The theory of relativity and super-luminal-speeds

According to some local properties of Lorentz transformation, Einstein stated: Velocities greater than that of light have no possibility of existence. He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speed. This paper shows that if we think of the possibility of the existence of the superluminal-speed and redescribe the special theory of relativity following Einstein's way, a new kinematic theory would be founded. The new theory would retain all kinematical meaning of the special theory of relativity when matters move with subluminal-speed and would give new content when matters move with superluminal-speed. The paper also discusses the observation principle for the motions with superluminal-speed.     

Changes in concepts of time from Aristotle to Einstein

The meaning of time and motion is discussed, at first tracing conceptual changes from Aristotle to Galileo/Newton to Einstein. Different views of time in 20th century physics are then examined, with primary focus on the revolutionary changes that came with the theory of general relativity. Implications of its new view in all domains of physics are discussed — from elementary particles to cosmology. The special role of Hamilton's quaternion calculus in equations of motion in general relativity is shown.     

Energy distributions of Kantowski-Sachs space-time in the theory of teleparallel gravity

We calculate the energy density and energy distribution of Kantowski-Sachs space-time, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in the theory of teleparallel gravity. A comparison of the results shows that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy density and energy distribution, but the definition of Landau-Lifshitz does not concur with them. We show that the space-time under consideration gives a counterexample that the energy distribution is the same either in general relativity or teleparallel gravity.     

Stationary axisymmetric solutions and their energy contents in?teleparallel equivalent of Einstein theory

We apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general relativity and M?ller’s tetrad theory of gravitation.     

Cosmological Scalar in the Jordan-Brans-Dicke Theory. I

A variant of the Jordan-Brans-Dicke (JBD) theory is examined which contains a cosmological scalar that is written so that on going to the Einstein representation it becomes the ordinary cosmological constant of general relativity theory. This paper is divided into two parts. In Part I we examine the cosmological solutions for the Einstein representation of the JBD theory, i.e., in the presence of a minimally coupled scalar field. In Part II we shall study the cosmological solutions in the proper representation of the JBD theory with a self consistent scalar field. The analysis of these solutions is of interest in connection with modern concepts of the evolution of the universe, in particular, with the observed acceleration of cosmological expansion and estimates of the density of dark matter and dark energy.__________Translated from Astrofizika, Vol. 48, No. 3, pp. 455–462 (August 2005).     

Exact Bianchi Type-I Cosmological Micro Model in Modified Theory of General Relativity

An anisotropic, homogeneous Bianchi type-I cosmological micro model is obtained in Barber's modified theory of general relativity. Some properties of the model are discussed. Further, it is found that this theory leads to Einstein theory as the coupling parameterλ → 0 in micro level (i.e., quantum level) in general. This revised version was published online in July 2006 with corrections to the Cover Date.     

Anisotropic spheres with uniform energy density in bimetric theory of relativity

In this paper we have obtained interior solutions of the field equations for anisotropic sphere in the bimetric general relativity theory formulated by Rosen (Lett. Nuovo Cimento 25, 1979). A class of solutions for a uniform energy-density source of the field equations is presented. The analytic solutions obtained are physically reasonable, well behaved in the interior of the sphere. The solutions agree with the Einstein’s general relativity for a physical system compared to the size of the universe such as the solar system.     

On the Origin of the Spin of Planets and Stars and its Connection with Gravitomagnetism

The origin of the spin of planets and stars is, to a certain extent, still unexplained. In general, we attribute their rotation to the swirl of their constituent primitive gases. In this paper, we try to show that the rotation of celestial bodies depends only on their mass, apparent radius and tilt of their spin axes. We reach this conclusion within the framework of gravitomagnetism, implied by the Einstein’s general relativity theory (GR). Our results show that it might possible, in principle, to calculate the mass of spinning objects by measuring their apparent radius, the speed of rotation and the tilt of the axis of rotation.     

Energy Of The Universe In Bianchi-Type I Models In MØLler’S Tetrad Theory Of Gravity

In this paper, using the energy definition in MØller’s tetrad theory of gravity we calculate the total energy of the universe in Bianchi-type I cosmological models which includes both the matter and gravitational fields. The total energy is found to be zero and this result agrees with a previous works of Banerjee and Sen who investigated this problem using the general relativity version of the Einstein energy-momentum complex and Xulu who investigated same problem using the general relativity versions of the Landau and lifshitz, Papapetrou and Weinberg’s energy-momentum complexes. The result that total energy of the universe in Bianchi-type I universes is zero supports the viewpoint of Tryon.     

Thermodynamics of the universe filled with perfect fluid having variable equation of state

Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Hor̃ava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein’s general relativity at large distances. Subsequently Lü et al. have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences have been analyzed. Also the thermodynamics of the FRW universe has been studied.     

