  We investigated the relation between the behavior of gravitational wave at
late time and the limit structure of future null infinity tangent which will
determine the topology of the event horizon far in the future. In the present
article, we mainly consider a spacetime with two black holes. Although in most
of cases, the black holes coalesce and its event horizon is topologically a
single sphere far in the future, there are several possibilities that the black
holes never coalesce and such exact solutions as examples. In our formulation,
the tangent vector of future null infinity is, under conformal embedding,
related to the number of black holes far in the future through the
Poincar\'e-Hopf's theorem. Under the conformal embedding, the topology of event
horizon far in the future will be affected by the geometrical structure of the
future null infinity. In this article, we related the behavior of Weyl
curvature to this limit behavior of the generator vector of the future null
infinity. We show if Weyl curvature decays sufficiently slowly at late time in
the neighborhood of future null infinity, two black holes never coalesce.
