= Komar mass
{c}
{title2=$M_K$}
{wiki}
<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,
$$
M_K=-\frac{1}{8\pi}\int_S\star dk.
$$
The <exterior derivative> and <Hodge star operator> turn the stationary gravitational field into a flux through the surrounding surface.<General Relativity by David Tong>[Section 4.3.3, Komar integrals and mass normalization]{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.
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