Showing papers in "General Relativity and Gravitation in 1980"

Exact spatially homogeneous cosmologies

Abstract: We consider perfect fluid spatially homogeneous cosmological models. Starting with a new exact solution of Blanchi type VIII, we study generalizations which lead to new classes of exact solutions. These new solutions are discussed and classified in several ways. In the original type VIII solution, the ratio of matter shear to expansion is constant, and we present a theorem which delimits those space-times for which this condition holds.

A review of the geometrical equivalence of metrics in general relativity

Abstract: We review the solution to the equivalence problem in general relativity given by Cartan and Brans and present a practically useful method to obtain a coordinate-invariant description of a geometry. The method, which can be seen as a generalized Petrov classification, automatically gives the dimensions of the isometry group and its isotropy subgroup. Finally, we illustrate the method using the Schwarzschild solution as a very simple example.

Null hypersurface initial data for classical fields of arbitrary spin and for general relativity

Abstract: A form of initial value problem is considered in which the initial hypersurface is not spacelike but null. This approach has the striking advantage over the more usual Cauchy problem that all constraints (initial data equations) are eliminated from the theory, for a wide class of interacting fields in special relativity and also for general relativity. The theory is most naturally described in terms of the two-component spinor calculus, for which an elementary introduction is given here. A general scheme for interacting fields, which holds both in special and general relativity, is presented which describes all fields in terms of sets of irreducible spinors. The concept of an exact set of such spinors is introduced and it is shown that this concept is the appropriate one for an initial value problem on a null cone without constraints. The initial data can be expressed in the form of a complex number, called a null datum, defined at each point of the null cone, one corresponding to each spinor. There is the curious feature of these null data that apparently it is sufficient here, to have onehalf as much information per point as in the corresponding Cauchy problem. The classical Maxwell-Dirac theory and the Einstein-Maxwell theory are two examples that can be put into the form of exact sets. The Einstein empty-space equations are also of particular note, and in this case the null datum describes essentially the intrinsic geometry of the null cone. The argument given here as applied to a general exact set is incomplete in two important respects. Firstly it depends on the null data being analytic, and secondly the initial hypersurface must be a cone. However, both these restrictions are removed in the case of certain elementary fields called basic free fields, examples of which are the Weyl neutrino field, the free Maxwell field, and the linearized gravitational field. For these cases a simple explicit formula is introduced which expresses the field at any point in terms of the null datum, as an integral taken over the intersection of the initial null hypersurface with the null cone of the point.

The stationary gravitational field near spatial infinity.

Abstract: Any stationary, asymptotically flat solution to Einstein's equation is shown to asymptotically approach the Kerr solution in a precise sense. As an application of this result we prove a technical lemma on the existence of harmonic coordinates near infinity.

Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part I. First post-Newtonian equations

Abstract: The iteration procedure of Anderson and DeCanio (1975) for obtaining hydrodynamic equations in the slow-motion approximation to general relativity is modified at each iteration step. These improvements keep all expressions needed for the 2 1/2 post-Newtonian approximation (PNA) manifestly finite, but fail to prevent some divergent terms in the third and higher PNAs. In this Part I, the improvements to the iteration scheme are outlined, and the calculation is completed through the second iteration, yielding Newtonian-like hydrodynamic equations in the first PNA. Paper II will complete the calculation through the 2 1/2 PNA, allowing the calculation of the gravitational radiation reaction force, and making explicit the source of the divergences which occur in the higher PNAs.

A Newman-Penrose-Type Formalism for Space-Times with Torsion

Abstract: The familiar Newman-Penrose formalism, in which the curvature of space-time is represented in terms of spin coefficients, is here extended to include the possibility of an asymmetric connection. It is hoped that this approach will be useful in dealing with certain problems in Einstein-Cartan theory, and also in other theories of gravitation that include torsion.

Plane waves in gauge theories of gravitation

Abstract: Exact solutions representing pp waves are found in a wide class of gauge theories of gravitation. Algebraic and symmetry properties are investigated and a special case of plane waves is discussed.

Measurement of the laboratory's absolute velocity

Abstract: The report is given on a local measurement of the absolute velocity of a laboratory. This is the resultant velocity due to all types of motion in which the laboratory takes part (about the Earth's axis, about the Sun, about the galactic center, about the center of the cluster of galaxies).

Post-Newtonian Generation of Gravitational Waves in a Theory of Gravity with Torsion

Abstract: We adapt the post-Newtonian gravitational-radiation methods developed within general relativity by Epstein and Wagoner to the gravitation theory with torsion, recently proposed by Hehl et al., and show that the two theories predict in this approximation the same gravitational radiation losses. Since they agree also on the first post-Newtonian level, they are at the present time-observationally-indistinguishable.

