General Relativity and Gravitation

, Volume 43, Issue 3, pp 871–895 | Cite as

Massive Nordström scalar (density) gravities from universal coupling

Research Article


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 Nordström’s “massless” theory, massive scalar gravities are strictly Special Relativistic, being invariant under the Poincaré 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.


Scalar gravity Klein–Gordon equation Nordström Massive Spinor Scalar density 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Physics, Department of Philosophy, and Reilly Center for ScienceTechnology and Values, University of Notre DameNotre DameUSA

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