Showing papers on "Four-force published in 1991"
Book•
30 Aug 1991TL;DR: In this paper, the characteristic initial value problem (INV) is used to solve differential geometry problems with spinors and asymptotics. But the problem is not solved in practice.
Abstract: Preface 1. Differential geometry 2. Spinors 3. Asymptopia 4. The characteristic initial value problem Appendices References Index.
321 citations
TL;DR: In this paper, a collection of essays by the authors and other people that deal with scientific opinions that led Einstein and his contemporaries to their views of general relativity is presented, which explores the passage from the special theory through a sequence of gravitational theories to the discovery of the field equations of the grand theory in November 1915.
Abstract: This book is a collection of essays by the authors and other people that deal with scientific opinions that led Einstein and his contemporaries to their views of general relativity. Some of the essays explore Einstein's passage from the special theory through a sequence of gravitational theories to the discovery of the field equations of the grand theory in November 1915. Two other essays discuss Einstein's public and private exchanges with Max Abraham and Tullio Levi-Civita in 1913 and 1914. A sympathetic picture of H.A. Lorentz's reaction to the general theory of relativity is included, and a careful and insightful essay on the early understanding of the Schwarzschild-Droste solution to the field equations of general relativity is presented. One paper presents a discussion on the state of the enterprise of general relativity between 1925 and 1928, and a short essay details the history of steps toward quantum gravitational through canonical quantization. A discussion of the history of derivations of the geodesic equation of motion from the field equation and conservation laws of the general theory is presented. The early history of geometrical unified field theories is included.
126 citations
01 Jan 1991
81 citations
TL;DR: In this paper, the action of quantum general relativity on a general state in the loop representation is coded in terms of loop derivatives, which are related to the infinitessimal generators of the group of loops.
63 citations
01 Jan 1991
TL;DR: In this paper, the Lagrangian approach to conserved currents in field theories is discussed and the results apply to general relativity and to relativistic field theories and the fundamental theory of conserved quantities associated to the gravitational field itself is discussed.
Abstract: Publisher Summary This chapter reviews general ideas and results concerning the geometric “Lagrangian” approach to conserved currents in field theories and shows how these results apply to general relativity and to relativistic field theories. Although general relativity is a well-established theory of gravity interacting with external matter, there is still no general agreement on the definition of mass and of conserved quantities associated to the gravitational field itself. The chapter reviews the fundamentals of the theory of conserved quantities as it follows from the Poincare–Cartan form approach to the higher-order calculus of variations. It further analyzes the interaction between matter fields and gravitation, the first-order covariant formulation of general relativity, and the field theories on a fixed background.
34 citations
TL;DR: In this paper, a new approximation scheme is proposed to describe a realistic inhomogeneous universe in general relativity, which allows one to treat more general situations where the local effect due to self-gravity of the matter dominates the effect of cosmic expansion.
Abstract: A new approximation scheme is proposed to describe a realistic inhomogeneous universe in general relativity. This scheme improves the former one and allows one to treat more general situations where the local effect due to self-gravity of the matter dominates the effect of cosmic expansion. A new statistical way of averaging spacetime is also discussed
18 citations
TL;DR: In this paper, it was shown that classically interpreted electromagnetism and special relativity already diverge in their predictions on the behavior of a simple electrodynamical system, even for low velocities.
Abstract: In connection with a note by Rindler on relativity and electromagnetism, it is shown that classically interpreted electromagnetism and special relativity already diverge in their predictions on the behavior of a very simple electrodynamical system, even for ‘‘low’’ velocities.
15 citations
Journal Article•
TL;DR: In this paper, complete representation formulae are derived for scalar-valued, vector valued and tensor-valued sunctions subjected to the principle of relativity with an arbitrary number of scalars, vectors and tensors (of the second order symmetric and skewsymmetric) as variables.
Abstract: In a Minkowsky space V , complete representation formulae are derived for scalar-valued, vector valued and tensor-valued sunctions subjected to the principle of relativity with an arbitrary number of scalars, vectors and tensors (of the second order symmetric and skewsymmetric) as variables.
14 citations
TL;DR: In this article, the authors show that the pure connection action for general relativity with a cosmological constant by Capovilla, Dell and Jacobson (1989) correctly yields the usual constraints of general relativity as given by Ashtekar (1986).
Abstract: The authors show that the recently proposed pure-connection action for general relativity with a cosmological constant by Capovilla, Dell and Jacobson (1989) correctly yields the usual constraints of general relativity as given by Ashtekar (1986). They also point out alternative possibilities for the Capovilla-Dell-Jacobson action.
01 Jan 1991
Posted Content•
TL;DR: A review of recent work on topology changing solutions to the first order form of general relativity is given in this article, where the importance of considering degenerate metrics is discussed, and the possibility that quantum effects can suppress topology change is briefly examined.
Abstract: A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The importance of considering degenerate metrics is discussed, and the possibility that quantum effects can suppress topology change is briefly examined.
TL;DR: In this article, a comparison of general relativity with the theory of skyrmions is used to develop a method for counting the number of Finkelstein-Misner kinks in any given general relativistic metric.
Abstract: A comparison of general relativity with the theory of skyrmions is used to develop a method for counting the number of Finkelstein–Misner kinks in any given general relativistic metric. Some examples of kink number computations are presented.
TL;DR: In this article, the relativistic expression for the kinetic energy, as well as the inertia of energy, could be derived entirely from the principle of conservation of energy in addition to the two usual postulates of special relativity.
