On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

Über die mögliche lineare Form von LORENTZ-kovarianten Gravitationstheorien

LORENTZ -covariant theories of gravitation which fulfil EINSTEIN 's weak principle of equivalence and which contain a pure Newtonian theory as an approximation are tensortheories with the linear approximative form for the field equations. In the case of EINSTEIN 's strong principle of equivalence the exact field equations must be the general relativistic EINSTEIN -equations (or the bimetrical EINSTEIN -ROSEN -equations). This follows from the dynamical equations and the BIANCHI identity according to JÁNOSSY and TREDER . However, from NEWTON 's axiom of reaction together with the weak principle of equivalence results that the strong principle of equivalence must be valid for the linear approximation of the field equations with sources. Therefore, the linear approximation of all physically meaningful Lorentz-covariant theories of gravitation is given by the linearized EINSTEIN -equations (with HILBERT -conditions): , that is by the ansatz α = 2. The main point of our arguments is LAUE 's postulate of the self-consistency of perfect static systems of isolated gravitational masses. In the lowest order of approximation this self-consistency is only possible if the gravitational matter-tensor is identical with the special-relativistic energy-momentum-tensor T_μv. LAUE 's postulate is fulfilled exactly for the general relativistic field equations according to the theorems of BIRKHOFF , TOLMAN and EINSTEIN and PAULI .     

Explizite Darstellungsformeln GREENscher Funktionen von kovarianten Wellengleichungen im schwachen Gravitationsfeld. II. Linearisierte EINSTEINsche Gravitationsgleichungen

The propagation equations for small perturbations of a background gravitational field satisfying the EINSTEIN equations are considered. For the perturbation potential the covariantly generalized EINSTEIN -HILBERT gauge is chosen. With the aid of the method used in [10], bitensor GREEN 's functions for the propagation equations in a weak vacuum field are given explicitly. The tail term is obtained to be an integral of the first-order RIEMANN curvature tensor. As an application of the formulae, GREEN 's functions for perturbations of the SCHWARZSCHILD metric are calculated to first order in the mass parameter.     

The energy tensor of matter in the projectve theory of relativity

In the projective theory of relativity the 5-dimensional field equation \(_{\mu \nu } \) and the resulting equation of motion Tμυ_;μ = 0 are investigated. There Tμυ stands for the 5-dimensional tensor of macroscopic matter. The 4-dimensional field equations and equation of motion obtained by projection are a generalization of Einstein's theory of general relativity and Maxwell's electrodynamics, involving a scalar field φ.They contain a single constant φ₀.The weak field approximation is investigated for the case of an ideal fluid and leads to Newton's mechanics, including Newton's gravitational law, and to Maxwell's electrodynamics. For the constant φ₀ one obtains the approximate value φ₀c⁴/γ_N with Newton's gravitational constant γ_N.For homogeneous and isotropic cosmological models consisting of matter only the general solution for the radius K of curvature is given. This solution is independent of the equation of state of matter For a pure dust universe the general solution for the scalar field φ is given. For a closed universe a power law φ ?K^?1 is valid which leads to Mach's principle. The calculation of the age of a closed universe yields over 7×10⁹y,if one uses mean values of the present cosmological data.     

Can quantum gravitational forces stop gravitational collapse?

We consider, in lowest order of the gravitational coupling constant G, the gravitational potential between two neutrons. As we have previously pointed out [1],the quantum (including spin) contributions to the gravitational field dominate for distances smaller than the Compton wavelength of the neutron. At such distances the gravitational force between two neutrons may be repulsive. In particular, the gravitational forces which are analogous to the familiar Darwin and Fermi forces of quantum electrodynamics are capable of stopping gravitational collapse. Our discussion is within the framework of Einstein's theory, but on a microscopic level. We conclude that gravitational collapse may be halted without the necessity of extending Einstein's theory à la Cartan or otherwise.     

A unified theory of matter. II. Derivation of the fundamental physical law

The equation for the fundamental field quantity ? is obtained. It is Div \(\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } \) ,where h is an arbitrary function oft andr, and [,]_? is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ?.(2) Relativistic covariance of the equations governing ?.(3) Principle of continguous action.(4) Conservation of total amount of ?. The equation appears to be unique. It is suggested that the physical world corresponds to ? being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential A^μ is identified with ε ρ^μ dΩ. Conservation laws on various measures of ? are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ? to the metric is made via Einstein's gravitational equation G_μυ =_KT_μυ.     

Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

The effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly-trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.     

Equation of motion for non-geodesic laboratory bodies

The gravitational equation of motion of laboratory bodies made up of electrically interacting molecules, the bodies being coupled to non-geodesic laboratories, is obtained for metrical theories of gravity. Application is made to the experiment of Witteborn and Fairbank in which electrons or positrons are ‘dropped’ inside a conducting shield. We show that the inertial and gravitational weight of a body depends on the location of the supporting force, and that a laboratory body, in general, possesses an inertial or gravitational masstensor which differs from the body's energy content divided by the speed of light squared.     

Toward a nonlocal theory of gravitation

The nonlocal theory of accelerated systems is extended to linear gravitational waves as measured by accelerated observers in Minkowski spacetime. The implications of this approach are discussed. In particular, the nonlocal modifications of helicity‐rotation coupling are pointed out and a nonlocal wave equation is presented for a special class of uniformly rotating observers. The results of this study, via Einstein's heuristic principle of equivalence, provide the incentive for a nonlocal classical theory of the gravitational field.     

