Showing papers on "Introduction to the mathematics of general relativity published in 1989"
Book•
01 Jan 1989
TL;DR: In this paper, a critical analysis of the general theory of relativity shows that adoption of its concepts leads, first, to abandonment of the conservation laws for energy, momentum, and angular momentum of matter and the gravitational field taken together, and, second, to the abandonment of a classical field of the type of Faraday and Maxwell that possesses and energy-momentum density.
Abstract: A critical analysis of the general theory of relativity shows that adoption of its concepts leads, first, to abandonment of the conservation laws for energy, momentum, and angular momentum of matter and the gravitational field taken together, and, second, to the abandonment of the notion of the gravitational field as a classical field of the type of Faraday and Maxwell that possesses and energy-momentum density. Disagreeing with what has just been said, the authors of Ref. 3 assert that it is possible to give a field formulation of general relativity with "all the necessary attributes of such a theory - and action and equations of motion, energy-momentum tensor of the gravitational field, and conservation laws that reflect the symmetry of the background space-time." The error of this assertion can already be seen from the fact that general relativity in principle does not contain in its field equations a background Minkowski space-time, so that there cannot be any talk of a 10-parameter group of motions of space-time, as a consequence of which conservation laws for matter and the gravitational field cannot exist in general relativity, and it is also impossible to introduce the concept of an energy-momentum tensor of the gravitational field. All this is now obvious and has been considered in detail in our monograph, 1 which also gives references to original studies. In connection with the publication of the paper of Ref. 3, it has become necessary to give a brief exposition of the basic propositions of the relativistic theory of gravitation so that the reader can more readily understand what is under discussion; in the course of the exposition I shall consider, as briefly as possible, the main errors of the authors of Ref. 3. Of course, I do not intend to analyze all their errors contained in Ref. 3, since I see no need for that. The relativistic theory of gravitation (RTG), 1 which
157 citations
TL;DR: In this paper, the integrability conditions for the embedding of a d-dimensional world manifold generated by a (d-1)-dimensional extended object in a flat space are examined.
Abstract: The integrability conditions for the embedding of a d-dimensional world manifold generated by a (d-1)-dimensional extended object in a flat space are examined. It is shown that, for the case of non-minimal world manifolds with d>2, these conditions contain the Einstein and Yang-Mills equations as an independent set of equations, where the first and third fundamental forms act as gravitation and gauge fields respectively, while the second fundamental form plays the role of the source field. Using these results the string model of relativity is shown to be compatible with general relativity.
62 citations
TL;DR: In this paper, a shear-free spherically symmetric cosmological model with heat flow was studied and a general method to generate solutions to the Einstein equations was presented.
Abstract: We study a shear-free spherically symmetric cosmological model with heat flow and present a general method to generate solutions. Using this solution generating scheme we obtain new classes of solutions to the Einstein equations.
37 citations
TL;DR: The variational theory of an ideal fluid with spin is formulated in Riemannian spacetime within the framework of general relativity theory in this article, and applied in cosmology, showing the very weak influence of spin on gravity.
Abstract: The variational theory of an ideal fluid with spin is formulated in Riemannian spacetime within the framework of general relativity theory. It is applied in cosmology, showing the very weak influence of spin on gravity.
28 citations
TL;DR: In this article, the authors analyse exact static solutions of the vacuum Einstein equations obtained from the Appell ring solution to the Laplace equation and show that the solution may be interpreted as the field of a shell of infinite negative total mass bordered by a ring of infinite positive total mass.
Abstract: The authors analyse exact static solutions of the vacuum Einstein equations obtained from the Appell ring solution to the Laplace equation. They first perform a Newtonian analysis and show that the Appell solution may be interpreted as the field of a shell of infinite negative total mass bordered by a ring of infinite positive total mass. This situation can be reproduced in general relativity, but a different interpretation, not requiring the shell as a source, is also possible pasting two spacetimes through the ring. The superposition of a particle with an Appell ring is also considered and in this case the shell interpretation is found to be inconsistent.
28 citations
TL;DR: In this article, a unified description of singular hypersurfaces in general relativity is proposed, and a relation between the singular part of the stress energy tensor and the discontinuities of fundamental forms associated with the hypersurface is established.
Abstract: The author proposes a unified description of arbitrary singular hypersurfaces in general relativity. The author obtains a relation, valid for any hypersurface (spacelike, timelike or null), between the singular part of the stress-energy tensor and the discontinuities of fundamental forms associated with the hypersurface.
26 citations
TL;DR: In this article, a null test of the tracelessness of the Riemann tensor and detection of the Lense-Thirring term in the earth's gravity field are discussed.
21 citations
TL;DR: In this article, a special relativistic energy-momentum tensor was derived from the nonrelativistic Lagrangian for a continuous, elastic medium with finite deformations, and the elastic stress tensor is proportional to the strain gradient of the elastic energy in appropriate coordinates.
