Newtonian gravitational theory: Interaction with light

The interaction of light with the gravitational field of a mass point described by a Newtonian gravitational field theory gives the same gravitational red shift as accepted theory. The dual force which is an integral part of the classical field theory and which has been shown to give the same advance of the perihelion of the orbit as Einstein's General Theory of Relativity is also the reason that light is deflected in the neighborhood of a massive particle. The deflection predicted is slightly more than 10% larger than Einstein's value, but within the experimental error of observational data. The dual force and its effects must be taken seriously. Its role in electrodynamics and quantum mechanics is briefly discussed.     

Simulation model for anomalous precession of the perihelion of mercury's orbit

The ‘anomalous perihelion precession’ of Mercury, announced by Le Verrier in 1859, was a highly controversial topic for more than half a century and invoked many alternative theories until 1916, when Einstein presented his theory of general relativity as an alternative theory of gravitation and showed perihelion precession to be one of its potential manifestations. As perihelion precession was a directly derived result of the full General Theory and not just the Equivalence Principle, Einstein viewed it as the most critical test of his theory. This paper presents the computed value of the anomalous perihelion precession of Mercury's orbit using a new relativistic simulation model that employs a simple transformation factor for mass and time, proposed in an earlier paper. This computed value compares well with the prediction of general relativity and is, also, in complete agreement with the observed value within its range of uncertainty. No general relativistic equations have been used for computing the results presented in this paper.     

Perihelion Precession in the Special Relativistic Two-Body Problem

The classical two-body system with Lorentz-invariant Coulomb work function V = -k/ is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stückelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attractive orbit, and the semiclassical hydrogen spectrum subsequently contains no fine structure corrections. It is argued that this prediction is indicative of the correct classical special relativistic two-body theory.     

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor φ, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the n-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order c ⁻².     

Relativistic perihelion precession of orbits of Venus and the Earth

Among all the theories proposed to explain the “anomalous” perihelion precession of Mercury’s orbit first announced in 1859 by Le Verrier, the general theory of relativity proposed by Einstein in November 1915 alone could calculate Mercury’s “anomalous” precession with the precision demanded by observational accuracy. Since Mercury’s precession was a directly derived result of the full general theory, it was viewed by Einstein as the most critical test of general relativity from amongst the three tests he proposed. With the advent of the space age, the level of observational accuracy has improved further and it is now possible to detect this precession for other planetary orbits of the solar system — viz., Venus and the Earth. This conclusively proved that the phenomenon of “anomalous” perihelion precession of planetary orbits is a relativistic effect. Our previous papers presented the mathematical model and the computed value of the relativistic perihelion precession of Mercury’s orbit using an alternate relativistic gravitational model, which is a remodeled form of Einstein’s relativity theories, and which retained only experimentally proven principles. In addition this model has the benefit of data from almost a century of relativity experimentation, including those that have become possible with the advent of the space age. Using this model, we present in this paper the computed values of the relativistic precession of Venus and the Earth, which compare well with the predictions of general relativity and are also in agreement with the observed values within the range of uncertainty.      

Lorentzinvariante Gravitationstheorie

A Lorentz-invariant Theory of Gravitation A Lorentz-invariant theory of gravitation is developed. For the three well known effects, i.e., red shift, deflection of light and perihelion shift the theory gives the same results as the General Theory of Relativity.     

Teilchen-Modelle und effektive Radien in der Allgemeinen Relativitätstheorie

Particle Models and Effective Radius in the General Theory of Relativity We discuss the role of the classical particle radius defined in the classical field models of particles for the general relativistic particle problem suggested by EINSTEIN. The main point is that in General Relativity the point-like particles without field masses may be self-consistent but not the model particles with an effective radius given by the Schwarzschild radius of the mechanical particle mass.     

Modified gravity with arbitrary coupling between matter and geometry

The field equations of a generalized f(R)$f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the particular case in which the Lagrange density of the matter is an arbitrary function of the energy-density of the matter only. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the model is also considered. The perihelion precession of an elliptical planetary orbit in the presence of an extra force is obtained in a general form, and the magnitude of the extra gravitational effects is constrained in the case of a constant extra force by using Solar System observations.     

The Limits of Special Relativity

The Special Theory of Relativity and the Theory of the Electron have had an interesting history together. Originally the electron was studied in a non-relativistic context and this opened up the interesting possibility that lead to the conclusion that the mass of the electron could be thought of entirely in electromagnetic terms without introducing inertial considerations. However the application of Special Relativity lead to several problems, both for an extended electron and the point electron. These inconsistencies have, contrary to popular belief not been resolved satisfactorily to date, even within the context of Quantum Theory. Thus they are not merely of historical interest. Nevertheless these and subsequent studies bring out the interesting result that Special Relativity (and the theory of the electron) breaks down within the Compton scale or when the Compton scale is not neglected. This again runs contrary to an uncritical notion that Special Relativity is valid for point particles. Furthermore, it is pointed out that experiments have been recently suggested to test these ideas. These considerations lead to a characterization of the Planck constant in classical terms.     

Energy spectrum of the dirac equation for the Scharzschild and Kerr fields

We consider the effect of relativistic corrections and rotation of the central body on the structure of the energy spectrum of a particle with spin in the Schwarzchild and Kerr fields. A splitting of levels is obtained, which corresponds to the classical shift of the perihelion of the orbit and precession of the plane of the gravitational spin-orbit interaction and several nonlinear spin effects are calculated.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 2, pp. 86–92, February, 1988.     

Calculation of the Precession of the Perihelion of Mercury’s Orbit Within the Framework of the Generalized Law of Universal Gravitation with Allowance for the Ellipticity of Planet Orbits

Russian Physics Journal - The precession of the perihelion of Mercury’s orbit is simulated numerically within the framework of the generalized law of universal gravitation in the field of the...     

