Showing papers on "Introduction to the mathematics of general relativity published in 1987"
TL;DR: In this paper, it was shown that an analog of Birkhoff's theorem of general relativity exists in the scale-covariant theory of gravitation when the gauge function which occurs in the theory is independent of time.
Abstract: It is shown that an analog of Birkhoff's theorem of general relativity exists in the scale-covariant theory of gravitation when the gauge function which occurs in the theory is independent of time.
45 citations
TL;DR: The geometric optics approximation in general relativity is critically examined in this paper, where the well-known result that rays of radiation follow null geodesics of the gravitational field is shown to be valid only in the limit of vanishing wavelength.
40 citations
TL;DR: In this paper, a theory for gravity in which the linear connections are assumed to be arbitrary, except that they are restricted to satisfy the metric condition ∇μgλν=0.
Abstract: We study a theory for gravity in which the linear connections are assumed to be arbitrary, except that they are restricted to satisfy the metric condition ∇μgλν=0. A scalar field is added to the theory, and a conformally invariant action integral, linear in the curvature tensor, is defined. The linear connections emerging from the variational principle contain torsion that is related to a propagating spin-1 vector field, identified as the electromagnetic gauge potential. We obtain a set of conformally invariant equations for the metric field, and conclude that Einstein's equations arise from a particular choice of gauge. Finally, spin-1/2 fields are introduced by means of the vierbein formalism, and the qualitative features of the theory are maintained.
39 citations
32 citations
TL;DR: In this article, it was shown that space-times admitting more than one independent Killing-Yano tensor belong to a small collection of highly idealised space times, and a new characterization of Robertson-Walker space times arises as a corollary of the main theorem.
Abstract: It is shown that space-times admitting more than one independent Killing-Yano tensor belong to a small collection of highly idealised space-times. A new characterization of Robertson-Walker space-times arises as a corollary of the main theorem.
28 citations
TL;DR: In this paper, the authors considered metric gab with conformally flat 3-space and the Ricci tensor has at most two different eigenvalues and the 4-velocity is an eigenvector of this tensor.
Abstract: Metrics of the form ds2=N2(x1, xn)(dx1)2+gab(xn) xadxb are considered which are subject to the conditions that the time-like 3-space (with metric gab) is conformally flat, that its Ricci tensor has at most two different eigenvalues and that the 4-velocity is an eigenvector of this Ricci tensor. The perfect fluid (or dust) solutions are necessarily of Petrov type D or O, and in the general case they do not admit a Killing vector. All rotating solutions are given explicitly. The non-rotating solutions are either conformally flat (and thus known) or (if of type D) contained in the class of solutions investigated, for example, by Szekeres (1975), Tomimura (1977), and Szafron and Wainwright (1977).
26 citations
01 Jan 1987
25 citations
TL;DR: In this article, a slice theorem for the action of Diff on the space of solutions of the Einstein equations in the asymptotically flat case is proved, which is the case in which we are interested in this paper.
23 citations
TL;DR: The structure of the Poisson-brackets algebra of constraints of general relativity is reexamined using the recently introduced spinorial variables to provide a point of departure for a nonperturbative quantization scheme for general relativity.
Abstract: The structure of the Poisson-brackets algebra of constraints of general relativity is reexamined using the recently introduced spinorial variables. Three different combinations of constraints are analyzed and their relative merits are discussed. In each case we construct the corresponding expression of the Becchi-Rouet-Stora-Tyutin charge. These expressions provide a point of departure for a nonperturbative quantization scheme for general relativity.
22 citations
TL;DR: In this paper, it was proved that a Lagrangian field theory based on a linear connection in space-time is equivalent to Einstein's general relativity interacting with additional matter fields.
Abstract: It is proved that a Lagrangian field theory based on a linear connection in space-time is equivalent to Einstein's general relativity interacting with additional matter fields.
20 citations
TL;DR: In this article, four boundary conditions allowing an unambiguous definition of angular momentum of a Cauchy data set in general relativity are presented, and four sets of boundary conditions for general relativity.
Abstract: Four sets of boundary conditions allowing an unambiguous definition of angular momentum of a Cauchy data set in general relativity are presented.
TL;DR: In this article, a pseudotensor-based conserved quantity for isolated systems in general relativity, in a way which allows an arbitrary asymptotic behavior of the coordinate system used, is presented.
Abstract: We show how to calculate pseudotensor-based conserved quantities for isolated systems in general relativity, in a way which allows an arbitrary asymptotic behavior of the coordinate system used. Our method is a generalization of that given by Persides [1], and allows the asymptotic evaluation of energy, momentum, and angular momentum in any coordinate system. We carry out the calculation for the Schutz-Sorkin gravitational Noether operator, which is a pseudotensorial operator on vector fields that reduces to the familiar pseudotensors for particular choices of the fields.
