Geroch energy

In general relativity, the Geroch energy (also called the Geroch mass) is a proposed quasi-local mass associated with a closed two-dimensional surface embedded in a three-dimensional Riemannian manifold. It was introduced by Robert Geroch as a geometric quantity intended to measure the mass contained within a finite region, using only the geometry of the bounding surface. A key feature of the Geroch energy is its monotonicity under outward deformations of surfaces that later became formalized as the inverse mean curvature flow, a property that was crucial in the proof of the Penrose inequality in the time-symmetric case.