Equations of radiation gas dynamics in tetrad form for astrophysical applications

This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory.     

Cosmological considerations and the special theory of relativity

From the special theory of relativity it follows that the Universe is expanding during the expansive evolutionary phase with the limit velocity of the signal propagationc. The discovery of this fact throws a new light on a number of cosmological questions.     

Physical uniformity of the Universe

The question of the spatial homogeneity of the Universe is re-examined from the viewpoint of the hypothesis on the physical unity of the universe. It is shown that the demand for the universal validity of the theory of relativity implies that the average value of the Newtonian world potential is constant everywhere in the universe which is spatially homogeneous on a large scale. It turns out that Mach's principle is compatible with the special theory of relativity if the average value of the normalized world potential is exactly equal to–c ². This fact may be interpreted as a consequence of the fundamental idea of the general relativity that cosmic matter determines the space-time metric in agreement with Mach's principle.     

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

The classical Poisson equations of rotational motion are used to study the attitude motions of an Earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate Earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the Earth.A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Longterm solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.This paper represents a part of the author's Ph. D. dissertation for the Mathematics Department, Auburn University.     

The Confrontation between General Relativity and Experiment

We review the experimental evidence for Einstein's general relativity. Tests of the Einstein Equivalence Principle support the postulates of curved spacetime and bound variations of fundamental constants in space and time, while solar-system experiments strongly confirm weak-field general relativity. The Binary Pulsar provides tests of gravitational-wave damping and of strong-field general relativity. Future experiments, such as the Gravity Probe B Gyroscope Experiment, a satellite test of the Equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves. This revised version was published online in July 2006 with corrections to the Cover Date.     

EINSTEIN and MICHELSON The Context of Discovery and the Context of Justification

The philosopher of science is not much intersted in the thought processes which lead to scientific discoveries; he looks for a logical analysis of the completed theory, including the relationships establishing its validity. That is, he is not interested in the context of discovery, but in the context of justification … it appears amazing to what extent the logical analysis of relativity coincides with the original interpretation by its author, as far as it can be constructed from the scanty remarks in EINSTEIN 's publications. In contradistinction to some developments in quantum theory, the logical schema of the theory of relativity corresponds surprisingly with the program which controlled its discovery.     

On the mode of propagation of light

Starting from the fundamental assumptions of the special theory of relativity which do not take into consideration gravitational effects the isotropic propagation of light and how to check experimentally the mode of propagation have been analyzed.     

Sources of stellar energy,Einstein–Eddington timescale of gravitational contraction and eternally collapsing objects

We point out that although conventional stars are primarily fed by burning of nuclear fuel at their cores, in a strict sense, the process of release of stored gravitational energy, known as, Kelvin–Helmholtz (KH) process is either also operational albeit at an arbitrary slow rate, or lying in wait to take over at the disruption of the nuclear channel. In fact, the latter mode of energy release is the true feature of any self-gravity bound object including stars. We also highlight the almost forgotten fact that Eddington was the first physicist to introduce special relativity into the problem and correctly insist that, actually, total energy stored in a star is not the mere Newtonian energy but the total mass energy (E = Mc²). Accordingly, Eddington defined an “Einstein time scale” of Evolution where the maximum age of the Sun turned out to be t_E ≈ 1.4 × 10¹³ yr. This concept has a fundamental importance though we know now that Sun in its present form cannot survive for more than 10 billion years. We extend this concept by introducing general relativity and show that the minimum value of depletion of total mass–energy is t_E = ∞ not only for Sun but for and sufficiently massive or dense object. We propose that this time scale be known in the name of “Einstein–Eddington”. We also point out that, recently, it has been shown that as massive stars undergo continued collapse to become a Black Hole, first they become extremely relativistic radiation pressure supported stars. And the life time of such relativistic radiation pressure supported compact stars is indeed dictated by this Einstein–Eddington time scale whose concept is formally developed here. Since this observed time scale of this radiation pressure supported quasistatic state turns out to be infinite, such objects are called eternally collapsing objects (ECO). Further since ECOs are expected to have strong intrinsic magnetic field, they are also known as “Magnetospheric ECO” or MECO.     

Lorentz violation from gamma-ray bursts

The constancy of light speed is a basic assumption in Einstein’s special relativity, and consequently the Lorentz invariance is a fundamental symmetry of space–time in modern physics. However, it is speculated that the speed of light becomes energy-dependent due to the Lorentz invariance violation (LV) in various new physics theories. We analyse the data of the energetic photons from the gamma-ray bursts (GRBs) by the Fermi Gamma-Ray Space Telescope, and find more events to support the energy dependence in the light speed with both linear and quadratic form corrections. We provide two scenarios to understand all the new-released Pass 8 data of bright GRBs by the Fermi-LAT Collaboration, with predictions from such scenarios being testable by future detected GRBs.