In general relativity, the Komar superpotential,[1] corresponding to the invariance of the Hilbert–Einstein Lagrangian
, is the tensor density: associated with a vector field
denotes covariant derivative with respect to the Levi-Civita connection.
The Komar two-form: where
α β
denotes interior product, generalizes to an arbitrary vector field
the so-called above Komar superpotential, which was originally derived for timelike Killing vector fields.
Komar superpotential is affected by the anomalous factor problem: In fact, when computed, for example, on the Kerr–Newman solution, produces the correct angular momentum, but just one-half of the expected mass.
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