Doubling of Asymptotically Flat Half-spaces and the Riemannian Penrose Inequality

Building on previous works of Bray, of Miao, and of Almaraz, Barbosa, and de Lima, we develop a doubling procedure for asymptotically flat half-spaces (M, g) with horizon boundary $$ and mass $$. If $$, (M, g) has non-negative scalar curvature, and the boundary $$ is mean-convex, we obtain the Riemannian Penrose-type inequality as a corollary. Moreover, in the case where $$ is not totally geodesic, we show how to construct local perturbations of (M, g) that increase the scalar curvature. As a consequence, we show that equality holds in the above inequality if and only if the exterior region of (M, g) is isometric to a Schwarzschild half-space. Previously, these results were only known in the case where $$ and $$ is a connected free boundary hypersurface.