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The Stringy Uncertainty relations, and corrections thereof, were explicitly derived recently from the New Relativity Principle that treats all dimensions and signatures on the same footing and which is based on the postulate that the Planck…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
We study higher dimensional scenarios of massive bigravity, which is a very interesting extension of nonlinear massive gravity since its reference metric is assumed to be full dynamical. In particular, the Einstein field equations along…
We address the problem of observables in generally invariant spacetime theories such as Einstein's general relativity. Using the refined notion of an event as a ``point-coincidence'' between scalar fields that completely characterise a…
We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum…
Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a…
In this series of papers I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable manifold, and their dimension is one unit…
A five dimensional space without invariance under local Lorentz transformations is studied, and the transformations under which the theory is invariant are introduced. We show that the Lorentz force is included in the ensuing equations of…
Using the language of differential forms, the Kaluza-Klein theory in 4+1 dimensions is derived. This theory unifies electromagnetic and gravitational interactions in four dimensions when the extra space dimension is compactified. Without…
The field equations for gravitation and electromagnetism with sources in four dimensions can be interpreted as arising from the vacuum Einstein equations in five dimensions. Gauge invariance of the electromagnetic potentials leads to a…
The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain…
We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann-Lema\^itre-Robertson-Walker metric in the context of a Gauss-Bonnet-Scalar field theory where the quintessence scalar field is coupled to the…
The N=2 supergravity action in D=5 is generalized by the inclusion of dimensionally continued Euler-Poincare form. The spacetime torsion implied by the Einsteinean supergravity is imposed by a Lagrangian constraint and resulting variational…
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
We live in a 3+1 space-time that is intended as a description of the universe with three space dimensions and one time dimension. Space-time dimensionality seems so natural that it is rarely criticized. Experiments and the highly successful…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
We consider the five-dimensional Einstein-Gauss-Bonnet gravity, which can be obtained by means of an apropriate choice of coeficients in the five-dimensional Lanczos-Lovelock gravity theory. The Einstein-Gauss-Bonnet field equations for the…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in…
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…