20 citations
TL;DR: In this paper, it was shown that no static nonsingular solution of the general relativity equations exists for the gravitational field of an uniformly planar matter distribution under very general assumptions.
Abstract: It is shown that, under very general assumptions, no static nonsingular solution of the general relativity equations exists for the gravitational field of an uniformly planar matter distribution.
17 citations
01 Mar 1989
TL;DR: In this article, it was shown that the principles of the special relativity can be realized not only on the Minkowskian spacetime but also on the spacetimes of non-zero constant curvature.
Abstract: We show that Einstein's principles of the special relativity can be realized not only on the Minkowskian spacetime but also on the spacetimes of non-zero constant curvature.
13 citations
TL;DR: A close study of all known solutions in general relativity which can be written in terms of Painleve transcendental functions reveals that they can all be derived from a solution found by Leaute and Marcilhacy in 1984 as mentioned in this paper.
Abstract: A close study of all known solutions in general relativity which can be written in terms of Painleve transcendental functions reveals that they can all be derived from a solution found by Leaute and Marcilhacy in 1984. In the course of this analysis a new solution of the Einstein-Maxwell equations was found, generalising some well known metrics. Also the complex transformations relating cylindrically symmetric and stationary axisymmetric solutions were fully exploited to derive previously unidentified metrics.
TL;DR: In this article, the complete set of solutions of the five-dimensional vacuum Einstein equations in Kaluza-Klein theory with energy-momentum tensor equal to zero was obtained.
Abstract: In a recent paper Ross obtained the five-dimensional vacuum Einstein equations in Kaluza-Klein theory with energy-momentum tensor equal to zero and solved the equations for a particular case. Here we obtain the complete set of solutions of these equations.
01 Nov 1989
TL;DR: In this paper, an exact solution of the Einstein equations for a static, planar domain wall with finite thickness is presented, where the density and pressure distribution are symmetric about the central plane of the wall whereas the space-time metric and therefore also the gravitational field experienced by a test particle is asymmetric.
Abstract: An exact solution of the Einstein equations for a static, planar domain wall with finite thickness is presented. At infinity, density and pressure vanish and the space-time tends to the Minkowski vacuum on one side of the wall and to the Taub vacuum on the other side. A surprising feature of this solution is that the density and pressure distribution are symmetric about the central plane of the wall whereas the space-time metric and therefore also the gravitational field experienced by a test particle is asymmetric.
TL;DR: In this paper, a method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory.
Abstract: A method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory. The analogue of the Kerr solution in general projective relativity has been obtained as an example. Finally, a relation between the stationary and static axially symmetric vacuum fields in general projective relativity has been derived.
TL;DR: In this paper, the results predicted by Newtonian gravity and general relativity are compared regarding the field produced by an infinite gauge string with constant density λ. The existence of the usual Newtonian limit is discussed in this case.
Abstract: The results predicted by Newtonian gravity and general relativity are compared regarding the field produced by an infinite gauge string with constant density λ. A simple gedankenexperiment is suggested to stress the remarkable differences between these two theories. The existence of the usual Newtonian limit is discussed in this case.
Dissertation•
01 Jan 1989
TL;DR: Bini et al. as discussed by the authors derived a compact analytical parametric approximate solution of Padé type which gives density curves and stellar radii in good accordance with already existing numerical results.
Abstract: The “effective geometry” formalism is used to study the perturbations of a white dwarf described as a self-gravitating fermion gas with a completely degenerate relativistic equation of state of barotropic type. The quantum nature of the system causes an absence of homological properties manifested instead by batropic stars and requires a parametric study of the solutions both at numerical and analytical level. We have explicitly derived a compact analytical parametric approximate solution of Padé type which gives density curves and stellar radii in good accordance with already existing numerical results. After validation of this new type of approximate solutions, we use them to construct the effective acoustic metric governing perturbations of any type following Chebsch’s formalism. Even in this quantum and relativistic case the stellar surface exhibits a curvature singularity due to the vanishing of density, as already evidenced in past studies on non relativistic and non quantum self-gravitating polytropic star. The equations of the theory are finally numerically integrated, in the simpler case of irrotational spherical pulsating perturbations including the effect of back-reaction, in order to have a dynamical picture of the process occurring in the acoustic metric. 10. Bini D., de Felice F., Geralico A., Accelerated orbits in black hole fields: the static case Classical and Quantum Gravity, vol. 28 225012, 2011. Abstract We study non-geodesic orbits of test particles endowed with a structure, assuming the Schwarzschild spacetime as background. We develop a formalism which allows one to recognize the geometrical characterization of those orbits in terms of their Frenet-Serret parameters and apply it to explicit cases as those of spatially circular orbits which witness the equilibrium under conflicting types of interactions. In our general analysis we solve the equations of motion offering a detailed picture of the dynamics having in mind a check with a possible astronomical set up. We focus on certain ambiguities which plague the interpretation of the measurements preventing one from identifying the particular structure carried by the particle. 11. Bini D., Geralico A., Jantzen R.T., Semeřák O.,
TL;DR: In this article, it was shown that apparent velocities of distant objects may exceed 2c without implying physical velocity greater than c in standard cosmological models. And the contribution due to this effect in measurements of distant superluminal expansions is calculated.
