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

  title={Second-order scalar-tensor field equations in a four-dimensional space},
  author={Gregory W. Horndeski},
  journal={International Journal of Theoretical Physics},
  • G. W. Horndeski
  • Published 1 September 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. 
Conformally Invariant Scalar-Tensor Field Theories in a Four-Dimensional Space
In a four-dimensional space, I shall construct all of the conformally invariant scalar-tensor field theories, which are flat space compatible; i.e., well-defined and differentiable when evaluated for
The most general second-order field equations of bi-scalar-tensor theory in four dimensions
A bstractThe Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following
Higher derivative scalar-tensor theory through a non-dynamical scalar field
We propose a new class of higher derivative scalar-tensor theories without the Ostrogradsky's ghost instabilities. The construction of our theory is originally motivated by a scalar field with
Comments on models of scalar-tensorial field equations in general relativity
In this paper we consider some of the proposed models for introducing the long-range scalar interaction in Riemannian space-times. The relationship among these models is discussed. Particular
Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis
  • Xian Gao
  • Mathematics
    Journal of Cosmology and Astroparticle Physics
  • 2020
We investigate the ghostfree scalar-tensor theory with a timelike scalar field, with the derivatives of the scalar field up to the third order and with the Riemann curvature tensor up to the
Mechanics of isolated horizons in scalar-tensor theories
Based on the first-order action for scalar-tensor theories with the Immirzi parameter, the symplectic form for the spacetimes admitting a weakly isolated horizon as internal boundary is derived by
Family of scalar-nonmetricity theories of gravity
We extend the class of recently formulated scalar-nonmetricity theories by coupling a five-parameter nonmetricity scalar to a scalar field and considering a mixed kinetic term between the metric and
Two-form gauge theory dual to scalar-tensor theory
We generalize the electromagnetic duality between a massless, canonical scalar field and a 2-form gauge field in 4-dimensional spacetime to scalar-tensor theories. We derive the action of 2-form
Generalized instantaneous modes in higher-order scalar-tensor theories
We consider higher-order, scalar-tensor theories which appear degenerate when restricted to the unitary gauge but are not degenerate in an arbitrary gauge. We dub them U-degenerate theories. We


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.
The Euler-Lagrange expression and degenerate lagrange densities
It is well known that many of the field equations from theoretical physics (e.g. Einstein field equations, Maxwell's equations, Klein-Gordon equation) can be obtained from a variational principle
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
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
Dimensionally dependent identities
  • D. Lovelock
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1970
Abstract In the general theory of relativity a number of apparently unrelated identities peculiar to a 4-dimensional space are frequently used. However, the proofs usually presented appear to have no
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