Il Nuovo Cimento B (1971-1996)

, Volume 106, Issue 3, pp 273–289

# First-order field equations in general relativity

• M. Mattes
• M. Sorg
Article

## Summary

The metric tensor of a Riemannian space-time is composed quadratically of timelike and spacelike tetrad fields. A system of first-order field equations for the tetrad fields is postulated, which determines the geometric structure of space-time as well as the second-order dynamics of the fields. The energy-momentum content of the fields automatically corresponds to the geometric structure of the space-time according to the Einstein field equations. The spin contribution of the fields is mutually compensated and therefore spin does not influence the space-time geometry. As a consequence, it is not necessary to include torsion into the general theory of relativity and nevertheless the equivalence principle can be used to consistently transfer energy-momentum tensors from flat to curved space.

## References

PACS 04.20 General relativity PACS 04.20.Cv Fundamental problems and general formalism

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