Related papers: Form Invariance of Differential Equations in Gener…
Einstein Gravity in 2+1 dimensions arises as a consequence of the equations of motion of a gauge model in an external metric. Newton's constant appears as an order parameter of a spontaneously broken discrete symmetry. Matter is coupled in…
Newton's gravitational constant $G$ has been measured to high accuracy in a number of independent experiments. For currently unresolved reasons, indicated values from different well-designed and thoroughly analyzed experiments differ by…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
General Relativity is not the definitive theory of Gravitation due to several shortcomings which are coming out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological scales) the attempts to match…
Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form S = \int L_{1} \Phi d^4x + \int L_{2}\sqrt{-g}d^4x where \Phi is a density built out of degrees of…
In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact…
Lie group analysis of the difference equations of the form \begin{align*} x_{n+1} =\frac{x_{n-4}x_{n-3}}{x_{n}(a_n +b_nx_{n-4}x_{n-3}x_{n-2}x_{n-1})}, \end{align*} where $a_n$ and $b_n$ are real sequences, is performed and non-trivial…
Inserting a varying Lambda in Einstein's field equations can be made consistent with the Bianchi identities by allowing for torsion, without the need to add scalar field degrees of freedom. In the minimal such theory, Lambda is totally free…
We present the Geodesic Deviation Equation (GDE) for the Friedmann-Robertson-Walker(FRW) universe and we compare it with the equation for Bianchi type I model. We justify consider this cosmological model due to the recent importance the…
A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…
Conventional quantization of two-dimensional diffeomorphism and Weyl invariant theories sacrifices the latter symmetry to anomalies, while maintaining the former. When alternatively Weyl invariance is preserved by abandoning diffeomorphism…
We study a class of almost scale-invariant modified gravity theories, using a particular form of $f(R, G) = \alpha R^2 + \beta G \log G$ where $R$ and $G$ are the Ricci and Gauss-Bonnet scalars, respectively and $\alpha$, $\beta$ are…
Einstein equations can be written in the so-called Fully Constrained Formulation (FCF). This formulation has two different sectors: the elliptic sector, formed by the Hamiltonian and Momentum constraints together with the equations derived…
The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of…
Variational formalism in the extended phase space for fields is applied to gravity. It is shown that the requirement of invariance under arbitrary local inertial frames implies a coupling of torsion to a 3-form of matter fields on the one…
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The…
Nonlinear partial differential equations appear in many domains of physics, and we study here a typical equation which one finds in effective field theories (EFT) originated from cosmological studies. In particular, we are interested in the…
We formulate Friedmann's equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the $\beta$-times $t_\beta:=\int^t a^{-2\beta}$, where $a$ is the scale…