The Riemannian Penrose inequality is a result in differential geometry and general relativity that relates the total mass of a Riemannian manifold with boundary to the area of its boundary. It is an extension of the classical Penrose inequality, which is a key result in the theory of general relativity regarding the mass of gravitational systems.
Articles by others on the same topic
For complete asymptotically flat three-dimensional Riemannian initial data with nonnegative scalar curvature and an outermost compact minimal surface boundary of area , the Riemannian Penrose inequality gives the displayed bound. Equality is realized by the spatial exterior of Schwarzschild spacetime. Time-symmetric gravitational initial data have this form when the Einstein field equations and energy hypothesis give the required nonnegative curvature. This theorem does not justify substituting arbitrary non-time-symmetric apparent horizon area into the same formula.