TL;DR: The main idea is to include the spin as a thermodynamic variable in the theory to derive the equations of motion for a spinning fluid in the Einstein-Cartan theory.
Abstract: Methods used earlier to derive the equations of motion for a spinning fluid in the Einstein-Cartan theory are specialized to the case of general relativity. The main idea is to include the spin as a thermodynamic variable in the theory.
TL;DR: The case of a domain wall of finite thickness is examined and it is found that the equations of general relativity show that such walls cannot be in static equilibrium, and further even nonequilibrium walls can be consistent with Einstein's equations only under very special circumstances.
Abstract: The case of a domain wall of finite thickness is examined by use of two different expressions for the energy-stress tensor of domain walls but no symmetry condition. It is found that the equations of general relativity show that such walls cannot be in static equilibrium, and further even nonequilibrium walls can be consistent with Einstein's equations only under very special circumstances.
TL;DR: In this paper, the construction of real solutions of Einstein's vacuum field equations from certain half flat holomorphic metrics is described. But the authors do not consider the problem of finding the real solutions from the holomorphic metric.
Abstract: The construction of some real solutions of Einstein's vacuum field equations from certain half flat holomorphic metrics is described
01 Sep 1987
TL;DR: In this paper, the Lagrangian formulation of compact binary systems is considered in post-Newtonian approximations of general relativity, and the results concerning the equations of motion and associated Lagrangians are reported.
Abstract: We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third post-Newtonian order (∼ 1/c beyond the Newtonian acceleration). These equations are necessary when constructing the theoretical templates for searching and analyzing the gravitational-wave signals from inspiralling compact binaries in VIRGO-type experiments. c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS general relativity/equations of motion Sur le problème des deux corps en relativité générale Résumé. Nous considérons le problème des deux corps dans l’approximation post-newtonienne de la relativité générale. Nous présentons les résultats récents concernant les équations du mouvement, et la formulation lagrangienne associée, de systèmes binaires d’objets compacts, au troisième ordre post-newtonien (∼ 1/c après l’accélération newtonienne). Ces équations sont utilisées dans la construction des filtres théoriques pour la détection et l’analyse des signaux d’ondes gravitationnelles provenant des binaires compactes spiralantes dans les expériences du type VIRGO. c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS relativité générale/équations du mouvement Note présentée par First name NAME S1296-2147(01)01171-?/FLA c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés. 1
TL;DR: In this article, it was shown that a static solution of the Einstein equations inside an infinite plate of an ideal liquid with continuous metric coefficients and their first derivatives cannot have a plane of mirror symmetry.
Abstract: It is shown that a static solution of the Einstein equations inside an infinite plate of an ideal liquid with continuous metric coefficients and their first derivatives cannot have a plane of mirror symmetry. As a consequence, the boundaries of the plate are joined with qualitatively different vacuum solutions on both sides of the plate.
TL;DR: In this article, the self-creation theory of gravitation is solved for the Robertson-Walker space-time, by using a correspondence to known solutions of general relativity, by solving the vacuum field equations of the self creation theory.
Abstract: The vacuum field equations of the self-creation theory of gravitation are solved for the Robertson-Walker space-time, by using a correspondence to known solutions of general relativity.
TL;DR: In this article, a new system of linear equations whose solution describes a hierarchy of determinant solutions to the stationary axially symmetric Einstein equations in general relativity was considered, and the solution described the hierarchy of solutions to all the determinant determinant equations.
Abstract: This paper considers a new system of linear equations whose solution describes a hierarchy of determinant solutions to the stationary axially symmetric Einstein equations in general relativity.
TL;DR: In this paper, the authors define the quality factor of arbitrary metrics to be used as a measure of their approximation to a solution of Einstein's vacuum equations, and define a quality factor for any metric.
Abstract: I define the quality factor of arbitrary metrics to be used as a measure of their approximation to a solution of Einstein's vacuum equations.
TL;DR: In this article, a pseudotensor-based method for calculating conserved quantities for isolated systems in general relativity, independently of the asymptotic behaviour of the coordinate system used, is given.
