Showing papers on "Four-force published in 1975"
Book•
01 Jan 1975
TL;DR: In this article, the authors present a collection of 475 problems with solutions in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology, expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds.
Abstract: Important and useful to every student of relativity, this book is a unique collection of some 475 problems--with solutions--in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology. The problems are expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds. In their solutions, the authors have attempted to convey a mode of approach to these kinds of problems, revealing procedures that can reduce the labor of calculations while avoiding the pitfall of too much or too powerful formalism. Although well suited for individual use, the volume may also be used with one of the modem textbooks in general relativity.
305 citations
TL;DR: A singularity-free solution for a static charged fluid sphere in general relativity was obtained in this article, where the solution satisfies physical conditions inside the sphere and satisfies physical properties inside the fluid sphere.
Abstract: A singularity-free solution was obtained for a static charged fluid sphere in general relativity The solution satisfies physical conditions inside the sphere
226 citations
TL;DR: In this paper, a simple theorem whose physical interpretation is that an isolated, gravitating body in general relativity moves approximately along a geodesic is obtained, and the theorem is proved.
Abstract: A simple theorem, whose physical interpretation is that an isolated, gravitating body in general relativity moves approximately along a geodesic, is obtained.
109 citations
TL;DR: The Sagnac effect as mentioned in this paper is a phase shift observed between two beams of light traversing in opposite directions the same closed path around a rotating object, and it is defined as an operational definition of rotation.
Abstract: The Sagnac effect is a phase shift observed between two beams of light traversing in opposite directions the same closed path around a rotating object. A description of this experiment is obtained within the context of general relativity. In this context the effect provides an operational definition of rotation. An expression for the magnitude of the phase shift is derived under fairly general conditions. The general definition of rotation provided by this experiment is shown to reduce, in certain particular cases, to the usual definitions available. It is observed that the Sagnac effect represents a gravitational analog of the Aharanov−Bohm effect in electrodynamics.
94 citations
74 citations
TL;DR: A conformal invariant theory of gravitation is proposed in this article, which matches General Relativity in the classical limit and implies a dynamical origin for mass and a selection rule on “elementary” matter constituents.
49 citations
01 Jan 1975
35 citations
33 citations
32 citations
TL;DR: In this article, the stability of the Kerr space-time has not been established rigorously rigorously, since the exponentially decaying modes have not been shown to be complete, and there are normal modes with real frequencies.
Abstract: against infinitesimal perturbations is discussed No exponentially growing 'normal modes' occur However, since (a) the exponentially decaying modes have not been shown to be complete, (b) there are normal modes with real frequencies, the stability of the Kerr space-time has not been established rigorously
TL;DR: In this article, it is shown that Extended Relativity allows to derive the usual cross-relations of elementary particle (high-energy) physics and derive the CPT-covariance theorem as a particular case of G-civariance.
Abstract: Recently, Special Relativity has been straightforwardly extended to Superluminal inertial frames and faster-than-light objects. The ‘Extended Relativity’ theory not only allowed building up a self-consistent ‘classical theory’ of tachyons, but reveals itself useful also for the understanding of standard (subluminal) physics, i.e. of usual particles. In this paper, it is shown that Extended Relativity allows: (i) deriving the usual ‘Crossing Relations’ of elementary particle (high-energy) physics; and (ii) deriving the CPT-covariance theorem as a particular case of G-covariance (i.e., covariance under the new group of Generalised Lorentz transformations, both subluminal and Superluminal). In this framework, the ‘Analyticity’ postulate is unnecessary: it is better substituted by the G-covariance requirement. Moreover, new ‘crossing-type’ relations are predicted on the basis of mere Extended Relativity. They may well serve as a test for relativistic covariance of ‘force fields’ like strong interactions and, particularly, weak interactions, and possible new ‘interaction fields’ (whicha priori are not relativistically covariant).
TL;DR: In this paper, the definition of time is established as a fundamental physical principle and the laws of quantum geometrodynamics and, in the classical limit, those of general relativity theory are deduced.
Abstract: The definition of time is established as a fundamental physical principle. From this principle, in connection with the quantum and relativity principles, the laws of quantum geometrodynamics and, in the classical limit, those of general relativity theory, are uniquely deduced.
TL;DR: In this article, a generalization of the functional constitutive equations of continuous media of Truesdell and Noll has been proposed to give a definition of hyperelasticity in general relativity, on condition that the existence of a reference state of minimum free energy is postulated.
Abstract: This article is a study of elastic media in general relativity; it is based on a relativistic generalization of the functional constitutive equations of continuous media of Truesdell and Noll. We show that it is possible to give a definition of hyperelasticity in general relativity, on condition that the existence of a reference state of minimum free energy is postulated. This approach allows us also on the one hand to study the case of relativistic elasticity under high pressure (cf. certain stellar models), and on the other hand to study thermoelastic media without the paradox of infinite velocity of heat conduction.
TL;DR: The chiral SU(3) quark model is shown to be a consequence of general relativity for Petrov type Id space-times, in much the same way as the Dirac equation as mentioned in this paper.
Abstract: The chiralSU(3) quark model is shown to be a consequence of general relativity for Petrov type Id space-times, in much the same way that the Dirac equation is a consequence of special relativity.
TL;DR: In this paper, an analysis of the complete Schwarzschild manifold M is performed and a physical interpretation of the peculiar feature of M of being the union of four regions with an infinitespace-like extension is suggested based on a general relativity generalization of the space-time previously introduced in the special relativity theory of superluminal frames.
