Tensors

Komar superpotential

In general relativity, the Komar superpotential, 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. (Wikipedia).

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Related pages

Christoffel symbols | Tensor density | Tensor calculus | Kerr–Newman metric | Einstein–Hilbert action | Riemann curvature tensor | Levi-Civita connection | Vector field | Killing vector field | Interior product