International Journal of Theoretical Physics

, Volume 10, Issue 6, pp 363–384

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


  • Gregory Walter Horndeski
    • Department of Applied MathematicsUniversity of Waterloo

DOI: 10.1007/BF01807638

Cite this article as:
Horndeski, G.W. Int J Theor Phys (1974) 10: 363. doi:10.1007/BF01807638


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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© Plenum Publishing Company Limited 1974