Komar charge

A Komar integral constructs a conserved gravitational charge from the exterior derivative of the one-form dual to a Killing vector. In four dimensions, a stationary mass is conventionally normalized as

Komar mass is the Komar charge associated with a stationary timelike Killing vector, using the normalization appropriate to gravitational mass.

For a spacetime with a non-flat reference background, replacing $k$ by $k-\bar{k}$ removes the background contribution and can make the Komar surface integral finite.