Abstract: The problem of measuring the velocity of separation of distant objects is considered. It is shown that, in the framework of general relativity, apparent velocities of separation may exceed 2c without implying physical velocities greater than c in standard cosmological models. The contribution due to this effect in measurements of distant superluminal expansions is calculated.
TL;DR: In this paper, the Ricci tensor is derived from a four-energy-space whose coordinates are composed as follows: (i) the internal energy of the body (it is involved as an unknown function of the rest-energy and the kinetic energy) and (ii) the coordinates e1, e2, e3 relate to the presence of gravitational, electromagnetic, and thermal energy at the location of a body respectively.
Abstract: In this Letter we propose to consider the ‘four-energy-space’ whose ‘coordinates’ are composed as follows: (i) the ‘coordinate’ e0 refers to the internal energy of the body (it is involved as an unknown function of the rest-energy and the kinetic energy of the body), and (ii) the ‘coordinates’ e1, e2, e3 relate to the presence of gravitational, electromagnetic, and thermal energy at the location of the body respectively. We involve yet the proper energy interval de2 by analogy to the four-interval ds2 in general relativity. From such ‘metric field’ we calculate the ‘Ricci tensor’ in the simplest case. In addition, we require its form to be the same one as that considered by Schwarzschild. Comparing both solutions we obtain Einstein's relationE=mc2.
TL;DR: In this article, the precessional frequency of a gyroscope in a reference frame that orbits about a gravitational body is compared between Einstein's tensor formulation of general relativity and the author's quaternion generalization, obtained from a factorization of the tensor form.
Abstract: The precessional frequency of a gyroscope in a reference frame that orbits about a gravitational body is compared between Einstein's tensor formulation of general relativity and the author's quaternion generalization—obtained from a factorization of the tensor form. The difference in predictions then suggests an experiment that could choose which of these formulations of general relativity is more valid in the analysis of gyroscopic motion.
TL;DR: In this paper, the general solution for a static sphere filled with a perfect fluid in the radiative case (µ = 3p) was given for the case of 3p.
Abstract: We find the general solution for a static sphere filled with a perfect fluid in the radiative case (µ = 3p).
01 Mar 1989
TL;DR: In this paper, a new Hamiltonian formulation of weak-field general relativity, based on canonical variables completely analogous to the electric and magnetic field strengths of Maxwell theory, was presented.
Abstract: Presents a new Hamiltonian formulation of weak-field general relativity, based on canonical variables completely analogous to the electric and magnetic field strengths of Maxwell theory. This formulation displays with particular clarity and duality invariance of weak-field general relativity. The author computes the generator of these duality symmetries, and thereby arrives at a new conserved quantity associated with weak gravitational fields.
TL;DR: In this article, it was proved that a class of static solutions of a self-consistent system of EKG equations dependent on one arbitrary function is set in correspondence with a static solution of the Einstein equations with any given energy-momentum tensor Tij.
Abstract: A theorem is proved according to which a class of static solutions of a self-consistent system of Einstein-Klein-Gordon equations dependent on one arbitrary function is set in correspondence with a static solution of the Einstein equations with any given energy-momentum tensor Tij. Two particular cases are examined as an illustration of this theorem. Methods of constructing the static solutions of a system of Einstein-Klein-Gordon equations with an ideal fluid energy-momentum tensor and a massive scalar field are indicated therein.
TL;DR: In the theory of general relativity, it is well known that the integrability conditions for Einstein's field equations are the conservation equations as mentioned in this paper, which ensures the consistency of the field equations and underlies the initial value approach to their solution.
Abstract: In the theory of general relativity, it is well known that the integrability conditions for Einstein's field equations are the conservation equations. The latter guarantee that if the constraint equations Goa = kToa hold on an initial surface, and if Gav = kTav at all times, then the constraint equations will hold at all earlier and later times. This ensures the consistency of the field equations and underlies the initial value approach to their solution. We investigate the corresponding result in the scale co-variant theory of gravitation.
TL;DR: The solitary wave solution published by Burt (see ibid., vol.6, p.611, 1989) does not satisfy the Einstein vacuum equations; when corrected, it is flat spacetime as discussed by the authors.
Abstract: The solitary wave solution published by Burt (see ibid., vol.6, p.611, 1989) does not satisfy the Einstein vacuum equations; when corrected, it is flat spacetime.