Massive Nordström Scalar (Density) Gravities from Universal Coupling

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 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.

Forthcoming in General Relativity and Gravitation

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Cited by in corpus (9)

• Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang-Mills and Gravitational Theories
• Space-time Philosophy Reconstructed via Massive Nordström Scalar Gravities? Laws vs. Geometry, Conventionality, and Underdetermination
• The Nontriviality of Trivial General Covariance: How Electrons Restrict 'Time' Coordinates, Spinors (Almost) Fit into Tensor Calculus, and 7/16 of a Tetrad Is Surplus Structure
• Universally Coupled Massive Gravity, III: dRGT-Maheshwari Pure Spin-$2$, Ogievetsky-Polubarinov and Arbitrary Mass Terms
• Einstein's Equations for Spin $2$ Mass $0$ from Noether's Converse Hilbertian Assertion
• Kant, Schlick and Friedman on Space, Time and Gravity in Light of Three Lessons from Particle Physics
• Space-time Constructivism vs. Modal Provincialism: Or, How Special Relativistic Theories Needn't Show Minkowski Chronogeometry
• Does a Second-Class Primary Constraint Generate a Gauge Transformation? Electromagnetisms and Gravities, Massless and Massive
• Change in Hamiltonian General Relativity with Spinors