Open Journal Systems

Is Spacetime Non-metric?

Mark D. Roberts


If one assumes higher dimensions and that dimensional reduction from higher dimensions produces scalar-tensor theory and also that Palatini variation is the correct method of varying scalar-tensor theory then spacetime is nonmetric. Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation equations occur are discussed: it is found that the Jordan frame has more information, this can be expressed in several ways, the simplest is that the extra information corresponds to the function multiplying the Ricci scalar in the action. The Einstein frame has the advantages that stress conservation implies no currents and that the field equations are easier to work with. This is illustrated by application to Robertson-Walker spacetime.


Jordan frame; Einstein frame; non-metrcity; palatini variation

Full Text:



Asymptotic freedom in infaltionary cosmology with a non-minimally coupled Higgs field.Andrei O. Barovnisky, Alexander Yu. Kamshchik, Claus Kiefer, Alexei A. Starobinsky and Christian F. Steinwachs.JCAP 12 (2009) 003, 0904.1698 2

Higgs boson, renormalization group and naturalness in cosmology. Andrei O. Barovnisky, Alexander Yu. Kamshchik, Claus Kiefer, Alexei A. Starobinsky and Christian F. Steinwachs.Eur. Phys. J. C72 (2012) 2219, 0910.1041 2

Standard model Higgs boson mass from inflation: two loop analaysis.F. Bezrukov and M. Shaposhnikov.JHEP 0907(2009)089, 0904.1537 2

Palatini variational principle for an extended Einstein-Hilbert action.Howard Steven Burton and Robert B. Mann.Phys.Rev.D57(1998)4754-4759, gr-qc/9711003 2, 3

On the Palatini Variation and Connection Theories of Gravity.Howard Steven Burton.Ph.D.Thesis, Waterloo Canada, (1998). 2, 3

Gianluca Calcagni, Classical and Quantum Cosmology, ISSN 1868-4513 Springer (2017) 2

Tensor multi-scalar theories of gravitation.Thilbault Damour and Gilles Esposito-Farese.Class.Q.Grav.9(1992)2093-2176. 2, 3

Newtonian limit of the singular f(R) gravity in the Palatini formalism. Alfredo E.Dom´ınguez and Daniel E.Barraco. Phys.Rev.D70(2004)043505, gr-qc/0408069 2

Conformal transformations in classical gravity and in cosmology.Valerio Faraoni, Edgard Gunzig and Pasquale 2

f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints.St´ephane Fay, Reza Tavakol and Shinj Tsujikawa. gr-qc/0701479 2

The Universality of Einstien Equations.Marco Ferraris, Mauro Francaviglia and Igor 2

Variational Formulation of General Relativity from 1915 to 1925 ”Palatini’s Method” Discovered by Einstein in 1925.Marco Ferraris, Mauro Francaviglia, C. Reina.Gen.Rel.Grav.14(1982)243-254. 2

Palatini Form of 1/R Gravity.´Eanna ´E. Flanagan. Phys.Rev.Lett.92(2004)071101. astro-ph/0308111 2

The conformal frame freedom in theories of gravitation.´Eanna ´E. Flanagan. Class.Q.Grav.21(2004)3817. gr-qc/0403063 2, 3

Scalar-tensor cosmology at the general relativity limit: Jordan vs Einstein frame.Laur J¨arv, Piret Kuusk and Margus Saal.0705.4644 2

Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton.A. Palatini.Rend.Circ.Mat.Palermo43(1919)215. [English translation by R.Hojman and C.Mukku in P.G.Bergmann and V. De Sabbata (eds.), Cosmology and Gravitation,Plenum Press, New York (1980)] 2

Spherically Symmetric Fields in Gravitational Theory.Mark D.

Roberts.Ph.D.Thesis, University of London (1986). 6, 10

Scalar Field Counter-Examples to the Cosmic Censorship Hypothesis. Mark D. Roberts. Gen.Rel.Grav.21(1989)907-939. 10

The World Function in Robertson-Walker Spacetime.Mark D. Roberts. Astrophys.Lett. & Commun.28(1993)349-357. 10

Imploding Scalar Fields.Mark D. Roberts. J.Math.Phys.37(1996)4557-4573. 10

Vacuum Energy.Mark D. Roberts. Poster at the L¨uderitz (2000) Conference. hep-th/0012062. 9

Non-metric mass.Mark D. Roberts.Il Nuovo Cimento 119 B(2005)1015-1040. gr-qc/9812091. 4, 6

Strings and Unified Field Theory.Mark D. Roberts.Theoretical Physics ISP to appear, hep-th/0607118 2, 11

Non-metric Scalar-Tensor Quantum Cosmology. Mark D. Roberts.1611.09221 10 introduction to tensor analysis and its geometrical applicationsJ.A. SchoutenSpringer(1954)Math.Rev.0066025 4

Metric-affine f(R) theories of gravity. Thomas P. Sotiriou and Stefano Liberati, gr-qc/0604006 2

Theory and Experiment in Gravitational Physics.Clifford M. Will Cambridge University Press (1981/1993),Math.Rev.86j:83001 2

(166 Abstract Views, 113 PDF Downloads)


  • There are currently no refbacks.

Copyright (c) 2018 Expert Opinion on Astronomy and Astrophysics