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Recent developments in observational cosmology have led to attempts to make modifications on both sides of the Einstein equation to explain some of the puzzling new findings. What follows is an examination of the source of gravity that we…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
The starting point of quantum mechanics is the relationship between energy and momentum: energy is proportional to the squared momentum! As a result, energy and momentum have not been treated equally. The wave equation required by…
Starting from the action function, we have derived a theoretical background that leads to the quantization of gravity and the deduction of a correlation between the gravitational and the inertial masses, which depends on the kinetic…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
Two alternative ways of description an evolution constrained by mass-shell equation are given by the hyperbolic and the periodic angles. In the both cases the angles are proportional to the mass. The differential operators with respect to…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
This work refines arguments forbidding non-linear dynamical gravity from appearing in the low energy effective description of field theories with local kinematics, even for those with instantaneous long-range interactions. Specifically, we…
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time,…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for…
The intrinsic metric symmetries for energy-momentum in warped space-time universally reinforce strict spatial flatness in the GR metric formalism. The passive/active energy-charge for the 1686, 1913, and 1915 gravitational laws maintains…
We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisation of the relative equilibrium point notion to a…
Static spherically symmetric solution of the Einstein's equations is found representing averaged properties of an infinite self-gravitating gas in the dynamical equilibrium. It depends upon three parameters: the core radius, the…
The relativistic equations for the electromagnetic and gravitation interactions are similar: The only Lagrangian equation is the equation with Lorentz force. The potential satisfies the wave equation with the right - hand side proprtional…
In this note we explore a modified theory of gravitation that is not based on the least action principle, but on a natural generalization of the original Einstein's field equations. This approach leads to the non-covariant conservation of…
The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can…
Black holes and gravitational waves are consequences of the nonlinear character of the Einstein equations. Yet, the remarkable properties of General Relativity point to the existence of other effects. Here we uncover new nonlinear facets of…