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A new Lagrangian for the vacuum einstein equations and its tetrad form

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Abstract

We give a modification of the Palatini Lagrangian for the free gravitational field that yields the vanishing of the torsion as a result of the field equations and requires only the assumption of the symmetry of the metric. We transcribe this Lagrangian into the tetrad formalism and show how the tetrad form of the Einstein field equations follows from it. Some remarks on possible generalization to a theory with nonvanishing torsion in the presence of matter conclude the paper.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Institut Henri Poincaré, Paris

    A. Papapetrou

  2. Joseph Henry Laboratories, Princeton University, Princeton, New Jersey

    John Stachel

Authors
  1. A. Papapetrou
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  2. John Stachel
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Additional information

An earlier version of the results of this paper are found in [6].

On leave from the Department of Physics, Boston University, Boston, Massachusetts.

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Papapetrou, A., Stachel, J. A new Lagrangian for the vacuum einstein equations and its tetrad form. Gen Relat Gravit 9, 1075–1087 (1978). https://doi.org/10.1007/BF00756575

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  • DOI: https://doi.org/10.1007/BF00756575

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