Showing papers on "Gravitational field published in 1976"

Vacuum expectation value of the stress tensor in an arbitrary curved background: The covariant point-separation method

Abstract: A method known as covariant geodesic point separation is developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field. The vacuum expectation value will diverge because the stress-tensor operator is constructed from products of field operators evaluated at the same space-time point. To remedy this problem, one of the field operators is taken to a nearby point. The resultant vacuum expectation value is finite and may be expressed in terms of the Hadamard elementary function. This function is calculated using a curved-space generalization of Schwinger's proper-time method for calculating the Feynman Green's function. The expression for the Hadamard function is written in terms of the biscalar of geodetic interval which gives a measure of the square of the geodesic distance between the separated points. Next, using a covariant expansion in terms of the tangent to the geodesic, the stress tensor may be expanded in powers of the length of the geodesic. Covariant expressions for each divergent term and for certain terms in the finite portion of the vacuum expectation value of the stress tensor are found. The properties, uses, and limitations of the results are discussed.

The relationship between bathymetry and gravity in the Atlantic Ocean

Abstract: The free air gravity anomaly and depth are sampled at 2-km intervals along two long, reasonably straight ship tracks across the Atlantic Ocean. The resulting series are then processed as if they were time series, and filters are obtained to predict the gravity observations from the bathymetry. More than half the energy in the gravity field can be predicted by this means, and that which cannot emphasizes unusual structures beneath the sea floor. More information can be obtained by comparing the gravity and the bathymetry after both series have been Fourier-transformed. Isostatic compensation begins when the wavelength exceeds about 100 km and increases with increasing wavelength. The results are compared with predictions from various simple models and agree best with a model in which the topography results from variations of crustal thickness and the plate thickness is little greater than 10 km when the compensation occurs. These observations can be understood if the topography results from large-scale intrusions into the lower crust within tens of kilometers of the spreading center. Though such a model for a slowly spreading ridge differs from most of those which have been previously put forward and must be regarded with skepticism until it is supported by evidence from other sources, it appears to be compatible with the limited information now available.

Correlations in the liquid–vapor interface

Abstract: A liquid–vapor system in a gravitational field is examined using the grand canonical distribution functions ρs(r1...rs) and direct correlation functions cs(r1...rs) for a nonuniform system. The limit of zero field is taken under the assumption that ρ1(z) approaches a limit representing a two‐phase system. The limiting behavior is discussed in terms of an infinite continuous matrix calculated from c2(r1,r2) and ρ1(z). The vanishing of eigenvalues in zero field implies the appearance of long‐ranged correlations. The correlations are shown to be in the horizontal directions, confined to the interface, and macroscopic in range. The situation in an interface is briefly contrasted with the effect of a rigid wall in order to illustrate the fact that spontaneous symmetry breaking rather than the inhomogeneity of ρ1(z) is responsbile for the long‐ranged correlations. The invariance properties of a system in a gravitational field are used to give a new derivation of the conventional choice of the dividing surface. A microscopic expression for the surface tension is used to calculate the range of the interfacial correlations.

The boundary problems of physical geodesy

Abstract: The purpose of this paper is to discuss the determination of the figure of the earth and its gravity field from astrogeodetic and gravimetric data (By gravity we mean the resultant of the attractive force of the masses of the earth, also called gravitation, and the centrifugal force of the earth's rotation) Let us recall that at the surface of the earth: (a) astronomic observations allow one to determine the direction of the gravity vector G; (b) gravimetric measurements give the length I GI of the gravity vector; (c) levelling combined with gravimetric measurements gives the differential of the gravity potential W, and thus yields W apart from an additive constant We assume the measured data G and W corrected for, say, the gravitational interaction with the moon, the sun and the planets, for the precession of the earth, and so on, so that we have the following idealized situation:

Verification of the Principle of Equivalence for Massive Bodies

Abstract: Analysis of 1389 measurements, accumulated between 1970 and 1974 of echo delays of laser signals transmitted from Earth and reflected from cube corners on the Moon show gravitational binding energy to contribute equally to Earth’s inertial and passive gravitational masses to within the estimated uncertainty of 1.5%. The corresponding restriction on the Eddington-Robertson parameters is 4β - ϒ - 3 = -0.001 ± 0.015. Combination with other results, as if independent, yields β = 1.003 ± 0.005 and ϒ = 1.008 ± 0.008, in accord with general relativity.

