Showing papers on "Gravitation published in 1981"

Theory and Experiment in Gravitational Physics

Abstract: New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been designed to fill a new need for a complete treatment of techniques for analyzing gravitation theory and experience. The Einstein equivalence principle and the foundations of gravitation theory are considered, taking into account the Dicke framework, basic criteria for the viability of a gravitation theory, experimental tests of the Einstein equivalence principle, Schiff's conjecture, and a model theory devised by Lightman and Lee (1973). Gravitation as a geometric phenomenon is considered along with the parametrized post-Newtonian formalism, the classical tests, tests of the strong equivalence principle, gravitational radiation as a tool for testing relativistic gravity, the binary pulsar, and cosmological tests.

Indirect Evidence for Quantum Gravity

Abstract: An experiment gave results inconsistent with the simplest alternative to quantum gravity, the semiclassical Einstein equations. This evidence supports (but does not prove) the hypothesis that a consistent theory of gravity coupled to quantized matter should also have the gravitational field quantized.

Static spherically symmetric scalar fields in general relativity

Abstract: In 1957, Bergmann and Leipnik attempted to find static spherically symmetric solutions of a special form of the field equations of general relativity. They were not able to find explicit expressions for the gravitational potentials, and they did not realize that such expressions could be found by using a different coordinate system. Although Buchdahl developed an elegant procedure for finding, by inspection, the solutions sought by Bergmann and Leipnik, his procedure is severely limited when applied to the spherically symmetric case. Indeed, his procedure fails to identify one whole class of such static solutions. The object of this paper is to show that, under the assumptions of Bergmann and Leipnik, the integration of the field equations is almost trivial, and to identify the missing class of solutions.

Errors in the use of isokinetic dynamometers.

Abstract: The use of constant velocity dynamometers in functional testing and in exercise and therapy programs has been increasing in the past few years. For movements in the horizontal plane there are no gravitational errors. However, in vertical movements the limbs are not only working against the dynamometer but also are either aided or opposed by gravity. Far too often these gravitational forces have not been taken into account, and the error involved can be quite large. 1. A study on four subjects using knee extension (against gravity) and flexion (with gravity) showed the error in mechanical work to vary from 26–43% in extension and from 55–510% in flexion. 2. A relatively simple solution is offered to overcome the problem by compensating for the gravitational errors over the full range of movement. The time course of the error is such as to cause erroneous magnitudes of recorded moments which are a maximum at low level contractions and minimum at high level contractions. 3. The effect of gravitational and other acceleration errors are such as to cause false early peaks in the muscle moment curves resulting in erroneous conclusions about muscle function.

Linkages in general relativity

Abstract: For an asymptotically flat space–time in general relativity there exist certain integrals, called linkages, over cross sections of null infinity, which represent the energy, momentum, or angular momentum of the system. A new formulation of the linkages is introduced and applied. It is shown that there exists a flux, representing the contribution of gravitational and matter radiation to the linkage. A uniqueness conjecture for the linkages is formulated. The ambiguities due to the possible presence of supertranslations in asymptotic rotations are studied using the behavior of the linkages under first‐order perturbations in the metric. While in certain situations these ambiguities disappear in the first‐order treatment, an example is given which suggests that they are an essential feature of general relativity and its asymptotic structure.

Metric-affine variational principles in general relativity II. Relaxation of the Riemannian constraint

Abstract: We continue our investigation of a variational principle for general relativity in which the metric tensor and the (asymmetric) linear connection are varied independently. As in Part I, the matter Lagrangian is minimally coupled to the connection and the gravitational Lagrangian is taken to be the curvature scalar, but we now relax the Riemannian constraint as far as possible—that is, as far as the projective invariance of the assumed gravitational Lagrangian will allow. The outcome of this procedure is a gravitational theory formulated in a volume-preserving space-time (i.e., with torsion and tracefree nonmetricity). The vanishing of the trace of the nonmetricity is due to the remaining vector constraint. We also discuss the physical significance of the relaxation of the Riemannian constraint, the possible relaxation of the vector constraint, the notion of the hypermomentum current, and its possible relation to elementary particle physics.

A gravitational analogue of the Aharonov-Bohm effect

Abstract: It is shown that particles constrained to move in a region where the Riemann tensor vanishes may nonetheless exhibit physical effects arising from nonzero curvature in a region from which they are excluded. This is a gravitational analogue of the Aharonov-Bohm effect.

