We generalize the result of Lukács et al. on asymptotic stability of the Schwarzschild metric with respect to perturbations in the RobinsonTrautman class of metrics to the case of Petrov type II twisting metrics, uder the condition of asymptotic flatness at future null infinity. The Bondi energy is used as the Lyapunov functional and we prove that the "final state" of such metrics is the Kerr metric.
Conventions and notationThe notation used here is similar to that of [1], with few exceptions. Partial derivatives are denoted by comma. Whenever asymptotically flat space-time is mentioned, it is understood as space-time that admits a piece of future null infinity R × S 2 . The standard metric of S 2 in stereographic coordinates is 2P −2 S dξdξ, where P S = 1 + 1 2 |ξ| 2 . Any other function P divided by P S will be denoted byP .