Showing papers on "Introduction to the mathematics of general relativity published in 1980"
TL;DR: In this paper, a computer-aided classification of geometries in terms of the curvature tensor and its covariant derivatives is presented, which extends the Petrov classification to a complete classification of the local geometry and the dimensions of the group of motions and its isotropy subgroup are obtained.
35 citations
TL;DR: In this article, a modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensor describing the space-time geometry and gravitation, there exists also a background metric tensors γ� μv======, the latter describes the spacetime of the universe if no matter were present and is taken to correspond to a space time of constant curvature with positive spatial curvature (k=1).
Abstract: A modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensorg
μv
describing the space-time geometry and gravitation, there exists also a background metric tensor γ
μv
The latter describes the space-time of the universe if no matter were present and is taken to correspond to a space-time of constant curvature with positive spatial curvature (k=1). Field equations are obtained, and these agree with the Einstein equations for systems that are small compared to the size of the universe, such as the solar system. Energy considerations lead to a generalized form of the De Donder condition. One can set up simple isotropic closed models of the universe which first contract and then expand without going through a singular state. It is suggested that the maximum density of the universe was of the order ofc
5
ħ
−1
G
−2∼1093 g/cm3. The expansion from such a high-density state is similar to that from the singular state (“big bang”) of the general relativity models. In the case of the dust-filled model one can fit the parameters to present cosmological data. Using the radiation-filled model to describe the early history of the universe, one can account for the cosmic abundance of helium and other light elements in the same way as in ordinary general relativity.
25 citations
24 citations
TL;DR: In this article, the field equations of general relativity have been solved to obtain the different solutions for the static charged gas sphere and these solutions are free from singularities and satisfy the necessary physical conditions.
Abstract: In the present paper the field equations of general relativity have been solved to obtain the different solutions for the static charged gas sphere. These solutions are free from singularities and satisfy the necessary physical conditions.
22 citations
01 Jan 1980
TL;DR: In this paper, the authors outline the present status of the issue of introducing a meaningful notion of angular momentum of isolated gravitating systems and summarize ways in which these difficulties have been overcome to a certain extent.
Abstract: The purpose of this article is to outline the present status of the issue of introducing a meaningful notion of angular momentum of isolated gravitating systems. More precisely, the aim is three-folds: i) to point out the conceptual difficulties which, in the framework of general relativity,make the introduction of angular momentum more difficult than than that of, say, energy-momentum; ii) to summarize ways in which these difficulties have been overcome to a certain extent; and, iii) to discuss theorems which unify the resulting definitions. The article is addressed to non-experts. The emphasis is therefore on the basic ideas involved; detailed proofs of various assertions can be found in the original papers which are referred to at appropriate places in the text. Also, the exposition is intended to be complementary to winicour’s review 007B1007D of the subject In particular, some of the issues discussed by Winicour in detail are skipped entirely or discussed only briefly and the developments that have taken place since the completion of {100} are stressed.
20 citations
TL;DR: The field equations of the bimetric general relativity theory proposed by one of the authors (N. Rosen) are put into a static form in this paper, and the equations are solved near the Schwarzschild sphere, and it is found that the field differs from that of the EGM theory: instead of a black hole, one has an impenetrable sphere.
Abstract: The field equations of the bimetric general relativity theory proposed recently by one of the authors (N. Rosen) are put into a static form. The equations are solved near the Schwarzschild sphere, and it is found that the field differs from that of the Einstein general relativity theory: instead of a black hole, one has an impenetrable sphere. For larger distances the field is found to agree with that of ordinary general relativity, so that solar system observations cannot distinguish between the two theories. For very large distances one gets a cosmic contribution to the field which may affect the dynamics of clusters of galaxies.
15 citations
15 citations
TL;DR: In this paper, it was shown that ghost neutrino fields can occur in Einstein-Cartan theory as well as in general relativity, contrary to an earlier result of Letelier.
14 citations
TL;DR: The Palatini Lagrangian is analyzed in this article for a symmetric metric and for a more general sesquilinear (Hermitian) form, and the connection is determined to bemetrical up to a real λ transformation.
Abstract: The Palatini variation of the Einstein Lagiangian is analyzed for a symmetric metric and for a more general sesquilinear (Hermitian) form. In the latter case the Lagrangian is no longer projectively invariant, and the connection is determined to bemetrical up to a real λ transformation. The Einstein-Straus equations emerge as a naturalgeometrical generalization of general relativity.
