Penrose inequalities and a positive mass theorem for charged black holes in higher dimension

Abstract

We use the inverse mean curvature flow to establish Penrose-type inequalities for time-symmetric Einstein-Maxwell initial data sets which can be suitably embedded as a hypersurface in Euclidean space ${\mathbb{R}}^{n+1}$, $n\ge 3$. In particular, we prove a positive mass theorem for this class of charged black holes. As an application we show that the conjectured upper bound for the area in terms of the mass and the charge, which in dimension $n=3$ is relevant in connection with the Cosmic Censorship Conjecture, always holds under the natural assumption that the horizon is stable as a minimal hypersurface.

13 pages; no figures

References in corpus (10)

• On the Riemannian Penrose inequality in dimensions less than 8
• Some Comments on Gravitational Entropy and the Inverse Mean Curvature Flow
• On the Penrose Inequality for Charged Black Holes
• Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum
• A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold
• Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces
• Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space
• A rigidity result for the graph case of the Penrose inequality
• On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture
• A Penrose inequality for asymptotically locally hyperbolic graphs