We introduce and discuss a notion of mass for static vacuum Einstein metrics with positive cosmological constant. In this context, we provide a positive mass statement as well as sharp area bounds for both cosmological horizons and black hole type horizons. In the first case, these area bounds represent the natural extension of a well known result by Boucher, Gibbons and Horowitz, whereas for black hole type horizons they can be seen as the analogue of the celebrated Riemannian Penrose Inequality.
As an application, we deduce a uniqueness statement for the Schwarzschild‐‐de Sitter static black hole. (Joint work with S. Borghini).
Lorenzo Mazzieri (Trento): On the mass of static vacuum Einstein metrics with positive cosmological constant
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