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Universal gravitational equations

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Il Nuovo Cimento B (1971-1996)

Summary

We show that for a wide class of Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the first-order formalism,i.e. treating the metric and the connection as independent variables, leads to «universal» equations. If the dimensionn of space-time is greater than two, these universal equations are Einstein equations for a generic Lagrangian. There are exceptional cases where a bifurcation appears. In particular, bifurcations take place for conformally invariant LagrangiansL =R(sun/2)√g. For 2-dimensional space-time we obtain that the universal equation is the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the Levi-Civita connection of the metric and an additional vector field.

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Author notes

  1. I. Volovich

    Present address: Steklov Mathematical Institute, Russian Academy of Sciences, Vavilov St. 42, GSP-1, 117966, Moscow, Russia

Authors and Affiliations

  1. Dipartimento di Matematica dell’Università, via Ospedale 72, 09124, Cagliari, Italia

    M. Ferraris & I. Volovich

  2. Istituto di Fisica Matematica dell’Università J.-L. Lagrange, via C. Alberto 10, 10123, Torino, Italia

    M. Francaviglia

Authors
  1. M. Ferraris
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  2. M. Francaviglia
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  3. I. Volovich
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Ferraris, M., Francaviglia, M. & Volovich, I. Universal gravitational equations. Nuov Cim B 108, 1313–1317 (1993). https://doi.org/10.1007/BF02741283

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  • DOI: https://doi.org/10.1007/BF02741283

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