On a Generalized Theory of Relativity

General Relativity and Gravitation, 2011

We prove that some basic aspects of gravity commonly attributed to the modern connection-based approaches, can be reached naturally within the usual Riemannian geometry-based approach, by assuming the independence between the metric and the connection of the background manifold. These aspects are: 1) the BFlike field theory structure of the Einstein-Hilbert action, of the cosmological term, and of the corresponding equations of motion; 2) the formulation of Maxwellian field theories using only the Riemannian connection and its corresponding curvature tensor, and the subsequent unification of gravity and gauge interactions in a four dimensional field theory; 3) the construction of four and three dimensional geometrical invariants in terms of the Riemann tensor and its traces, particularly the formulation of an anomalous Chern-Simons topological model where the action of diffeomorphisms is identified with the action of a gauge symmetry, close to Witten's formulation of threedimensional gravity as a Chern-Simon gauge theory. 4) Tordions as propagating and non-propagating fields are also formulated in this approach. This new formulation collapses to the usual one when the metric connection is invoked, and certain geometrical structures very known in the traditional literature can be identified as remanent structures in this collapse.

Contents 1. Special Relativity 2. Oblique Axes 3. Curvilinear Coordinates 4. Nontensors 5. Curved Space 6. Parallel Displacement 7. Christoffel Symbols 8. Geodesics 9. The Stationary Property of Geodesics 10. Covariant Differentiation 11. The Curvature Tensor 12. The Condition for Flat Space 13. The Bianci Relations 14. The Ricci Tensor 15. Einstein's Law of Gravitation 16. The Newtonian Approximation 17. The Gravitational Red Shift 18. The Schwarzchild Solution 19. Black Holes 20. Tensor Densities 21. Gauss and Stokes Theorems 22. Harmonic Coordinates 23. The Electromagnetic Field 24. Modification of the Einstein Equations by the Presence of Matter 25. The Material Energy Tensor 26. The Gravitational Action Principle 27. The Action for a Continuous Distribution of Matter 28. The Action for the Electromagnetic Field

2012

2018

A general theory of relativity is formulated without Einstein's equation. Einstein's tensor ties the space metric to the stress-energy tensor of a gravitational field. A homogeneous isotropic field metric is under consideration. In particular, the metric for a homogeneous isotropic universe possesses the anticipated density of our own universe. The speed of time progression at a distance from the observer slows according to an acceleration law asymptotically equal to Hubble's Law. A continuous field is homogeneous within the limits of small domains. This makes it possible to write a metric for a general continuous field and the single parameter given by the wave equation. The Schwarzschild problem has a continuous solution for r > 0. This solution approaches the Schwarzschild solution beyond the Schwarzschild radius and a second solution is obtained from the Schwarzschild problem-a stationary, expulsive, self-consistent field.

2013

We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional spacetime, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry ! This work is therefore in the continuation of the various attempts made since Einstein,

Since its final version and publication in 1916, it is widely reported in several specialized textbooks and research articles that General Relativity theory reduces to Newton's theory of gravity in the limit of a weak gravitational field and slowly moving material bodies. In the present paper, the so-called reducibility of Einstein's geodesic and field equations, to Newton's equation of motion and Poisson's gravitational potential equation, respectively, is scrutinized and proven to be mathematically, physically and dimensionally incorrect, and that the geometrization of gravity is unnecessary.

2008

Nature, 1961

Here we present a new point of view for general relativity and/or space-time metrics that is remarkably different from the well-known viewpoint of general relativity. From this unique standpoint, we attempt to derive a new metric as an alternative to the Schwarzschild metric for any planet in the solar system. After determining the metric by means of some simple mathematical and physical manipulations, we used this alternative metric to recalculate the perihelion precession of any planet in the solar system and deflection of light that passes near the sun, as examples of this new viewpoint. While we obtained the result of classical general relativity for the perihelion procession, we found a slightly different result, relative to classical general relativity, for the deflection of light.

The relativists have not understood the geometry of Einstein's gravitational field. They have failed to realise that the geometrical structure of spacetime manifests in the geometrical relations between the components of the metric tensor. Consequently, they have foisted upon spacetime quantities and geometrical relations which do not belong to it, producing thereby, grotesque objects, not due to Nature, but instead, to faulty thinking. The correct geometry and its consequences are described herein.

2006

There are now at least eight experiments extending over more than 100 years that have detected the anisotropy of the speed of light, implying the absolute motion of the detecting apparatus through a dynamical space. This light-speed anisotropy is consistent with relativistic effects and Lorentz symmetry, contrary to prevailing beliefs in physics. The theoretical and experimental evidence implies that physics has failed to realise the existence of a dynamical 3-space, and that motion relative to that space is the cause of various relativistic effects, as proposed by Lorentz in 1899. This has resulted in a necessary generalisation of the Maxwell, Schrodinger and Dirac equations, which then provide an explanation for gravity as an emergent phenomenon within the new physics. From the generalised Dirac equation we show that the spacetime formalism is derivable, but as merely a mathematical construct whose geodesics arise from the trajectories of quantum wavepackets in the 3-space. Howeve...