Cosmic no-hair conjecture and conformal vector fields

초록

In this paper, we investigate cosmic no-hair properties mathematically when agiven Riemannian manifold admits a nontrivial closed conformal vector field.Let ( , ) be a compact Riemannian -manifold with connected non-emptyboundary . Assume that there exists a smooth function on with > 0in ⧵ and = −1 (0) satisfying the static vacuum equation. We provethat if ( , ) admits a nontrivial closed conformal vector field, then must beisometric to a hemisphere +. We also discuss a static triple ( , , ) admittinga nontrivial conformal vector field which is not necessarily closed.

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