Second-order scalar-tensor field equations in a four-dimensional space

@article{Horndeski1974SecondorderSF,
  title={Second-order scalar-tensor field equations in a four-dimensional space},
  author={Gregory Walter Horndeski},
  journal={International Journal of Theoretical Physics},
  year={1974},
  volume={10},
  pages={363-384}
}
  • G. W. Horndeski
  • Published 1974
  • Mathematics
  • International Journal of Theoretical Physics
Lagrange scalar densities which are concomitants of a pseudo-Riemannian metric-tensor, a scalar field and their derivatives of arbitrary order are considered. The most general second-order Euler-Lagrange tensors derivable from such a Lagrangian in a four-dimensional space are constructed, and it is shown that these Euler-Lagrange tensors may be obtained from a Lagrangian which is at most of second order in the derivatives of the field functions. 
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References

SHOWING 1-9 OF 9 REFERENCES
The uniqueness of the Einstein field equations in a four-dimensional space
The Euler-Lagrange equations corresponding to a Lagrange density which is a function of gij and its first two derivatives are investigated. In general these equations will be of fourth order in gij.… Expand
The Einstein Tensor and Its Generalizations
The Einstein tensorGij is symmetric, divergence free, and a concomitant of the metric tensorgab together with its first two derivatives. In this paper all tensors of valency two with these properties… Expand
Comments on the scalar-tensor theory
Scalar-tensor theories are discussed as encompassing three classical long-range fields, including the electromagnetic field. In order to shed additional light on the restrictive assumptions made by… Expand
Mach's principle and a relativistic theory of gravitation
The role of Mach's principle in physics is discussed in relation to the equivalence principle. The difficulties encountered in attempting to incorporate Mach's principle into general relativity are… Expand
The Euler-Lagrange expression and degenerate lagrange densities
Dimensionally dependent identities
Divergence-free tensorial concomitants
Variational problems involving combined tensor fieds
Vittorio Braceo, La valle del Tanagro durante l'età Romana. (Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze morali, storiche e filologiche, serie VIII, vol. X, fasc. 6), 1962