Abstract: Langevin showed that the relativistic expression for the kinetic energy, as well as the inertia of energy, could be derived entirely from the principle of conservation of energy, in addition to the two usual postulates of special relativity. Unfortunately, this beautiful derivation, given in a lecture and not published by the author, passed almost unnoticed. The object of this paper is to popularize it in a modernized presentation. Langevin’s approach is compared with the well‐known one starting from the relativistic law of linear momentum conservation, following an idea of Lewis and Tolman.
TL;DR: The use of the concept of six-vectors makes possible a unitary description of the antisymmetric tensor fields of the second order on the Minkowski space as discussed by the authors.
Abstract: The use of the concept of six-vectors makes possible a unitary description of the antisymmetric tensor fields of the second order on the Minkowski space.
TL;DR: In this article, the assumption of homogeneity of space (or time) implies that the transformation formulae must be linear (see Equations (10) and (17) ).
Abstract: From the following discussion, we conclude that: (a) the homogeneity of space implies (in special relativity) the homogeneity of time, and vice versa; (b) the assumption of homogeneity of space (or time) implies that the transformation formulae must be linear (see Equations (10) and (17)). This last conclusion is contrary to Hoyer's affirmation in the paper quoted below.
TL;DR: The necessary and sufficient condition that a non-singular 4 × 4 complex matrix can be written as a Kronecker product of two 2 × 2 complex matrices is established in this article.
TL;DR: The reader is left with the impression that the main problems in turbulence modeling have not been solved, and may still require approaches very different from those presently considered.
Abstract: and balanced. As with Batchelor’s monograph [1 ], McComb’s principal concern is with theories of turbulence, and especially the modern theories which build on and attempt to go beyond Kolmogorov’s theory [2] and the ideas presented in [1]. McComb develops several theories systematically, based on renormalized perturbation theory, the renormalization group, and the graphical methods which aid in understanding the perturbation series. Several chapters summarize the insight obtained from computation and experiment. McComb compares theories with one another, with computation, and with experiment. McComb’s assessments appear to be well balanced in the main, and will be as valuable to the student as his careful expository writing. Boundary layer theory, pipe flow, and Reynolds averaged equations are discussed, but only briefly, and the book does not attempt to address in depth the questions ofengineering applications of turbulent flow. Chapters and 2 provide an introduction to turbulent flow, while Chapter 3 is a survey of the main ideas developed later in the book. These three chapters could be used as a text for an undergraduate course in turbulent flow, and they provide a solid introduction to those not familiar with the subject. Chapters 4 and 5 develop the basic tools for turbulence modeling: statistical formulations and renormalized perturbation theory. These methods are illustrated by a sketch oftheir use in other areas of physics, including N-particle systems and Debye screening in the electron gas. Graphical methods are explained and used to understand renormalized propagators. These tools are applied to turbulence modeling in Chapters 6-8, while Chapter 9 is devoted to the renormalization group. These chapters are the heart ofthe book. They present the modern theory of turbulence modeling clearly and systematically. Up to now this theory has been rather inaccessible from the standpoint of nonspecialists. In all, some eight approaches to turbulence modeling are presented. Chapter 8, which offers an assessment of these theories, is especially helpful. On the whole, the reader is left with the (no doubt correct) impression that the main problems in turbulence modeling have not been solved, and may still require approaches very different from those presently considered. Chapter 10 is a brief account of the numerical simulation of turbulence, while Chapter 11 concerns coherent structures in pipe and boundary layer flow. Chapters 12 and 13 discuss passive diffusion of some quantity (heat, dye by a turbulent flow field. Here the flow field is given externally as a random (and usually Gaussian) field, so this problem can be viewed as a linearization ofturbulence. The result of these theories is to compute an effective diffusivity generated by the turbulence. Chapter 14 develops non-Newtonian flow. These concluding chapters provide useful introductions to a number of advanced topics, each of which is the subject of book-length treatments in its own right.
01 Jan 1991
TL;DR: In addition to gravitational and electromagnetic fields, neutrino fields are objects of fundamental research in theoretical physics as mentioned in this paper, and the nature of the interaction of these three types of material fields in fairly general situations.
Abstract: In addition to gravitational and electromagnetic fields, neutrino fields are objects of fundamental research in theoretical physics. The subject of this chapter is the nature of the interaction of these three types of material fields in fairly general situations.
01 Jan 1991
TL;DR: The isometry group of a massless particle in general relativity is smaller than in special relativity as discussed by the authors, and this symmetry reduction comes from a necessary short-distance regularization, as in anomalous quantum field theories.
Abstract: The isometry group of a massless particle in general relativity is smaller than in special relativity. As in anomalous quantum field theories this symmetry reduction comes from a necessary short-distance regularization.
Journal Article•
TL;DR: In this article, an exact solution of the gravitational and electromagnetic field equations with a charged rotating source in new general relativity was given, and the solution has three parameters Q, h and a, and it gives a charged Kerr metric space-time.
Abstract: We give an exact solution of the gravitational and electromagnetic field equations with a charged rotating source in new general relativity. The solution has three parameters Q, h and a, and it gives a charged Kerr metric space-time. The parallel vector fields and the electromagnetic vector poten- \" tial are axially symmetric. In this space-time, we cannot discriminate new general relativity \"from general relativity, so far as scalar, the Dirac and the Yang-Mills fields and macroscopic bodies are used as probes. The space-time does not have singularities at all, although it has an \"effective singularity\". Two kinds of Reissner-Nordstrom metric solutions, one is our solution with h=O and the other is a solution given by Hayashi and Shirafuji, are physically equivalent with each other. Nevertheless, these are markedly different from each other with regard to the asymptotic behavior of the torsion tensor for r -+ 00 and the space-time singularities.