A comparative review of certain gauge theories of the gravitational field

Abstract: A general formal analysis is made trying to obtain a better understanding and greater synthesis of the mathematical structure of the gravitational field's gauge theories. Under this approach, some misstatements appearing in current theories are detected. A theory based on the direct product groupsT(4)×GL(4) andT(4)×O(1, 3) is suggested (in contrast to those using the Poincare group, semidirect product). Such a theory corrects the justmentioned deficiencies possessing the attributes of the preceding ones.

A geometrical approach to external potential problems in quantum field theory

Abstract: A geometrical framework for obtaining the5-operator description of quantum fields interacting with external potentials (including gravitation) is presented. An approach to quantum theory of mutually interacting Bose fields is suggested.

Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part II. Radiation reaction and higher-order divergent terms

Abstract: We continue the calculation begun in Part I of hydrodynamic equations in general relativity according to Fillers' suggested modification of the iteration scheme of Anderson and DeCanio. We carry out this calculation far enough into the third and fourth iterations to obtain two principal results: First, we obtain a Newtonian-like force equation which is manifestly finite through the leading term of the radiation-reaction force (the 21/2 post-Newtonian approximation). Going beyond the 21/2 PNA, we find, and explicitly present, divergent terms which cannot be canceled out within this scheme. The implications of these results are discussed.

Bimetric general relativity and cosmology

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.

Equilibrium of charged dust in general relativity

Abstract: Equilibrium of charged dust is studied in both the classical and relativistic theories. It is already known that the configuration of the dust is arbitrary if the ratio of the charge to mass densities,σ/ρ, is everywhere ± 1 (in relativistic units). I show here that there are equilibrium configurations for certain other valuesσ/ρ, including nonuniform ones. The solutions in these cases are arbitrary up to the choice of a harmonic function and a function of the electrostatic potential. In general they contain singularities.

The structure of tetrad formalisms in general relativity: The general case

Abstract: The sets of equations that form the basis for the tetrad formalism approach in general relativity contain considerable redundancy. Papapetrou has determined this redundancy explicitly in the form of three sets of identities and employed these in investigations of the Newman-Penrose tetrad formalism. In this paper Papapetrou's work is reviewed and some of his results that do not seem to be well known are emphasized, along with some general implications. The main new result that is established concerns the Geroch-Held-Penrose formulation of the tetrad formalism. When the sets of equations that are usually used in this formulation are considered in the light of Papapetrou's identities, it is found that certain formal simplifications can be made and that the Geroch-Held-Penrose formulation can be presented more concisely. It is emphasized that the results in this paper apply in the most general case only. Any special cases (e.g., simplified tetrad and/or Riemann tensor) need to be considered separately.

The Robertson-Walker metrics expressible in static form

Abstract: It is shown that there are six, and only six, Robertson-Walker metrics which can be expressed in static form. They are precisely those Robertson-Walker metrics whosespacetime curvature is constant. The coordinate transformations which transform these metrics into their static form are also given. An error in Robertson and Noonan's Book [1] is pointed out and corrected.

Static charged gas spheres in general relativity

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.

General solutions for a static isotropic metric in the Brans-Dicke gravitational theory

Abstract: The complete set of vacuum solutions for the metric tensor of a static spherically symmetric field is given, some of these solutions showing the remarkable feature of not agreeing-even in first order-with the classically well-known weak-field solutions of the Brans-Dicke (B.D.) equations. The existence of a particular two-parameter family of solutions raises severe doubts about the so-called Machian aspect of B.D. theory.

A global analysis approach to the general relativistic fluid ball problem

Abstract: That a self-gravitating perfect fluid in empty space has a spherical equilibrium configuration if it is static-i.e., nonrotating-is considered physically evident, but has not yet been rigorously derived from Einstein's field equations together with suitable asymptotic conditions. In this paper the global analysis techniques developed recently mainly by Fischer, Marsden, and Cantor are used to derive the result that if a family of static perfect fluid solutions with fixed total gravitational massm and fixed equation of stateϱ(p) satisfying 0 ⩽p ⩽ ϱ and 0 ⩽dϱ/dp < ∞ depends differentiably on a parameter and contains the spherically symmetric solution then it must consist of solutions diffeomorphic to the spherically symmetric one.

