Massless or massive graviton?

Mathematics – Logic

Scientific paper

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Missing Mass: Cosmology

Scientific paper

The author shows that, in the application of Riemannian geometry to gravity, there exists a superpotential Vij of the Riemann-Christoffel tensor which is the tensor generalization of Poisson's classical potential. Leaving open the question of a zero or nonzero rest mass k of the graviton he shows that, in the latter case, k2Vij is an energy-momentum density, or "Maxwell-like tensor", of the gravity field itself, adding to the "material tensor" in the right-hand sides of both the (generalized) Poisson equation and the Einstein gravity equation, but that, nevertheless, Einstein's requirement of geodesic motion of a point particle is rigorously preserved. Two interesting possibilities are thus opened: a tentative explanation of the cosmological "missing mass" and quantization of the Riemannian gravity field along a standard procedure.

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