 Komar mass

Komar mass is a gravitational surface charge associated with a stationary Killing vector field that is timelike at infinity. In four spacetime dimensions with $G=c=1$, let $k$ be the one-form dual to the Killing field, normalized to unit time translation at infinity. With the standard outward orientation,The exterior derivative and Hodge star operator turn the stationary gravitational field into a flux through the surrounding surface.^[ref]

In a vacuum region with zero cosmological constant, the field equations make this flux independent of smooth surface deformations that cross no source or inner boundary. A nonzero charge can therefore surround a vacuum black hole. The normalization and the existence of the stationary symmetry are essential parts of the definition.