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This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under…
According to Einstein, the trajectory of a particle that is predicted by special relativistic mechanics is well approximated by the trajectory predicted by Newtonian mechanics if the particle speed is low, i.e., much less than the speed of…
In his monumental discoveries, the driving force for Einstein was, I believe, consistency of concept and principle rather than conflict with experiment. Following this Einsteinian dictum, we would first argue that homogeneity (universal…
I combine the effects of Planck length, general relativity and Newtonian gravity in one equation, to come up with a semi-classical model of gravity in the form of deviation from Newtonian gravity. Einstein explained nuclear forces in terms…
According to Einstein's principle of general covariance, all laws of nature are to be expressed by manifestly covariant equations. In recent work, the covariant law of energy-momentum conservation has been established. Here, we show that…
In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a…
Einstein-aether theory is extended by allowing for spinning degrees of freedom of the aether. In addition to the acceleration, shear, expansion, and vorticity of the aether velocity field, a spin rotation describing the dynamics of a…
A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition…
The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
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…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety…
A new direction to understand gravity has recently been explored by considering classical gravity to be a derived interaction from an underlying theory. This underlying theory would involve new degrees of freedom at a deeper level and it…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
Newton second law of dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the special theory of relativity,…