13 citations
9 citations
TL;DR: The curvature collineation equations have been solved for the two families of Petrov type-N plane-fronted gravitational wave solutions of Einstein's vacuum field equations in general relativity as mentioned in this paper.
Abstract: The curvature collineation equations have been solved for the two families of Petrov type-N plane-fronted gravitational wave solutions of Einstein's vacuum field equations in general relativity. Both of these solutions always have non-trivial curvature collineations, i.e. vector fields xi with respect to which the components Rmu nu alpha beta of the Riemann tensor for those solutions are Lie derivable.
TL;DR: In this article, an analysis of a stationary axisymmetric solution of Einstein's equations is given, and the invariants of the Weyl tensor, the first few multipole moments, and stationary limit surfaces and the axis are discussed.
Abstract: An analysis of a stationary axisymmetric solution of Einstein’s equations recently derived by Hoenselaers, Kinnersley, and Xanthopoulos is given. We derive the metric of the full space–time, the invariants of the Weyl tensor, the first few multipole moments, and discuss the stationary limit surfaces and the axis.
TL;DR: For a stochastic stress-energy tensor associated with cosmic turbulence, it is observed that Einstein's equations imply fluctuations in the space-time metric tensor as discussed by the authors, and such metrical fluctuations are shown to engender modified values for the average effective proper density and total pressure and thus to alter the solutions to the Friedman equations.
Abstract: For a stochastic stress-energy tensor associated with cosmic turbulence, it is observed that Einstein’s equations imply fluctuations in the space-time metric tensor. Such metrical fluctuations are shown to engender modified values for the average effective proper density and total pressure and thus to alter the solutions to the Friedman equations.
TL;DR: In this paper, a theory requiring this flickering at the light speed is presented, where the zitterbewegung is considered as a real motion and it is shown that the flickering can be achieved at the speed of light.
Abstract: Atoms with point particles in general relativity have either no bound states or a continuous range of energy. This drawback is overcome by conceiving the zitterbewegung as a real motion. A theory requiring this flickering at the light speed is presented.
TL;DR: In this article, the equations of motion of two charged particles in the 0th order were given for the case of n particles, where n is the number of particles in a metric tensor.
Abstract: Starting with the Einstein-Maxwell field equations in general relativity we construct the general differential equations governing the components of the metric tensor. We do this in a fashion completely analogous to that which we follow in Einstein-Infeld-Hoffmann and Einstein-Infeld theory. These equations allow us to findhif in various orders. An answer to our problem up to the first relativistic corrections is a computational work to find4h00, since the other terms2h00,2hαβ and3h0α are as in a pure gravitational case. On the other hand, using the defined Einstein-Maxwell tensor, we give the equations of motion of two charged particles in the 0th order; also, the generalization is given in the case ofn particles.
TL;DR: In this paper, the author presents his impression of the principal landmarks in the development of general relativity during the first 30 years after its founding from his vantage point of the present: it is a personal statement.
Abstract: In this paper the author presents his impression of the principal landmarks in the development of general relativity (exclusive of cosmology) during the first 30 years after its founding from his vantage point of the present: it is a personal statement.
TL;DR: In this article, the Taub plane symmetric static and homogeneous vacuum solutions are matched on a natural hypersurface and the space-times obtained in this way have distribution valued curvature tensors along the joining hypersurfaces.
Abstract: The Taub plane symmetric static and homogeneous vacuum solutions are matched on a natural hypersurface. The space–times obtained in this way have distribution valued curvature tensors along the joining hypersurfaces. Our treatment of this problem follows Taub’s presentation of space–times with distribution valued curvature tensors. We find that the surfaces of the join may be interpreted as thin null pressureless fluid shocks. The nature of these surfaces are further investigated by examining the behavior of geodesics crossing the surfaces.
TL;DR: In this article, a technique using orthonormal tetrads is presented for algebraic manipulation of Einstein's equations by computer and ease of physical interpretation for spherically symmetric case and Birkhoff's theorem is proved in the formalism.
