Cosmic no‐hair conjecture and conformal vector fields

In this paper, we investigate cosmic no‐hair properties mathematically when a given Riemannian manifold admits a nontrivial closed conformal vector field. Let be a compact Riemannian ‐manifold with connected non‐empty boundary . Assume that there exists a smooth function on with in and satisfying the static vacuum equation. We prove that if admits a nontrivial closed conformal vector field, then must be isometric to a hemisphere . We also discuss a static triple admitting a nontrivial conformal vector field which is not necessarily closed.