraints in the conformal frame turn out to be the same as those for a vacuum space-time without. As initial data, we consider Brill's waves in the conformal frame and discuss the trapped and antitrapped surfaces in the physical frame. Just as Brill's wave in asymptotically flat space-time, the gravitational "mass" of our case is positive; however, the waves with a large gravitational mass do not always provide trapped surfaces in contrast with the case of =0. The large amount of gravitational waves, hence, does not seem to be an obstacle to the cosmic no-hair conjecture.