Spontaneously Generated Gravity

Abstract: We show, following a recent suggestion of Adler, that gravity may arise as a consequence of dynamical symmetry breaking in a scale- and gauge-invariant world. Our calculation is not tied to any specific scheme of dynamical symmetry breaking. A representation for Newton's coupling constant in terms of flat-space quantities is derived. The sign of Newton's coupling constant appears to depend on infrared details of the symmetry-breaking mechanism.

Newtonian gravity measurements impose constraints on unification theories

Abstract: Theories which attempt to unify gravity with the other forces of nature can be coarsely classified according to the mass scale of the new particles they introduce or equivalently the length scale at which new phenomena occur. This mass scale can be expressed as mp(mH/mp)n, where mH is a typical hadron mass and mp is the Planck mass. In most current theories n is 0 or 1. However, in some theories n = 2, which offers the possibility of experimental consequences at kilometre scales. Here using satellite and geophysical data we place constraints on such theories and find that they are not viable unless mH>103 GeV.

Geophysical evidence for non-newtonian gravity

Abstract: Measurements of the variation of gravity with depth in mines and boreholes permit the densities of intervening rock strata to be inferred. In the few cases in which reliable absolute values of density have been independently determined, the calculations can be used to check the value of the newtonian gravitational constant, G. Such large-scale measurements of G are important because the validity of the inverse square law of gravity at short range is being questioned. We have made such a series of measurements and have found four other data sets in the literature that suffice for the estimation of G. We also report here a statistical analysis of 1,100 km2 of overlapping sea floor and sea surface gravity data from the Gulf of Mexico (made available by Exxon). All these estimates of G give values that are higher than the conventional, laboratory-determined one. While the possibilities of systematic errors in these data sets preclude a definite conclusion that Newton's law of gravity fails at short range, the strong circumstantial evidence suggests that well controlled large-scale experiments on the inverse square law are urgently required.

Geon Type Solutions of the Nonlinear {Heisenberg-Klein-Gordon} Equation

Abstract: As a model for a "unitary" field theory of extended particles we consider the nonlinear Klein-Gordon equation---associated with a "squared" Heisenberg-Pauli-Weyl nonlinear spinor equation---coupled to strong gravity. Using a stationary spherical ansatz for the complex scalar field as well as for the background metric generated via Einstein's field equation, we are able to study the effects of the scalar self-interaction as well as of the classical tensor forces. By numerical integration we obtain a continuous spectrum of localized, gravitational solitons resembling the geons previously constructed for the Einstein-Maxwell system by Wheeler. A self-generated curvature potential originating from the curved background partially confines the Schr\"odinger-type wave functions within the "scalar geon." For zero-angular-momentum states and normalized scalar charge the spectrum for the total gravitational energy of these solitons exhibits a branching with respect to the number of nodes appearing in the radial part of the scalar field. Preliminary studies for higher values of the corresponding "principal quantum number" reveal that a kind of fine splitting of the energy levels occurs, which may indicate a rich, particlelike structure of these "quantized geons."

Proposed optical test of metric gravitation theories

Abstract: An optical test of the metric theories of gravitation which employs a ring laser interferometer in an earthbound laboratory is suggested and analyzed. The proposed test would be sensitive to the presence of a preferred frame of the universe and to the geodetic and Lense-Thirring (frame-dragging) rotations of the local inertial frames relative to fixed stars. The frequency difference of the counterpropagating beams in a Sagnac-type experiment is determined within the framework of the parametrized post-Newtonian formalism. The precision with which the various parameters involved in the expression for the frequency difference can be measured is discussed.

Signals and Discontinuities in General Relativistic Nonlinear Electrodynamics

Abstract: A theory of nonlinear electrodynamics in an arbitrary curved space–time is developed from the fundamental action functional for a charged perfect fluid The equations for small perturbations on a fixed nonlinear background are then the initial point for a comprehensive study of the characteristic surfaces The essential distinctions between linear and nonlinear electrodynamic interactions under the influence of gravitation are exhibited Discontinuities in the first derivatives of small perturbations are encountered (1) which may be of general algebraic types for both the electrodynamic and gravitational fields and (2) which may have spacelike propagation A specific set of constraints which would permit the propagation of these extraordinary radiative fronts is presented If the physical organization of a particular problem is presumed to be sufficiently sensitive to the nonlinear nature of the dynamical interactions, then the application of traditional causal concepts may be unreliable when intuition derived from Maxwellian electrodynamics with noninteracting photons is anticipated to provide event horizons

