A Penrose-type inequality for static spacetimes

Abstract

We establish a lower bound on the total mass of the time slices of (n + 1)-dimensional asymptotically flat standard static spacetimes under the timelike convergence condition. The inequality can be viewed equivalently as a Minkowski-type inequality in these spaces, i.e. as a lower bound on the total mean curvature of the boundary, and thus extends inequalities from [3], [22], [19], and [10]. Equality is achieved only by slices of Schwarzschild space and is related to the characterization of quasi-spherical static vacuum metrics from [10]. As a notable special case of the main inequality, we obtain the Riemannian Penrose inequality in all dimensions for static spaces under the TCC.

14 pages, asymptotic assumptions improved

References in corpus (7)

• Uniqueness of the static Einstein-Maxwell spacetimes with a photon sphere
• Mass-capacity inequalities for conformally flat manifolds with boundary
• Large isoperimetric regions in asymptotically hyperbolic manifolds
• No static bubbling spacetimes in higher dimensional Einstein-Maxwell theory
• On inverse mean curvature flow in Schwarzschild space and Kottler space
• On the Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space
• On a Minkowski-like inequality for asymptotically flat static manifolds