Journal ArticleDOI
Second-order scalar-tensor field equations in a four-dimensional space
TLDR
In this article, the second-order Euler-Lagrange tensors are derived from a Lagrangian which is at most of second order in the derivatives of the field functions.Abstract:
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.read more
Citations
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On avoiding Ostrogradski instabilities within Asymptotic Safety
TL;DR: In this article, the authors studied the renormalization group flow of gravity coupled to scalar matter using functional renormalisation group techniques and found that the flow of the gravity-matter system possesses a fixed point structure suitable for asymptotic safety.
Journal ArticleDOI
Hairy black hole solutions in U(1) gauge-invariant scalar–vector–tensor theories
TL;DR: In this paper, the properties of black holes on a static and spherically symmetric background were studied in U (1) gauge invariant scalar-vector-tensor theories with second-order equations of motion.
Journal ArticleDOI
Selected topics in scalar-tensor theories and beyond
TL;DR: In this paper, a review of the asymptotic dynamics of cosmological models based on the Brans-Dicke, scalar-tensor and Horndeski theories is presented.
Journal ArticleDOI
Cosmological matching conditions and galilean genesis in Horndeski's theory
TL;DR: In this paper, the cosmological matching conditions for the homogeneous and isotropic background and for linear perturbations in Horndeski's most general second-order scalar-tensor theory are derived.
Journal ArticleDOI
Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis
Xian Gao,Zhi-Bang Yao +1 more
TL;DR: In this paper, a large class of gravity theories that respect spatial covariance, and involve kinetic terms for both the spatial metric and the lapse function, were investigated, and the condition requiring the kinetic terms to be degenerate is not sufficient to evade the unwanted scalar mode in general.
References
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Journal ArticleDOI
Mach's principle and a relativistic theory of gravitation
Carl H. Brans,R. H. Dicke +1 more
TL;DR: In this paper, the role of Mach's principle in physics is discussed in relation to the equivalence principle and the difficulties encountered in attempting to incorporate Mach's principles into general relativity are discussed.
Journal ArticleDOI
The Einstein Tensor and Its Generalizations
TL;DR: In this paper, the number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.
Journal ArticleDOI
Comments on the scalar-tensor theory
TL;DR: In this article, the ponderomotive laws of a scalar-tensor theory are constructed free of approximations in the form of integral laws, and the integrals are extended over two-and three-dimensional domains that lie entirely in empty space but surround the regions containing matter.
Journal ArticleDOI
The uniqueness of the einstein field equations in a four-dimensional space.
TL;DR: In this article, the Euler-Lagrange equations corresponding to a Lagrange density which is a function of g ≥ 2 and its first two derivatives are investigated and necessary and sufficient conditions for these equations to be of second order are obtained and it is shown that in a four-dimensional space the Einstein field equations (with cosmological term) are the only permissible second order Euler Lagrange equations.
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