Theoretical Modeling Of The Magnetic And Gravitational Fields Of An Arbitrarily Shaped Three–Dimensional Body

Abstract: An analytical method is developed for modeling the magnetic field or the gravitational attraction of a homogenous, arbitrarily shaped, three–dimensional body. In this method, the body to be modeled is represented by a polyhedron composed of triangular facets. A convenient method for inputting the apices and assembling the facets of a polyhedron is developed. As the solution is analytic, the polyhedron facets can be any size, and the number of input points depends only upon the number of apices required to outline the body.

New Test of the Equivalence Principle from Lunar Laser Ranging

Abstract: An analysis of six years of lunar-laser-ranging data gives a zero amplitude for the Nordtvedt term in the earth-moon distance yielding the Nordtvedt parameter eta = 0.00 plus or minus 0.03. Thus, earth's gravitational self-energy contributes equally, plus or minus 3%, to its inertial mass and passive gravitational mass. At the 70% confidence level this result is only consistent with the Brans-Dicke theory for omega greater than 29. We obtain the absolute value of beta - 1 less than about 0.02 to 0.05 for five-parameter parametrized post-Newtonian theories of gravitation with energy-momentum conservation.

Post-Newtonian gravitational radiation from orbiting point masses

Abstract: General formulas are derived which describe the gravitational radiation at large distances from a system of bodies whose sizes are small compared with their separations. The calculation is carried out through post-Newtonian order within general relativity. More explicit formulas are derived for two-body systems, and detailed results are presented for circular orbits, gravitational bremsstrahlung, and head-on collisions.

Particle creation from vacuum in homogeneous isotropic models of the Universe

Abstract: Particle creation in Friedman models of the open, closed, and quasi-Euclidean types is considered. The new method of calculation of probabilities of pair creation from vacuum by nonstationary external gravitational field is developed. This method is based on the diagonalization of the energy operator with the help of time-dependent canonical transformations. Finite numerical estimates for the densities of created particles and antiparticles are obtained both for early and modern stages of the evolution of the Universe.

Dynamics of tensor fields in hyperspace. III

Abstract: The dynamics of tensor fields with derivative gravitational coupling on a given Riemannian background is formulated as Hamiltonian dynamics of hypersurface projections of these fields propagating in hyperspace. The first‐order spacetime action is transformed into an equivalent hypersurface form. The supermomentum and different parts of the super‐Hamiltonian are identified with projected pieces of the (symmetrical, canonical, and spin) energy–momentum tensors, and their kinematical and dynamical roles are analyzed. Hypersurface variables are included among the canonical variables, and the resulting first‐order generalized Hamiltonian dynamics of hypertensor fields is discussed. The closing relations for the constraint functions in the generalized Hamiltonian dynamics are derived from the foliation independence of the hypersurface action. The elimination of the λ‐multipliers, which are characteristic to the first‐order theory, is accomplished. The general formalism is specialized to the n‐form fields with nonderivative gravitational coupling.

Experimental examination of the gravitational inverse square law

Abstract: IN a previous paper1 we pointed out that earlier data on the measurement of the gravitational constant suggest a systematic shift in the value with the separation of the masses. This laboratory has been examining this question for about a year, and the early data gave a discrepancy of 0.4%. New, intensive experiments have given 92 data points, with a resulting discrepancy of 0.37%.

Collision of two black holes: Theoretical framework

Abstract: Highly nonspherical time-dependent collisions between black holes may be powerful sources of gravitational radiation. We consider various attempts at estimating the efficiency of the generation of radiation by such collisions. To determine the actual efficiency as well as to understand the details of the dynamical coalescence of black-hole event horizons, we have developed a numerical method for solving the Einstein gravitational field equations in these high-velocity strong-field regions. The head-on collision of two nonrotating vacuum black holes is chosen as an example of our technique. We use the geometrodynamical model of a black hole as an Einstein-Rosen bridge. The initial data to be evolved are the time-symmetric conformally flat data discovered by Misner. A new set of spatial coordinates for these data is derived. Then the general space plus time decomposition of Einstein's equations is presented and specialized to the axisymmetric nonrotating case. Details of the evolution will be given in later papers. (AIP)

Astrophysical upper limits on the photon rest mass

Abstract: The main ideas and methods currently used to obtain upper limits on the photon rest mass from astrophysical data are briefly reviewed One method is based on the fact that if the photon has nonzero rest mass m magnetoacoustic waves cannot have frequencies lower than a certain critical frequency, which depends on m If wisps in the Crab Nebula are interpreted as magnetoacoustic waves of extremely low frequency, then the data of many-year observations of the wisps put an upper limit on m which is much better than the one established under terrestrial conditions An error is pointed out in a different method which has been proposed in the literature in which the contribution of the energy of the galactic magnetic field (or rather, the vector potential) to the mass of Galaxy is estimated on the basis of gravitational effects The point is that in the general theory of relativity not only energy but also pressure has a weight In the case under consideration, these two contributions cancel each other and the galactic magnetic field cannot produce anomalously strong gravitational fields The most stringent upper limit on the photon rest mass, m? 3?10?60 g, is obtained from the analysis of the mechanical stability of magnetized gas in the galaxies with allowance for the specific pressure forces of the vector potential This upper limit is 12 orders of magnitude better than the best upper limits obtained under terrestrial conditions This result clearly demonstrates the effectiveness of astrophysical methods

