The goal of this paper is to introduce and to study analogues of the Euclidean Funk and Hilbert metrics on open convex subsets of the hyperbolic space and of the sphere . We highlight some striking similarities among the three cases (Euclidean, sp...
The most general formulation of Penrose's inequality yields a lower bound for Arnowitt-Deser-Misner mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the a...