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 , and where denotes covariant derivative with respect to the Levi-Civita connection.

The Komar two-form:

where 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.[2]

See also

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Notes

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  1. ^ Arthur Komar (1959). "Covariant Conservation Laws in General Relativity". Phys. Rev. 113 (3): 934. Bibcode:1959PhRv..113..934K. doi:10.1103/PhysRev.113.934.
  2. ^ J. Katz (1985). "A note on Komar's anomalous factor". Class. Quantum Gravity. 2 (3): 423. doi:10.1088/0264-9381/2/3/018. S2CID 250898281.

References

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