Towards a unified gauge theory of gravitational and strong interactions

Abstract: We study the space-time properties of leptons and hadrons and find it necessary to extend general relativity to the gauge theory based on the four-dimensional affine group. This group translates and deforms the tetrads of the locally Minkowskian space-time. Its conserved currents, momentum, and hypermomentum, act as sources in the two field equations of gravity. A Lagrangian quadratic in torsion and curvature allows for the propagation of two independent gauge fields: translationale-gravity mediated by the tetrad coefficients, and deformational Γ-gravity mediated by the connection coefficients. For macroscopic mattere-gravity coincides with general relativity up to the post-Newtonian approximation of fourth order. For microscopic matter Γ-gravity represents a strong Yang-Mills type interaction. In the linear approximation, for a static source, a confinement potential is found.

A remark on a cylindrically symmetric rotating metric

Abstract: It is shown that the stationary cylindrically symmetric solution of Einstein's field equations as given recently by Vishveshwara and Hoenselaers [1] is identical with the well-known Godel solution.

Kerr-Schild-Vaidya fields with axial symmetry

Abstract: This paper contains the Kerr-Schild-Vaidya fields with axial symmetry (all metric functions independent of Vaidya's coordinateβ) in closed form. The general problem of Kerr-Schild pure radiation fields without any symmetry can be reduced to a single partial differential equation by means of Kerr's theorem.

Notes on recent U 4 theories of gravitation.

Abstract: Some of the proposed Lagrangians and their corresponding field equations for a gravitational theory based on a Riemann-Cartan space with metric-compatible connection (U 4, theory) are compared and a new one is suggested. This Lagiangian, and that of P. von der Heyde and F. W. Hehl et al. are examined applying the “Gordon-decomposition” argument. Finally, Einstein's field equations with cosmological term are shown to be included in some sense, but the cosmological constant λ naturally has microphysical origin. To simplify notation, Cartan's calculus is used throughout.

Gravitational fields, spinor fields, and groups of motions

Abstract: The problem of finding the most general spinor field possessing the same symmetry as a given gravitational field is solved for every group of motions. Its connection with the resolution of Einstein-Dirac equations is briefly pointed out.

Gravitational energy-momentum: The Einstein pseudotensor reexamined

Abstract: By using a suitable two-point scalar field, a covariant formulation of the Einstein pseudotensor is given. A unique choice of scalar field is made possible by examining the role of linear and angular momentum in their correct geometric context. It is shown that, contrary to many text-book statements, linear momentum is not generated by infinitesimal coordinate transformations on space-time. Use is made of the nonintersecting lifted geodesies on the tangent bundle,TM, to space-time, to define a globally regular three-dimensional Lagrangian submanifold ofTM, relative to an observer at some pointz in space-time. By integrating over this submanifold rather than a necessarily singular spacelike hypersurface, gravitational linear and angular momentum, relative toz, are defined, and shown to have sensible physical properties.

Shearfree congruences of null geodesies and killing tensors

Abstract: In this communication, the mutual connections between quantities that are generalizations of the notion of a Killing vector field are investigated. A classification of these quantities in terms of a complex vector fieldαa is given. A common feature of all these quantities is that they imply the existence of a pair of shearfree geodetic null congruences. There are no explicit restrictions posed on the Ricci tensor.

On a coordinate-invariant description of Riemannian manifolds

Abstract: A coordinate-invariant description of a Riemannian manifold is known to be furnished by the curvature tensor and a finite number of its covariant derivatives relative to a field of orthogonal frames. These tensors are closer to measurements than the metrical tensor is. The present article discusses this description's usefulness in general relativity and the redundancy among the curvature tensor and its derivatives.

Palatini Variation of a Generalized Einstein Lagrangian

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.

Gravitational collapse with charge and small asymmetries. II. Interacting electromagnetic and gravitational perturbations

Abstract: Paper I analyzed the evolution of nonspherical scalar-field perturbations of an electrically charged, collapsing star; this paper treats coupled electromagnetic and gravitational perturbations. It employs the results of recent detailed work in which coupled perturbations were studied in a gauge-invariant manner by using the Hamiltonian (Moncrief s) approach and the Newman-Penrose formalism, and the relations between the fundamental quantities of these two methods were obtained.

Constructive approach to supergravity

Abstract: Starting from a first-order formulation of the Lagrangian of noninteracting massless helicity-2 and helicity-3/2 particles, we deduce global supersymmetry transformations. Then, allowing the supersymmetry transformations to become local requires, if supersymmetry is to be maintained, the introduction of a unique primitive interaction through the “gravitino” stress tensor and torsion. Finally, the imposition of exact supersymmetry invariance leads by a short, constructive process to full supergravity and the complete form of the supersymmetry transformations. In particular, no explicit use is made of general coordinate invariance, and the self-consistency of the gravitational coupling emerges from the local supersymmetry requirement alone.