On pseudoparticle solutions in Yang's theory of gravity

Abstract: Within the framework of differential geometry, Yang's parallel-displacement gauge theory is considered with respect to “pure” gravitational fields. In afour-dimensional Riemannian manifold it is shown that thedouble self-dual solutions obey Einstein's vacuum equations with the cosmological term, whereas the doubleanti-self-dual configurations satisfy the Rainich conditions of Wheeler'sgeometrodynamics. Conformal methods reveal that the gravitational analog of the “instanton” or pseudoparticle solution of Yang-Mills theory was already known to Riemann.

A Finslerian extension of general relativity

Abstract: A Finslerian extension of general relativity is examined with particular emphasis on the Finslerian generalization of the equation of motion in a gravitational field. The construction of a gravitational Lagrangian density by substituting the osculating Riemannian metric tensor in the Einstein density is studied. Attention is drawn to an interesting possibility for developing the theory of test bodies against the Finslerian background.

Evolution of small perturbations of isotropic cosmological models with one-loop quantum gravitational corrections

Abstract: Equations have been derived for small perturbations of homogeneous isotropic cosmological models, which take into account in the one-loop approximation the quantum gravitational effects produced as a result of interaction of the quantum fields of matter with the self-consistent gravitational field.

Double Dual Solutions of Generalized Theories of Gravitation

Abstract: Solutions to the Stephenson-Yang theory of gravity and its generalizations are discussed. By considering the inclusion of a cosmological term in the action spherically symmetric static solutions are presented that do not fall into the vacuum Einstein class. A simple double-duality ansatz is responsible for all the solutions that are discussed.

On the gravitational phase transition in the Thomas–Fermi model

Abstract: The first order phase transition in an infinite system of gravitating fermions is analyzed in the canonical ensemble. Except for the question of nonmonotonicity of the mass distribution as a function of the chemical potential, we give an analytical proof for the existence of the phase transition. A single phase region is shown to exist for temperatures high compared to the gravitational energy.

Stability of the Minkowski vacuum in the renormalised semiclassical theory of gravity

Abstract: By making use of the dimensional regularisation and renormalisation group arguments the author shows that the conclusion of Horowitz (1980, 1981) with regard to the instability of flat space-time in the semiclassical theory of gravity also holds for the coupling of a massive real scalar quantum field to the classical gravity gmu nu , but only on condition that the mass of the field is not too large.

Field of a charged particle in Brans-Dicke theory of gravitation

Abstract: Field equations in the Brans-Dicke scalar-tensor theory of gravitation are obtained for a static charged point mass with the aid of a spherically symmetric conformally flat metric. A closed-form exact solution of the field equations is presented, and may be considered as describing the field due to a charged mass point at the origin surrounded by a scalar-tensor field in a conformally flat space.

The Complexion of Forces in an Anisotropic Self-Gravitating System

Abstract: Chandrasekhar and von Neumann developed a completely stochastic formalism to analyze the complexion of forces acting upon a test star situated in an infinite, homogeneous distribution of field stars. This formalism is generalized here to allow for more realistic inhomogeneous and anisotropic systems. It is demonstrated that the forces acting upon a test star decompose ''naturally'' into the incoherent sum of a mean force associated with the average spatial inhomogeneity and a fluctuating force associated with stochastic deviations from these mean conditions. Moreover, as in the special case considered by Chandrasekhar and von Neumann, one can apparently associate the fluctuating forces with the effects of particularly proximate field stars, thereby motivating the ''nearest neighbor'' interpretation first introduced by Chandrasekhar.

Gauge invariance and string interactions in a generalized theory of gravitation

Abstract: The gauge invariance of the Lagrangian in the nonsymmetric extension of general relativity is investigated. The skew parts of the nonsymmetric Hermitian ${g}_{\ensuremath{\mu}\ensuremath{ u}}$, in the weak-field approximation, act as gauge potentials that correspond to the exchange of massless scalar mesons between one-dimensionally extended objects (strings) in spacetime. For open strings a massive vector particle, associated with the torsion, is also exchanged between the end points of the strings.