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arXiv · 1010.0227

Massive Nordstr\"om Scalar (Density) Gravities from Universal Coupling

J. Brian Pitts
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Abstract

Both particle physics and the 1890s Seeliger-Neumann modification of Newtonian gravity suggest considering a "mass term" for gravity, yielding a finite range due to an exponentially decaying Yukawa potential. Unlike Nordstr\"{o}m's "massless" theory, massive scalar gravities are strictly Special Relativistic, being invariant under the Poincar\'{e} group but not the conformal group. Geometry is a poor guide to understanding massive scalar gravities: matter sees a conformally flat metric, but gravity also sees the rest of the flat metric, barely, in the mass term. Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source. All are new except the Freund-Nambu theory. The smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities. The ease of accommodating electrons, protons and other fermions using density-weighted Ogievetsky-Polubarinov spinors in scalar gravity is noted.

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J. Brian Pitts. 2010-10-01. Massive Nordstr\"om Scalar (Density) Gravities from Universal Coupling. https://doi.org/10.1007/s10714-010-1100-7

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