Abstract: An analysis of the complete Schwarzschild manifold M is performed. The Finkelstein time is assumed to order the events causally, instead of the Kruskal time. As a consequence of this assumption, the mutual causal behavior of the four Schwarzschild regions contained in M allows one to conceive of a dynamical mechanism which could produce the main features of M in some region of spacetime. Assuming the strong principle of equivalence, one predicts a significant blue shift of the radiation emitted by matter emerging from the r = 0singularity. This phenomenon has not been observed. A way to reconcile the assumption that M is physical with the absence of blue shifts is to require only a weaker equivalence principle, namely the local validity of the principle of (special) relativity in any local inertial frame. From such an equivalence principle, which one cannot renounce without giving up the whole theory of relativity, it is possible to deduce the ratio between the frequencies (as measured by an observer at rest in the asymptotically flat domain) emitted by two identical transmitters at the Schwarzschild times at which they reach the same 3-space point of the exterior Schwarzschild region along different geodesics. A physical interpretation of the peculiar feature of M of being the union of four regions with an infinitespace-like extension is suggested. Such an interpretation is mainly based on a general relativity generalization of the space-time previously introduced in the special relativity theory of superluminal frames.
TL;DR: In this paper, different approaches are presented in a didactic way in order to lead to an understanding of the concept and equations describing relative velocity in an invariant way from the point of view of the special theory of relativity.
Abstract: Different approaches are presented in a didactic way in order to lead to an understanding of the concept and equations describing relative velocity in an invariant way from the point of view of the special theory of relativity.
TL;DR: In this article, it was shown that given any good coordinate condition in Hamiltonian general relativity, one can construct an associated many-time formulation in which the constraints can be solved for some of the momenta as functionals of the remaining canonical variables.
TL;DR: In this article, the identifications of the field equations and Bianchi identities of the yA−formalism with the main equations and constraint equations of a metric in a Bondi coordinate system were investigated.
Abstract: This paper applies the ’’yA−formalism’’ of a previous paper (Paper I) to a Lagrangian formulation of the characteristic initial−value problem in general relativity. The essential content of the paper is the respective identifications of the ’’field equations’’ and ’’Bianchi identities’’ of the yA−formalism with the ’’main equations’’ and ’’constraint equations’’ of a metric in a Bondi coordinate system. The identifications are developed in detail in the case of Bondi’s (axially symmetric) radiating metric.
TL;DR: In this article, a Lagrangian formalism (the yA−formalism) was developed for use in investigating the Cauchy problem in general relativity, which enables one to define field equations and Bianchi identities for metrics containing arbitrary functions in the case when the arbitrary functions are treated as the field variables.
Abstract: This paper develops a Lagrangian formalism (the yA−formalism) for use in investigating the Cauchy problem in general relativity. In particular it will be used in a subsequent paper to present a Lagrangian formulation of the characteristic initial−value problem in general relativity. The formalism enables one to define ’’field equations’’ and ’’Bianchi identities’’ for metrics containing arbitrary functions in the case when the arbitrary functions are treated as the field variables.
01 Sep 1975
TL;DR: In this article, the equations satisfied by perturbations of solutions of the Euler-Lagrange equations corresponding to a Lagrangian density L are derived from the first and second variations of L and used to construct Noether and Euler identities.
Abstract: The equations satisfied by perturbations of solutions of the Euler-Lagrange equations corresponding to a Lagrangian density L are derived from the first and second variations of L and these new Lagrangian densities are used to construct Noether and Euler identities. It is shown how these identities can be used in general relativity to construct conserved quantities and local uniqueness theorems.
TL;DR: In this paper, it was shown that there is a unique conserved vector associated with the Lagrangian which is an invariant density and a concomitant of a set of independent geometrical objects.
Abstract: Given a Lagrangian which is an invariant density and a concomitant of a set of independent geometrical objects, it is shown that there is a unique conserved vector associated with the Lagrangian. For cases of interest the vector is constructed and is seen to be identical with Komar’s conserved vector for general relativity. For a general Lagrangian we also construct the ’’compatability identity’’ relating the Euler−Lagrange tensors. The connection between these identities, the invariance identities of Rund, and Lie derivatives of invariant densities is found.
01 Jan 1975
TL;DR: In this paper, it was pointed out that in the linear approximation of the Cartan theory, a set of rotating bodies and a fluid with the classical model of spin give the same metric of space-time.
Abstract: It is pointed out that in the linear approximation of the Einstein-- Cartan theory a set of rotating bodies and a fluid with the classical model of spin give the same metric of space-time. (auth)
TL;DR: In this article, it was shown that the first and second betti numbers of compact space-times with Cauchy surfaces whose fundamental groups are abelian are upper bounds.
Abstract: It is shown that there are upper bounds on the first and second betti numbers of compact space-times or space-times with Cauchy surfaces whose fundamental groups are abelian. Homological classifications of compact space-times and space-times with compact Cauchy surfaces are given.
TL;DR: In this article, the existence of tachyons is re-examined and it is shown that they are moving backward in time for some moving systems, and this would contradict the principle of causality.
Abstract: In this paper, the hypothetical existence of tachyons is re-examined. It has previously been doubted whether tachyons would exist, for it can be shown with the space-time diagram used in the Special Theory of Relativity that they are moving backward in time for some moving systems, and this would contradict the principle of causality.
TL;DR: In this paper, the covariant formulas for the total four-momentum and angular momentum of an isolated physical system in general relativity were derived in weak-field approximation, for which they were shown to be expressible in surface integral form, to be unique, and to represent covariantly conserved quantities.