Difference between special relativistic gravitational theory and general relativity: Weak field limit

In the case of weak fields, we compare the gravitational fields and the dynamical equation of a particle deduced from special relativistic gravitational theory with the corresponding results deduced from general relativity. Then both gravitational theories can be tested by experiments.     

Critical phenomena and relativistic gravitational collapse

Recent calculations have shown the existence of critical phenomena in general relativity associated with the collapse of wavepackets of massless fields that are near, in parameter space, the onset of black hole formation (the critical point). Two physically distinct systems have been explored: collapse of spherically-symmetric massless scalar field and collapse of vacuum, axisymmetric gravitational waves. Nonlinear effects dominate near the critical point. Black-hole mass serves as an order parameter and has a power-law dependence on critical separation in the supercritical region of parameter space. Remarkably, the values of the critical exponent of the power law are nearly identical in the two systems. The nonlinearity induces the fields to oscillate. Each successive oscillation is an echo, obeying a spatial and temporal scaling relation.     

Workshop on gravitational waves and relativistic astrophysics

Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to observations of supermassive black holes dominated the workshop sessions on gravitational waves and relativistic astrophysics in the ICGC-2004. A summary of seven papers that were presented in these workshop sessions has been provided in this article.     

New relativistic gravitational effects using charged-particle interferometry

A new class of gravitational effects, in the quantum interference of charged particles, are studied in electron interferometry and superconducting Josephson interferometry. These include phase shifts due to the gravitationally induced Schiff-Barnhill field, rotationally induced London moment, and the modification of the Aharonov-Bohm type of phase shifts, due to the general relativistic coupling of the electromagnetic field to the gravitational field. These effects are interesting, even from a purely theoretical point of view, because they involve an elegant interplay between gravitation, electromagnetism, and quantum mechanics. But new predictions are also made which, if confirmed, would provide the first observation of relativistic gravitational effects, involving the electric charge, at the quantum mechanical level. The possibility of using these effects to detect gravitational waves is also discussed.This essay received the first award from the Gravity Research Foundation for the year 1983-Ed.     

Special relativistic Newtonian gravity

Newtonian gravity is modified minimally to obtain a Lorentz covariant theory of gravity in a background flat space. Gravity is assumed to appear as a potential. Constraint Hamiltonian dynamics is used to determine particle trajectories in a manifestly covariant fashion. The resulting theory is significantly different from the general theory of relativity. However, all known experimental results (precession of planetary orbits, bending of the path of light near the sun, and gravitational spectral shift) are still explained by this theory.     

Dispersion of gravitational waves in a relativistic gas

The propagation of gravitational waves in a relativistic gas which is in a static gravitational field in the unperturbed state is considered. The group velocity of the transverse gravitational waves and the decrements of collisional and collisionless damping are calculated.     

Singularities in gravitational theory

It is shown that in the absolute parallelism theory a unique choice of field equations can be made by requiring that the solutions extend beyond possible singularities, while for the equations of the general theory of relativity and R²-gravitation this condition is not satisfied. The system of equations thus produced is also distinguished by the fact that it makes possible validity of the equivalence principle with certain limitations related to the presence of symmetry.Kemerov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 73–78, July, 1992.     

Newtonian gravitational field theory

A field theory for gravitation is developed within the framework of the special theory of relativity. This is achieved by exploiting the similarity in mathematical structure of two relations which are found in both Newton's gravitational theory and Maxwell's electromagnetic theory. These relations are: (1) the law of force between the relevant physical entities (mass and electric charge), and (2) the equation of continuity (conservation of charge). The field equations describe the propagation of gravitational waves with the velocity of light in much the same way that Maxwell's field equations describe electromagnetic waves. Both fields have such similar mathematical structures that they are developed in parallel up to the point where their inherently different physical content cause their paths of evolution to diverge. At this stage, the field equations for both theories are determined. The physical significance of the field variables of both theories imposes a mathematical formalism which doesnot give rise to self-interactions. A calculation for the energy in the field of two particles representative of either the electromagnetic or gravitational field is shown to give the correct finite value. The reason that conventional calculations yield an infinite energy is readily seen to lie in the calculation of a physically meaningless quantity. The mathematical formalism required by the field theories is used to develop generalizations of the usual conservation laws. Two conservation laws are derived which are consequences of the consistent physical interpretation of the field variables. These laws do not appear in conventional theory. The approach followed here in developing the field theories leads to the appearance of forces dual to the well-known forces. Thus, for the electromagnetic field, we find a dual to the Lorentz force and, in the gravitational field, we find a dual to Newton's law of gravitation. These results are not due to the introduction of the fields, for they can be expressed in terms of the particle variables. They emerge from the consistent application of the physical interpretation of the particle and field variables. A basic physical principle, which underlies both theories, is best expressed by the statement: It is the interactions between the elements of a physical event and not the elements themselves which are the physical observables.     

General relativistic analysis of simplest optical gravitational wave detectors

In this article we continue to study the simplest forward trip optical position meter in the frame-work of general relativity. We demonstrate the apparent paradox arising from careless analysis of these system in the laboratory reference frame (corresponding to the transeverse-traceless gauge) and show the way to overcome this problem in the proper reference frame of observer (corresponding to the local Lorentz gauge). Then we show that careful taking into account initial synchronization procedure solves this problem even in transeverse-traceless gauge.     

Conformally invariant gravitational waves in a modified gravitational theory

International Journal of Theoretical Physics - An attempt is made to obtain a conformally invariant gravitational wave equation in an isotropic background universe by modifying the Einstein field...     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

On relativistic deformable solids and the detection of gravitational waves

In this paper, the purpose of which is to complement a preceding work [1], it is shown, in agreement with the theory of relativistic deformable solids developed by A.C. Bringen and his coworkers, that the simplest conceivable dissipative constitutive equation — that of a socalled KelvinVoigt viscoelastic solid — yields a gravitational wave equation of propagation different from that of Weber: specifically, the following third order partial differential equation, $$\frac{{\partial ^2 \theta }}{{\partial t^2 }} - \left( {A + A'\frac{{\partial ^2 \theta }}{{\partial t}}} \right)\frac{{\partial ^2 \theta }}{{\partial x^2 }} = c^2 R_{1441'} $$ which can be solved by use of Fourier transform techniques, and where A and A′ are positive material coefficients.     

On relativistic kinetic gas theory: XV. The Ritz method in relativistic Boltzmann theory

The transport coefficients of a multicomponent gas mixture are approximated by means of a variational technique. It is shown that the procedure is equivalent to a more heuristic method developed earlier.     

Hamiltonian structure of gravitational field theory

Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations.     

A mathematical theory of gravitational collapse

We study the asymptotic behaviour, as the retarded timeu tends to infinity, of the solutions of Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We prove that when the final Bondi massM ₁ is different from zero, asu , a black hole forms of massM ₁ surrounded by vacuum. We find the rate of decay of the metric functions and the behaviour of the scalar field on the horizon.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University