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A unique constraint is defined within the framework of scalar-tensor theories, whereby the conformal factor is fixed to the fluctuation associated to the effective mass of the Hamilton-Jacobi equation for a Klein-Gordon field. The effective mass is extended to its exponential form to remove any ghost (energy) states. The constraints Lagrange multiplier $lambda$, referred to as the mediating field, is shown to act as a mediator between the scalar and tensor degrees of freedom. In its linear form, Heisenbergs uncertainty principle appears as a natural artifact of the mediating field. In its exponential form, the mediating field is shown to be bound, nonsingular, and of increasing significance for smaller masses. Furthermore, in acquiring the stress-energy tensors, the cosmological constant $Lambda$ is formulated for a stationary solution of the particle density and mediating field. As a result, the mysterious variation in $Lambda$ is properly evaluated from its cosmological value to that of an electron, from which a 77 order difference is obtained. In our final remarks, the mediating field $lambda$ is suggested to be characteristic of the vacuums energy density.
It is known that the standard Schwarzschild interior metric is conformally flat and generates a constant density sphere in any spacetime dimension in Einstein and Einstein--Gauss--Bonnet gravity. This motivates the questions: In EGB does the conforma
In Einstein-Maxwell gravity with a conformally coupled scalar field, the black hole found by Bocharova, Bronnikov, Melnikov, and Bekenstein breaks when embedded in the external magnetic field of the Melvin universe. The situation improves in presence
Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This
We consider the weak field limit of gravity in the vierbein-Einstein-Palatini formalism, find the action and the equations for perturbations around an arbitrary background, and compare them with the usual metric perturbation equations. We also write
We present exact dynamical and inhomogeneous solutions in three-dimensional AdS gravity with a conformally coupled scalar field. They contain stealth configurations of the scalar field overflying the BTZ spacetime and also solutions with a non-vanish