Static vacuum metrics are solutions to the Einstein Field Equations with vanishing stress‐energy tensor and featuring a very special metric structure (warped product).
Such a structure induces a natural foliation of the spacetime into space‐like slices which are all isometric to each other, so that the corresponding physical universe is static. We discuss the problem of the classi_cation of such solutions in the case of positive cosmological constant. To this end, we introduce an appropriate notion of mass, showing that it satis_es a Positive Mass Statement and a Riemannian Penrose {like inequality. Building on this, we prove a uniqueness result for the Schwarzschild
{de Sitter solution, which is somehow reminiscent of the well known Black Hole Uniqueness Theorem for the Schwarzschild solution.
Stefano Borghini (Italy): Static vacuum Spacetime with positive Cosmological Constant
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