Related papers: One common solution to the singularity and perihel…
The dynamics of extended bodies is a fundamental problem in any gravitational theory. In the case of General Relativity, this problem is under study since the theory was published. Several methods have been developed and different…
The theory of point-particles in classical electrodynamics has a well-known problem of infinite self-energy, and the same is true of quantum electrodynamics. Instead of concluding that there is no such thing as a true point-particle, it is…
In the framework of the field theory it is shown that a time (viewed as a scalar temporal field) is an internal property of the physical system, which defines its causal structure and evolution. A new concept of internal time allows to…
This work introduces a new approach to velocity averaging lemmas in kinetic theory. This approach -- based upon the classical energy method -- provides a powerful duality principle in kinetic transport equations which allows for a natural…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
The paper deals with the concepts of mass and gravity in the formalism of 4-dimensional optics, previously introduced by the author. It is shown that elementary particles can be associated with 4-dimensional standing wave patterns with the…
We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small…
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows…
The common nature of the dark sector - dark energy and dark matter - as shown in [1] follows readily from the consideration of generalized Newtonian potential as a weak-field General Relativity. That generalized potential satisfying the…
Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in…
The classical problem of self-energy divergence was studied in the framework of Lagrangian formulation of Relativistic Mechanics. The conclusion was made that a revision of mass-energy concept is needed for the development of…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is…
Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts,…
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
A Lagrangian description of a classical particle in a 9-dimensional flat Finslerian space with a cubic metric function is constructed. The general solution of equations of motion for such a particle is obtained. The Galilean law of inertia…
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 establish the existence of at least two solutions of the {\it Prandtl-Batchelor} like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable and hence the usual…
There are few opportunities in introductory physics for a genuine discussion of the philosophy of science, especially in cases where the physical principles are straightforward and the mathematics is simple. Terrestrial classical mechanics…