Abstract:
We derive Einstein's equations from a linear theory in flat space–time using
free-field gauge invariance and universal coupling. The gravitational
potential can be either covariant or contravariant and of almost any density
weight. We adapt these results to yield universally coupled massive variants
of Einstein's equations, yielding two one-parameter families of distinct
theories with spin 2 and spin 0. The Freund–Maheshwari–Schonberg theory
is therefore not the unique universally coupled massive generalization of
Einstein's theory, although it is privileged in some respects. The theories
we derive are a subset of those found by Ogievetsky and Polubarinov by other
means. The question of positive energy, which continues to be discussed,
might be addressed numerically in spherical symmetry. We briefly comment on
the issue of causality with two observable metrics and the need for gauge
freedom and address some criticisms by Padmanabhan of field derivations of
Einstein-like equations along the way.
Citation:
J. B. Pitts, W. C. Schieve, “Universally coupled massive gravity”, TMF, 151:2 (2007), 311–336; Theoret. and Math. Phys., 151:2 (2007), 700–717
This publication is cited in the following 24 articles:
Susobhan Mandal, S. Shankaranarayanan, “Generation of effective massive Spin-2 fields through spontaneous symmetry breaking of scalar field”, Gen Relativ Gravit, 57:2 (2025)
J. Brian Pitts, “Does a second-class primary constraint generate a gauge transformation? Electromagnetisms and gravities, massless and massive”, Annals of Physics, 462 (2024), 169621
Daniel Linford, “On the Boundary of the Cosmos”, Found Phys, 53:4 (2023)
Charles T. Sebens, “The Mass of the Gravitational Field”, The British Journal for the Philosophy of Science, 73:1 (2022), 211
Duerr P.M., “Against ‘Functional Gravitational Energy’: a Critical Note on Functionalism, Selective Realism, and Geometric Objects and Gravitational Energy”, Synthese, 199:S2 (2021), 299–333
Pitts J.B., “Change in Hamiltonian General Relativity With Spinors”, Found. Phys., 51:6 (2021), 109
Linford D., “Neo-Lorentzian Relativity and the Beginning of the Universe”, Eur. J. Philos. Sci., 11:4 (2021), 111
Salimkhani K., “The Dynamical Approach to Spin-2 Gravity”, Stud. Hist. Philos. Mod. Phys., 72 (2020), 29–45
Le Bihan B., Linnemann N., “Have We Lost Spacetime on the Way? Narrowing the Gap Between General Relativity and Quantum Gravity”, Stud. Hist. Philos. Mod. Phys., 65 (2019), 112–121
Alshal H., Curtright T.L., “Massive Dual Gravity in N Spacetime Dimensions”, J. High Energy Phys., 2019, no. 9, 063
Pitts J.B., “Kant, Schlick and Friedman on Space, Time and Gravity in Light of Three Lessons From Particle Physics”, Erkenntnis, 83:2 (2018), 135–161
Pitts J.B., “Equivalent Theories and Changing Hamiltonian Observables in General Relativity”, Found. Phys., 48:5, SI (2018), 579–590
Pitts J.B., “Equivalent theories redefine Hamiltonian observables to exhibit change in general relativity”, Class. Quantum Gravity, 34:5 (2017), 055008
Pitts J.B., “Universally Coupled Massive Gravity, III: Drgt-Maheshwari Pure Spin-2, Ogievetsky-Polubarinov and Arbitrary Mass Terms”, Ann. Phys., 365 (2016), 73–90
Pitts J.B., “Einstein?s Equations for Spin 2 Mass 0 from Noether?s Converse Hilbertian Assertion”, Stud. Hist. Philos. Mod. Phys., 56 (2016), 60–69
Borka D., Capozziello S., Jovanovic P., Jovanovic V.B., “Probing hybrid modified gravity by stellar motion around Galactic Center”, Astropart Phys., 79 (2016), 41–48
Pitts J.B., “Space–time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry, conventionality, and underdetermination”, Stud. Hist. Philos. Mod. Phys., 53 (2016), 73–92
Borka D., Jovanovic P., Jovanovic V.B., Zakharov A.F., “Constraining the Range of Yukawa Gravity Interaction From S2 Star Orbits”, J. Cosmol. Astropart. Phys., 2013, no. 11, 050
Pitts J.B., “Universally coupled massive gravity, II: Densitized tetrad and cotetrad theories”, Gen Relativity Gravitation, 44:2 (2012), 401–426
Citation in format AMSBIB
Contact us: