# 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 W. Horndeski}, journal={International Journal of Theoretical Physics}, year={1974}, volume={10}, pages={363-384} }

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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