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.     

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.     

Newtonian gravitational field theory: Two-body problem

The effects of a dual force which appears in a consistent field theory of Newtonian gravitation are explored by a study of the motion of two bodies which interact with each other through the gravitational field. The equations of motion are solved exactly. Among the results obtained, we find that the present theory formulated in accordance with the Special Theory of Relativity leads to the same analytical result for the precession of the perihelion of the orbit as does Einstein's General Theory of Relativity. Another result is that classical particles are endowed with an intrinsic angular momentum of constant magnitude—a helicity of classical origin. Other results, such as the period of revolution, are similar to Kepler's law, except for relativistic corrections. A slight deviation from the planar orbit of classical theory results, and may be observable. This deviation is related to the magnitude of the precession of the perihelion of the orbit. The significance of these results for charged particles, viewed classically or quantum mechanically, are discussed.     

Planck's constant and the theory of the red shift

This paper deals with problems on the threshold between General Relativity Theory and Quantum Theory. It contains some simple reasoning from which it follows that the so-called constanth cannot, in fact, be regarded as constant in General Relativity Theory.     

On Metric and Matter in Unconnected, Connected, and Metrically Connected Manifolds

From Einstein's point of view, his General Relativity Theory had strengths as well as failings. For him, its shortcoming mainly was that it did not unify gravitation and electromagnetism and did not provide solutions to field equations which can be interpreted as particle models with discrete mass and charge spectra, As a consequence, General Relativity did (and does) not solve the quantum problem, either. Einstein tried to get rid of the shortcomings without losing the achievements of General Relativity Theory. Stimulated by papers of Weyl (Sitzungsber. Preuss. Akad. Wiss (1918) 465) and Eddington (Proc. R. Soc. Hond. 99 (1921) 194), from 1923 onward, he believed that, to reach this goal, one has to transit to space–times which possess more comprehensive geometrical structures than the Riemann space–time. This was the beginning of a decade's lasting search for a unitary field theory. We describe this exciting part of the history of physics, discuss achievements and failures of this development, and ask how these early attempts of a unified theory strike us today. Taking into account the fact that the Equivalence Principle only speaks for a geometrization of gravitation, we consider an alternative way to give those non-Riemannian structures which were introduced by the unitary field approach a physical meaning, namely the meaning of a generalized gravitational field. This is interesting since there are arguments in favor of such a generalization of General Relativity Theory, e.g., the problems the latter theory meets with if one tries to quantize it and to unify gravitation with other interactions.     

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.     

Geometrical spin symmetry and spin

Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.     

The Einsteinian Star Model in Treder's Tetrad Theory of Gravitation

By means of a simple star model proposed by EINSTEIN (point-particle cluster) the collapse behaviour in General Relativety and in TREDER 's [14] Tetrad Theory has been compared. Within both theories the heavy mass of a point-particle cluster with a fixed radius cannot exceed a critical value. However, contrary to General Relativity, within the framework of TREDER 's Tetrad Theory, for a fixed particle number N, the radius of the cluster is allowed to be arbitrarily small. In this sense, the Tetrad Theory is a collapse-free relativistic theory of gravitation.     

Massive Shell Models in the Gravitational Theories with Higher Derivatives

The model of a thin massive shell is investigated in the framework of gravitational theories with fourth-order derivatives. The corresponding jump conditions are derived, and their possible consequences for structure and motion of the matter sources are shortly discussed. The results are compared with the conditions obtained in General Relativity Theory.     

Photon motion in the ECSK theory

Working within the scheme of the Einstein-Cartan-Sciama-Kibble Theory (ECSK) we find the trajectory of the photon up to its third order with respect to the velocity of slow motion sources. For the general case, discrepancies from the predictions of General Relativity (GR) are found. We apply the results to a model of polarized spin and find that in this particular case ECSK and GR theories coincide. We also perform a multipole expansion of the gravitational potentials in order to find the motion of photons far away from localized sources.     

Optical Definition of Gravity Under Static Conditions

The experiment of Pound & Repka shows that light undergoes a frequency shift in the gravitational field of the earth in accordance with General Relativity. Conversely, in the static case, we can use only the observed frequency shifts to define the gravitational field, presupposing the (constant) 3-geometry of the 3-space slices is known. The latter can be probed in principle by rigid rods, but more elegantly by the light geometry as developed by Abramowicz, shortly reviewed here. Our optical definition is independent of the theory of relativity. However, in the second part, we show that, in the static case, it coincides with the predictions for the acceleration of test particles in General Relativity. For the non-static case, our definition of gravity is no substitute for that one given in General Relativity. However, the static case is sufficient for certain discussions about the validity of the Principle of Equivalence.     

