Gauge-Invariant Localization of Infinitely Many Gravitational Energies
  from All Possible Auxiliary Structures
  The problem of finding a covariant expression for the distribution and
conservation of gravitational energy-momentum dates to the 1910s. A suitably
covariant infinite-component localization is displayed, reflecting Bergmann's
realization that there are infinitely many conserved gravitational
energy-momenta. Initially use is made of a flat background metric (or rather,
all of them) or connection, because the desired gauge invariance properties are
obvious. Partial gauge-fixing then yields an appropriate covariant quantity
without any background metric or connection; one version is the collection of
pseudotensors of a given type, such as the Einstein pseudotensor, in_every_
coordinate system. This solution to the gauge covariance problem is easily
adapted to any pseudotensorial expression (Landau-Lifshitz, Goldberg,
Papapetrou or the like) or to any tensorial expression built with a background
metric or connection. Thus the specific functional form can be chosen on
technical grounds such as relating to Noether's theorem and yielding expected
values of conserved quantities in certain contexts and then rendered covariant
using the procedure described here. The application to angular momentum
localization is straightforward. Traditional objections to pseudotensors are
based largely on the false assumption that there is only one gravitational
energy rather than infinitely many.
