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In the report there are presented the general frameworks for the quartet-metric gravity based upon the two physical concepts. First, there exist in space-time the distinct dynamical coordinates, given by a scalar quartet, playing the role…
Effective field theories describing gravity coupled to matter are investigated, allowing for operators of arbitrary mass dimension. Terms violating local Lorentz and diffeomorphism invariance while preserving internal gauge symmetries are…
A modified-gravity theory with a four-form field strength $F$, a variable gravitational coupling parameter $G(F)$, and a standard matter action is considered here. Maxwell and Einstein equations are now derived when including to action also…
We explore the properties of physical theories in space-times with two time dimensions. We show that the common arguments used to rule such theories out do not apply if the dynamics associated with the additional time dimension is thermal…
We consider a theory of modified gravity possessing d extra spatial dimensions with a maximally symmetric metric and a scale factor, whose (4+d)-dimensional gravitational action contains terms proportional to quadratic curvature scalars.…
Several attempts to construct theories of gravity with variable mass are considered. The theoretical impacts of allowing the rest mass to vary with respect to time or an appropriate curve parameter are examined in the framework of Newtonian…
We obtain a new kind of $F(^{(4)}\!R,\varphi)$ modified gravity theory as an effective four-dimensional (4D) theory derived from $f(^{(5)}\!R)$ gravity in five dimensions (5D). This new theory exhibits a different matter coupling than the…
The main objective of this article is to derive a new set of gravitational field equations and to establish a new unified theory for dark energy and dark matter. The new gravitational field equations with scalar potential $\varphi$ are…
Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of…
Five-vectors theory of gravity is proposed, which admits an arbitrary choice of the energy density reference level. This theory is formulated as the constraint theory, where the Lagrange multipliers turn out to be restricted to some class…
We develop the principle of nongravitating vacuum energy, which is implemented by changing the measure of integration from $\sqrt{-g}d^{D}x$ to an integration in an internal space of $D$ scalar fields $\phi_{a}$. As a consequence of such a…
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…
The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing…
When 4-dimensional general relativity is extended by a 3-dimensional gravitational Chern-Simons term an apparent violation of diffeormorphism invariance is extinguished by the dynamical equations of motion for the modified theory. The…
The DGP-model with additional terms in the action is considered. These terms have a special form and include auxiliary scalar fields without kinetic terms, which are non-minimally coupled to gravity. The use of these fields allows one to…
We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, our results are…
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…
It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…