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Theoretical and Mathematical Physics

, Volume 151, Issue 2, pp 700–717 | Cite as

Universally coupled massive gravity

  • J. B. Pitts
  • W. C. Schieve
Article

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.

Keywords

massive gravity bimetric ghost positive mass causality 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • J. B. Pitts
    • 1
    • 2
    • 3
  • W. C. Schieve
    • 1
  1. 1.Department of PhysicsUniversity of Texas at AustinAustinUSA
  2. 2.Department of MathematicsSt. Edward’s UniversityAustin
  3. 3.History and Philosophy of Science Graduate ProgramUniversity of Notre DameNotre DameUSA

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