A critical analysis of Helmholtz's argument against Weber's electrodynamics

We present Helmholtz's argument against Weber's electrodynamics. It is related with a fixed charged nonconducting spherical shell and a charged particle moving inside it. Then we utilize Weber's electrodynamics plus Schrödinger's expression for gravitational interactions in order to obtain the equation of motion and to study this situation. We show that this approach avoids the problems pointed out by Helmholtz. Moreover, it indicates that the effective inertial mass of the charged particle will depend not only on the electrostatic potential of the shell but also on its velocity. This is a relevant aspect of Weber's theory.     

Theory of Gravitational-Inertial Field of Universe. II. On Critical Systems in Universe

Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which 1. all Galaxies in the Universe “disperse” from each other according to Hubble's law, 2. the “dispersion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, 3. for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximalinertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational “annihilation”. At the maximal value of inertial and gravitational potentials (= c²) the material mass is being completely “evaporated” transforming into radiation mass. The latter is being concentrated in the “horizon” of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.     

Field Equations of TREDER's Gravitational Theory which are Derivable from a Variational Principle. III

In TREDER 's theory of gravitation the active gravitational (SCHWARZSCHILD ) mass is, generally speaking, different from the inertial (rest) mass of a stationary space-bounded field producing system. We consider a certain class of field equations and show that the relative deviation of the inertial (rest) mass from the SCHWARZSCHILD ian mass is very small (≤1/15).     

On the Theory of Gravitational Field in Finsler Spaces - III

From the vector bundle-like standpoint, the Finslerian gravitational field is regarded as the total space of the vector bundle whose fibre is the internal (y)-field spanned by vectors {y} (i.e., the so-called internal space spanned by {y}) and whose base is the external (x)-field spanned by points {x} (i.e., the Einstein's gravitational field). Along this line, in this paper, different from a previous paper [1], the so-called mapping process of the (y)-field on the (x)-field is not taken into account and following Miron's method [2, 3], the Finslerian field equations will be derived from the Einstein's field equation for the total space. Some physical considerations will be made on those field equations.     

A new interpretation of the special theory of relativity

Assuming the “Big Bang” theory as well as the usual axioms in the Special Theory of Relativity, the time dilations and length contractions are treated as real physical effects. This becomes possible by relating everything to the hypothetical frame,S _a , at rest relative to the “Big Bang” event. This frame in many senses plays the role of the classical aether frame. A clock's real ryhthm, as opposed to its rhythm observed by restricted methods, is then a function of its velocity relative toS _a (assuming a uniform gravitational field). It is further assumed that gravitational radiation is composed of “electromagnetic-like” waves. Therefore when a clock changes its velocity in a uniform gravitational field it must receive a different total energy due to the average frequency shift (Doppler effect), the time dilations are then caused by the change in energy due to this frequency shift. That is, not wo clocks can be in the “same” gravitational field unless they have no relative velocity, and therefore the Special Theory of Relativity is a special case of the General Theory from this viewpoint. Two feasible experimental tests, using the Mössbauer effect, are described that would decide on these viewpoints. The principle of equivalence and the “twin paradox” are also discussed.     

Gravitational analog of Faraday’s law via torsion and a metric with an antisymmetric part

In this paper we show that in the presence of torsion and a metric with an antisymmetric part one can construct a gravitational analog of Faraday’s law of electromagnetism.     

New theory of superconductivity

Based on three earlier papers which treat electromagnetic, elastogravitational, and radiant-nonradiant thermal phenomena in terms of six types of electric or nonelectric charges, the authors classify states of matter as hyperefficient, efficient, semiefficient, and hypoefficient in transmitting a particular type of charge, by means of a generalization of Ohm's law to two or three dimensions. Conventional states of matter (solid, liquid, gas, vacuum) are associated with torsional (gravitational) charges. Applications are made to electric superconductivity of crystals at elevated temperatures, and to frequency shift (gravitational red shift, Lamb shift, and Zeeman and Stark effects).     

Vakuum-Lichtgeschwindigkeit und differentielle Aberration

Vacuum Light Velocity and Differential Abberation In the frame work of Newton's theories of gravity and of light Laplace (1796) has deduced that the effective velocity c* of light is dependent on the gravitational potential of its source: Laplace, Olbers, a. o. have demonstrated that this effect implies differential aberrations of the light of different cosmisc sources. - But, Einstein's principles of relativity imply the independence of the velocity of light on its sources. This assertion is the fundamental principle of the Einsteinian theories of relativity. However, there seems to be no direct experimental facts disproving Laplace's formula, till today.     

Über die Schwere des Lichtes in der Newtonschen und in der Einsteinschen Gravitationstheorie

The gravity theories of Newton and Einstein are giving opposite sentences about the velocity of light in gravitational field. According to the Newtonian theory the velocity v in gravitational field is greater than the velocity c in a field-free space: v > c. According to general relativity theory we have a smaller velocity: v < c. For a spherical symmetric gravitational field Newton's theory gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 + \frac{{fM}}{{c^2 r}}} \right) $\end{document} but Einstein's theory of 1911 gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - \frac{{fM}}{{c^2 r}}} \right) $\end{document} and general relativity gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - 2\frac{{fM}}{{rc^2 }}} \right) $\end{document}. Therefore, the radarecho-measurations of Shapiro are the experimentum crucis for Einstein's against Newton's theory.