Post-Newtonian limit of Finsler space theories of gravity and solar system tests

Finsler geometry is considered as a wider framework for analysing solar system tests of theories of gravity than is afforded by Riemannian geometry. The post-Newtonian limit for the spherically symmetric one-body problem is examined by expanding the Finsler metric about the Minkowski space of Special Relativity for those Finsler spaces whose null surface is Riemannian. In such a framework there are five PPN parameters instead of the three in Riemannian geometry. The classical solar system tests can readily be satisfied leaving two arbitrary parameters. These parameters could be determined from measurements of the second order gravitational red-shift and periodic perturbations in particle orbits, thus providing a consistency check on the Riemannian metric hypothesis of General Relativity. Such an experiment is possible on a satellite on an orbit with perihelion of a few solar radii.     

Non-Conservative Gravitational Equations

We propose a theory of gravity based on the interaction of the gauge field representing gravitation with a suitable vector substratum (physical vacuum). To build up the new theory, we exploit the formalism of the Symbolic Gauge Theory, an application to gauge theories of the General System Logic Theory, which results from the fusion of three mathematical structures, the logical theory of systems, the categorial algebra and the Lie algebra. The coupling of gravity to the substratum implies the nonconservation of the energy-momentum tensor. The derivative coupling term is approximated to the first order, and a Schwarzschild-like solution of the corresponding nonconservative gravitational equations is obtained. It is shown that, in this approximation, the main effect of the new theory is to introduce an extra-mass term in the standard Schwarzschild metric. The application of such a result to perihelion shifts and light deflection yields results comparable to those obtained in General Relativity. Gravitational-wave solutions of the new equations are derived in the weak field approximation. It is shown that our nonconservative theory of gravity implies a cosmological model with a locally varying, non-zero cosmological constant.     

A non-covariant theory of gravitation,II

This is a continuation of a previous paper, in which a theory of gravitation was developed based on the existence of a preferred frame of reference and a preferred time coordinate in the universe. The gravitational field equations are derived with the help of a variational principle containing three constants. Two relations among the constants are introduced, leaving one of them arbitrary. This constant does not affect the precession of the perihelion of Mercury but does affect the behaviour of gravitational waves. By changing one of the relations among the constants, one can account for the discrepancy in the precession of the perihelion associated with the oblateness of the sun, as found by Dicke and Goldenberg.     

Delta-Gravity

We present a model of the gravitational field based on two symmetric tensors. The equations of motion of test particles are derived: Massive particles do not follow a geodesic but massless particles trajectories are null geodesics of an effective metric. Outside matter, the predictions of the model coincide exactly with General Relativity, so all classical tests are satisfied. In Cosmology, we get accelerated expansion without a cosmological constant. Additionally, we study the quantization of the model. The main result being that the Effective Action is finite and receives one loop corrections only.     

Eine nichtlineare lorentzinvariante Gravitationstheorie

Nonlinear Lorentz-Invariant Theory of Gravitation A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3″, in good agreement with experimental results of DICKE .     

Cosmological constant and Minkowski space

Using the framework of classical gravitational field theory, it is shown that the equations of Einstein’s General Relativity with a cosmological constant, if requested to be compatible with the Minkowski space, change form and become the equations of Relativistic Theory of Gravitation. These equations, in contrast to General Relativity, lead us to fundamentally different physical conclusions about the Universe’s evolution and Collapse.     

On the phenomenological three-graviton vertex

In General Relativity, the graviton interacts in three-graviton vertex with a tensor that is not the energy-momentum tensor of the gravitational field. We consider the possibility that the graviton interacts with the definite gravitational energy-momentum tensor that we previously found in the G ² approximation. This tensor in a gauge, where nonphysical degrees of freedom do not contribute, is remarkable, because it gives positive gravitational energy density for the Newtonian center in the same manner as the electromagnetic energy-momentum tensor does for the Coulomb center. We show that the assumed three-graviton vertex does not lead to contradiction with the precession of Mercury’s perihelion. In the S-matrix approach used here, the external gravitational field has only a subsidiary role, similar to the external field in quantum electrodynamics. This approach with the assumed vertex leads to the gravitational field that cannot be obtained from a consistent gravity equation.     

Geodesies in the Erez-Rosen space-time

We investigate null and time-like geodesics in the Erez-Rosen space-time, that is, in the exterior gravitational field of a mass with quadrupole moment. By using the weak-field approximation of the Erez-Rosen metric, we find the solution of the equation for equatorial time-like geodesics and determine how they differ from the corresponding Schwarzschild geodesies. For the exact form of the Erez-Rosen metric, we only draw some qualitative conclusions about the influence of the quadrupole moment on the path of test particles and on the motion of photons. We derive the relativistic contribution of the quadrupole moment to the perihelion shift and to the precession of the ascending node.     

The two-body problem in Rosen's bimetric theory of gravitation

This is a continuation of a previous paper, in which the field equations in successive approximations and the post-Newtonian equations of motion in Rosen's theory of gravitation were derived. In this paper the energy integral and the center of mass for an insular system with an arbitrary structure are obtained in the post-Newtonian approximation. A many-body system is considered, and in the extreme case of point bodies (particles) the center-of-mass coordinates are found to be identical with the Einsteinian ones. The two-body problem is considered. For a system of two identical neutron stars of mass 1.3M (a possible model of the Hulse-Taylor binary pulsar system) the trajectory and the perihelion precession are calculated. It is found that the expressions obtained depend on the gravitational self-energy of the stars. The relations deduced from Rosen's bimetric gravitation in the case of small velocities and weak fields are compared with those of general relativity.In partial fulfillment of the requirements for Dr.Sc. degree at the Technion-Israel Institute of Technology.