Static solutions in the Freund – Nambu scalar-tensor theory of gravitation

Herein, the system of Einstein equations and the equation of the Freund – Nambu massless scalar field for static spherically symmetric and axially symmetric fields are considered. It is shown that this system of field equations decouples into gravitational and scalar subsystems. In the second post-Newtonian approximation, the solutions for spherically symmetric and slowly rotating sources are obtained. The application of the obtained solutions to astrophysical problems is discussed.

A brief note on the limit ω →∞ in Weyl geometrical scalar–tensor theory

We obtain vacuum solutions in the presence of a cosmological constant in the context of the Weyl geometrical scalar–tensor theory. We investigate the limit when [Formula: see text] goes to infinity and show by working out the solutions that in this limit there are some cases in which the scalar field tends to a constant (with the implicit consequence of the geometry becoming Riemannian), although the solutions do not reduce to the corresponding Einstein solutions. We have also extended a previous result, known in the literature, by showing that in the case of vacuum with cosmological constant the field equations of the Weyl geometrical scalar–tensor theory are formally identical to Brans–Dicke field equations, even though these theories are not physically equivalent.

Barbero–Immirzi value from experiment

We consider general relativity as a limit case of the scalar–tensor theory with Barbero–Immirzi (BI) field when the field tends to a constant. We use Shapiro time delay experimental value of [Formula: see text] provided by the Cassini spacecraft to find the present BI parameter value.

On the Coupling of Generalized Proca Fields to Degenerate Scalar-Tensor Theories

We prove that vector fields described by the generalized Proca class of theories do not admit consistent coupling with a gravitational sector defined by a scalar–tensor theory of the degenerate type. Under the assumption that there exists a frame in which the Proca field interacts with gravity only through the metric tensor, our analysis shows that at least one of the constraints associated with the degeneracy of the scalar–tensor sector is inevitably lost whenever the vector theory includes coupling with the Christoffel connection.

The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza–Klein dimensional reduction from $$D+1$$ D + 1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein–Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.