Abstract: A technique is presented using orthonormal tetrads which enables efficient algebraic manipulation of Einstein’s equations by computer and ease of physical interpretation. The results are applied to the spherically symmetric case and Birkhoff’s theorem is proved in the formalism. Several exact solutions such as Tolman’s and Schwarzschild’s are derived, and isotropic expansion of Pefect fluids considered.
TL;DR: In this article, the solution of the system of Maxwell-Einstein equations, which determines the external gravitational and electromagnetic fields of magneto-dipole configurations, has been obtained to a quadratic approximation of magnetic momentum.
Abstract: The solution of the system of Maxwell-Einstein equations, which determines the external gravitational and electromagnetic fields of magneto-dipole configurations, has been obtained to a quadratic approximation of magnetic momentum.
TL;DR: In this paper, a solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field plus pure radiation is obtained, and a particular case of the solution is considered which encompasses many known solutions.
Abstract: A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field plus pure radiation is obtained. The solution is algebraically special. A particular case of the solution is considered which encompasses many known solutions. Among them is a radiating Ruban metric.
01 Jan 1980
TL;DR: In this paper, a tensor force field of Lorentz type and a scalar force field V(xi) were reconstructed from a given metric of a four-dimensional Riemannian space-time and given properties of the motion of test bodies in this space.
Abstract: In a generally relativistic framework, we pose and solve problems of reconstructing a tensor force field of Lorentz type and a scalar force field V(xi) from a given metric of a four-dimensional Riemannian space-time and given properties of the motion of test bodies in this space. We solve the problem of finding the potentials giκ of the gravitational field from known tensor force field Fiκ = Fκi and from given properties of the motion of bodies in the gravitational field which is being sought. The functional arbitrariness in the solution of these inverse problems is established. Applications of the results to the general theory of relativity are demonstrated and reveal new possibilities of experimental determination of physical fields from their effect on test bodies.
01 Jan 1980
TL;DR: In this paper, an outline of general relativity is presented, where the traditional presuppositions concerning the geometry of space and of spacetime are to be abandoned in favor of the view that the geometry is not fixed but is dependent on the distribution of matter.
Abstract: This chapter elaborates an outline of general relativity. A key idea of general relativity is that the traditional presuppositions concerning the geometry of space and of spacetime are to be abandoned in favor of the view that the geometry of spacetime is not fixed but is dependent on the distribution of matter. Just as matter is regarded in Newtonian theory as a source of the gravitational field, so it is treated as a source of the geometric field or, as physicists put it, of the metric field. Apart from any other considerations, the a posteriori and variable character of the geometry suggests the desirability of formulating such a theory in a generally covariant form. It is found that the character of Newtonian space renders the Cartesian coordinate system a particularly suitable device for the labeling of points. The Cartesian vector is an especially useful geometric object for the expression of laws of nature which presuppose a background of Euclidean space.
TL;DR: In this paper, a solution to the equations of the relative dynamics of test bodies in the framework of general relativity is constructed for the case of slowly varying coefficients (when these last depend on the “truncated” proper time on a reference trajectory).
Abstract: A solution to the equations of the relative dynamics of test bodies in the framework of general relativity is constructed for the case of slowly varying coefficients (when these last depend on the “truncated” proper time on a reference trajectory). Nonlinear radial oscillations of a test body in the neighborhood of a point of equilibrium in the Nordstrom space are considered. Some nonlinear effects of stochastic forces in the relative dynamics of test bodies are considered in a space of constant curvature.
TL;DR: In this paper, a static spherically symmetric solution to the combined system of Einstein's equations and the equation of a massive vector field, the cosmological term being taken into account, was found.
Abstract: A static spherically symmetric solution is found to the combined system of Einstein's equations and the equation of a massive vector field, the cosmological term being taken into account. It is shown that such a self-gravitating configuration forms a closed inhomogeneous cosmological model.
01 Dec 1980
TL;DR: In this article, the authors formulated relations governing changes in the field vectors of a discontinuous electromagnetic field within the framework of special relativity theory, and derived a relation describing electrical charge conservation at the discontinuity.
Abstract: Relations governing changes in the field vectors of a discontinuous electromagnetic field are formulated in this paper within the framework of special relativity theory. The treatment emphasizes the physical aspects of the problem and for this reason the medium supporting the propagation of the discontinuity is conveniently assumed to be isotropic but otherwise to have arbitrary properties. Four field discontinuity conditions and a relation describing electrical charge conservation at the discontinuity are presented.