Dynamical evolution of gravitational waves in asymptotically de Sitter spacetime

We perform numerical computations to investigate the dynamical evolution of axisymmetric gravitational waves in asymptotically de Sitter spacetime. The final fates of such spacetimes are classified into two types: (1) de Sitter spacetime with small perturbations, and (2) Schwarzschild–de Sitter–like spacetime with both black-hole and cosmological apparent horizons. We also find that if the mass of gravitational waves is larger than the critical value, ${\mathit{M}}_{\mathrm{crit}}$≡(3 √Λ ${)}^{\mathrm{-}1}$, then the black hole is not formed even in the case that there exist highly nonlinear localized gravitational waves. In such a case, the Universe is initially dominated by gravitational waves rather than a cosmological constant Λ and eventually approaches a de Sitter universe. These results are consistent with the previous analysis by use of initial data.