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Komar superpotential

Hilbert–Einstein Lagrangian From Wikipedia, the free encyclopedia

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In general relativity, the Komar superpotential, named after Arthur Komar who wrote about it in 1952,[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]

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