Oscillating Flat FRW Dark Energy Dominated Cosmology from PeriodicFunctional Approach

I discuss the modification of Einstein's Theory of General Relativity based on a periodic functional approach. In this new approach, a corrected periodic gravitational coupling constant arises and plays the role of periodic damping term acting on the theory. It is found that it is achievable to have an oscillating universe dominated by dark energy and expanding acceleratedly in time.     

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.     

Equivalence Principle and the Principle of Local Lorentz Invariance

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFs that is associated with the PLLI. Next we give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent.     

New Weyl theory: Geometrization of electromagnetism and gravitation: Motivations and classical results

A geometrical unified field theory of electromagnetism and gravitation is developed in a Weyl space-time. The integrability conditions of the field equations cast the laws of classical perfect fluids under electromagnetic interactions. The purely gravitational limit of the theory is Einstein's General Relativity and the purely electromagnetic case coincides with the predictions of Maxwell's theory.     

The Post-Minkowskian Limit of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)-gravity

We formally discuss the post-Minkowskian limit of f(R)-gravity without adopting conformal transformations but developing all the calculations in the original Jordan frame. It is shown that such an approach gives rise, in general, together with the standard massless graviton, to massive scalar modes whose masses are directly related to the analytic parameters of the theory. In this sense, the presence of massless gravitons only is a peculiar feature of General Relativity. This fact is never stressed enough and could have dramatic consequences in detection of gravitational waves. Finally the role of curvature stress-energy tensor of f(R)-gravity is discussed showing that it generalizes the so called Landau-Lifshitz tensor of General Relativity. The further degrees of freedom, giving rise to the massive modes, are directly related to the structure of such a tensor.     

Covariant change of signature in classical relativity

This paper gives a covariant formalism enabling investigation of the possibility of change of signature in classical General Relativity, when the geometry is that of a Robertson-Walker universe. It is shown that such changes are compatible with the Einstein field equations, both in the case of a barotropic fluid and of a scalar field. A criterion is given for when such a change of signature should take place in the scalar field case. Some examples show the kind of resulting exact solutions of the field equations.     

The plane-fronted gravitational waves

This paper is a contribution to the theory of pure radiation in General Relativity. It gives a survey of the radiation fields which possess a twistfree and non-expanding null congruence, and characterizes their subclasses of different Petrov type by geometrical properties. The term “plane-fronted”, intuitive inMaxwell's theory, is generalized toEinstein's theory.     

New Einstein Gravitation*

Taking into account the experimental accuracy of the body motions in the solar system, we propose a General Relativity Theory which is new but nevertheless completely metric. *Presented at the IARD 2004 Conference, Saas-Fee Switzerland.     

Microscopic Relativity: The Basic Theory

In effort to investigate how quantum physics might modify Einstein's Theory of Relativity at speeds vc, the relationship between space-time coordinates of different reference frames is revisited by introducing only one new parameter x_o, a fundamental constant for the quantization of space. The starting point is three criteria: (a) real space-time data are conditioned by standard quantum effects on measurements; (b) since currently used apparatus are only capable of probing the aggregate behavior of these quanta the relevant model is one which maximizes the Entropy subject to certain defining constraints; and (c) the constraints simply involve fixed ensemble averages in the case of an inertial frame, or boundary conditions on running averages in the case of an accelerated frame. In this context it is found that both the Lorentz transformation and a simple scheme for the quantization of space-time which resembles identically Planck's photon picture of radiation are a direct consequence of the Principle of Relativity. Non-inertial behavior corresponds to local Entropy maxima, obtainable by solution of a diffusion equation which gives gradually varying ensemble averages across space-time, as demonstrated by the example of a profile which connects a central region of highly agitated quanta with an asymptotic ambient environment—the outcome is the Schwarzschild metric of General Relativity. Apart from the above, a new feature emerges from the theory: the space-time data of an observer, when referred to the frame of his moving partner, are subject to extra quantum fluctuations which increase indefinitely in severity as vc, with the Lorentz transformation providing only the mean data values. Thus for fast moving bodies like cosmic rays or matter at the horizon of a black hole, physical processes which affect them may not always be perceived by us to occur at the expected length or time scales.