Abstract: A method for calculating pseudotensor-based conserved quantities for isolated systems in general relativity, independently of the asymptotic behaviour of the coordinate system used, is given. This allows the evaluation of concepts like energy, momentum and angular momentum in any coordinate system. The calculation is carried out for the Schutz-Sorkin gravitational Noether operator, a pseudotensorial vector operator which reduces to the familiar pseudotensors for particular choices of the vector fields; it is illustrated for the Kerr metric using various fields and coordinates. The authors use this to prove a theorem of extremality of angular momentum for vacuum solutions of Einstein's equations, showing that any two of the following imply the third: (i) the metric is axisymmetric; (ii) Einstein's field equations are satisfied; (iii) the total angular momentum is an extremum against all perturbations satisfying a mild (and most reasonable) restriction. This theorem, valid for stationary and non-stationary metrics, is generalised to include matter fields, and, in particular, perfect fluids. A related theorem for extremising the angular momentum flux across a timelike hypersurface is also proved. This theorem provides an alternative way to solve the field equations for axisymmetric gravitational collapse.
TL;DR: In this paper, the PNA program for the ECSK theory is complete and the general post-Newtonian equations of motion for the source are derived for the case of an ideal fluid with spin, and the main results are compared with the corresponding ones of general relativity.
Abstract: We complete the PNA program for the ECSK theory. We find the general post-Newtonian equations of motion for the source. The different components of the complete affine connection, the torsion, and the energy-momentum tensor, as well as the conservation theorems of the theory, are developed for the case of an ideal fluid with spin in order to find the post-Newtonian trajectories of test particles exterior to the sources distribution. The main results are compared with the corresponding ones of general relativity.
TL;DR: The Hermitian theory of relativity is regarded as the theory of a field endowed with two sources: electromagnetic and color four-currents as discussed by the authors, and the equilibrium conditions for charges and currents are apparent in exact solutions of the field equations.
Abstract: The equilibrium conditions for charges and currents, apparent in exact solutions of the field equations, lead one to regard the Hermitian theory of relativity as the theory of a field endowed with two sources: electromagnetic and color four-currents.
TL;DR: In this paper, a generalization of general relativity to non-abelian geometries is proposed, where the diffeomorphisms of GRS may be regarded as transformations that preserve the abelian group structure of the translation operators.
Book•
01 Jun 1987
TL;DR: In this article, the main thread of development from Newton's laws to Einstein's theory of relativity is introduced, and the authors try to clarify the most fundamental ideas and concepts, which is difficult to do in a book of this size.
Abstract: This book aims to introduce to the reader the main thread of development from Newton's laws to Einstein's theory of relativity. Limited by its scope and avoiding as much as possible the use of mathematical apparatus, the authors try to clarify the most fundamental ideas and concepts. Both authors hold a deep reverence for Galileo and Einstein, and this book is dedicated to these two great scientists.
01 Mar 1987
TL;DR: The general projective relativity is based on the De Sitter universe, and the local curvature is described by the generalized Einstein equations as mentioned in this paper, and the equations of the scalar-tensor gravitational field, which ate similar to the Brans-Dicke equations.
Abstract: The general projective relativity is based on the De Sitter universe, and the local curvature is described by the generalized Einstein equations. As a particular case, we obtain the equations of the scalar-tensor gravitational field, which ate similar to the Brans-Dicke equations.
TL;DR: In this article, the authors considered an asymptotically flat and empty space-time generated by a bounded source of perfect fluid and derived an expression for the dominant term of gαβ,0 in the radiation zone in terms of the quadrupole moment of the source.
Abstract: We consider an asymptotically flat and empty space-time generated by a bounded source of perfect fluid. The vanishing of the conformal Weyl tensor onI+ and of the Ricci tensor nearI+ are used to simplify the expression obtained in the previous paper for the coefficient ofr− of the metric tensor after an expansion in powers ofc−1. The result is a very simple expression for the dominant term ofgαβ,0 in the radiation zone in terms of the quadrupole moment of the source. Using this expression and an invariant definition of the total energy, we calculate in the framework of full general relativity the radiated energy per unit time and prove that the first term is identical with the quadrupole radiation as given by the linearized version of general relativity.
TL;DR: In the context of the general theory of relativity, the system of Euler's equations is obtained from the variational equation under the assumption that the Lagrangian of the material depends on supplementary thermodynamic parameters, and when possible irreversible processes are taken into account.
TL;DR: The theory of GR still appears to be incomplete in the following ways as discussed by the authors, despite its beauty and grandeur, despite its ability to accommodate the asymmetric total energy momentum tensor whose asymmetry has been shown to exist in the presence of electromagnetism.
Abstract: Despite its beauty and grandeur the theory of GR still appears to be incomplete in the following ways:
(1)
It cannot accommodate the asymmetric total energy momentum tensor whose asymmetry has been shown to exist in the presence of electromagnetism.
(2)
The law of angular momentum balance as an exact equation is not an automatic consequence of the field equations as is the case with the law of linear momentum balance.
(3)
The four degrees of arbitrariness left by the contracted second Bianchi identity makes a unique solution of the field equations unattainable without extra (unphysical) postulates.