Generalization of Riemannian Penrose inequality in weak gravitational field
Riemannian Penrose inequality gives the upper bound of the area of the outermost minimal surface in an asymptotically flat spatial surface with nonnegative curvature. The inequality shows, roughly speaking, the upper-bound area of black hole horizon, that is, it can be applied in a region with strong gravitational field.
We deform this inequality so that it can be applied in weak gravitational field. Hence, we show a generalized area inequality.