Hamiltonian map to conformal modification of spacetime metric: Kaluza-Klein and TeVeS

Lawrence P. Horwitz*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this chapter, we discuss the cosmological problem of accounting for the radiation curves of galaxies. It has commonly been assumed that the disagreement of simulations using the Newtonian form for gravitational attraction (with forces proportional to 1/r2 between stellar bodies) with the Tulley-Fisher radiation curves (Tulley 1977) is due to a matter distribution that is not visible through emitted light (so-called “dark matter”), but it has been difficult to find a viable candidate for what that matter should be. Milgrom (1983) has proposed (MOND) that the Newton law be modified by a law which coincides with Newton’s for large accelerations, but differs from it when the accelerations are small. This suggestion has resulted in models which have been very successful in describing the galaxy radiation curves (e.g. Famaey 2012). However, as emphasized by Bekenstein (2004), it is difficult to change the basic Newton law without changing Einstein’s formulation of gravity in the framework of general relativity (e.g. Weinberg 1972). He proposed that the Einstein metric gμν be replaced by a conformal modification e−2φgμν is a scalar field; in this way the modification proposed by Milgrom can be achieved in the post-Newtonian limit.

Original languageEnglish
Title of host publicationFundamental Theories of Physics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
StatePublished - 2015

Publication series

NameFundamental Theories of Physics
ISSN (Print)0168-1222
ISSN (Electronic)2365-6425


  • Connection form
  • Dark energy
  • Dark matter
  • Gauge field
  • Gauge transformation


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