Gauge theory of gravitation

Abstract: Yang has laid the foundations for a "guage" type theory of gravitation, reintroducing the Lagrangian previously considered by Weyl and Stephenson. In this paper, I develop the full theory using a variational principle on this Lagrangian with sources. Analysis of the full set of Euler-Lagrange equations shows that Einstein spaces satisfying ${R}_{\ensuremath{\mu}\ensuremath{\kappa}}=\ensuremath{\omega}{g}_{\ensuremath{\mu}\ensuremath{\kappa}}$ with arbitrary cosmological constant $\ensuremath{\omega}$, are the only Riemannian vacuum solutions. This rules out the nonphysical, static, spherically symmetric solutions of Pavelle and Thompson; they only considered a subset of the Euler-Lagrange system of equations. The additional equations become important when sources to the gravitational field are considered. The full set of equations with sources have the following properties: The stress-energy tensor must be traceless. Other than a small exceptional class, all matter solutions must be non-Riemannian. The stress-energy tensor is not conserved if torsion is kept. The only Robertson-Walker cosmological solution which is Riemannian is static; all other homogeneous, isotropic cosmologies are non-Riemannian. The equations do not reduce to Poisson's equation for weak, static gravitational fields, thus violating the Newtonian limit. I finish by commenting on the "conceptually superior... integral formalism" proposed by Yang and used as a foundation for his gauge-type gravitational theory.

Maxwell form of the linear theory of gravitation

Abstract: A treatment of the linear theory is given that closely parallels the usual E and B formulation of electromagnetic theory. In Part I, an introductory exposition of gravitational radiation is presented. The tidal gravitational field strength E is defined, and it is shown that E is the measurable quantity which characterizes a gravitational wave. The important point is made that the problem of detecting gravitational waves is really the same problem as detecting tidal accelerations due to a time‐varying Newtonian gravitational field. In Part II, the magnetic‐type gravitational field strength B is defined and Maxwell‐like field equations are used to determine the polarization states of a gravitational wave. The detection of gravitational waves by Weber‐type cylinders is discussed.

Differential cross sections for weak-field gravitational scattering

Abstract: Differential cross sections are presented for the scattering of plane scalar, electromagnetic, and gravitational waves from the gravitational field of sources in the weak-field approximation. Comparison is made with the long- wavelength limit of analogous scattering off of spherical black holes. (AIP)

Wave Optics of the Spherical Gravitational Lens. Part I: Diffraction of a Plane Electromagnetic Wave by a Large Star

Abstract: This paper gives the Poynting vector of a plane electromagnetic wave diffracted by the gravitational field of a large spherical body (large compared to its Schwarzschild radius) and shows in detail how this body works as a gravitational lens. The most interesting results are (1) an extreme amplification of intensity near to the axis of symmetry in the far field behind the body, with a factor of 10 times the Schwarzschild radius divided by the wavelength of the light, and (2) the appearance of double images, differing in shape and position from the predictions of geometrical optics.

Axisymmetric gravitational fields

Abstract: In this review paper Einstein equations for axisymmetric vacuum fields are introduced in the form given by Lewis. Following Ernst they are reduced to one complex potential equation. Weyl-type, Schwarzschild, Kerr, Tomimatsu-Sato solutions, and their NUT-like generalizations are then discussed.

Particle creation by gravitational fields

Abstract: This paper presents a new and generally covariant approach to quantum field theory in curved space--time. Previously unknown expressions are obtained for particle creation amplitudes in oscillating gravitational fields. These expressions illuminate the physical origin of the particle creation. (AIP)

Theoretical frameworks for testing relativistic gravity. V. Post-Newtonian limit of Rosen's theory

Abstract: The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the post-Newtonian parameter alpha sub 2 (which is related to the difference in propagation speeds for gravitational and electromagnetic waves). Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific (but presumably special) form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity - and standard solar system experiments cannot distinguish between the two theories.

Some viscous fluid cosmological models of plane symmetry

Abstract: Two plane-symmetric cosmological models representing viscous fluid with free gravitational field of type D have been obtained. The effect of viscosity on various kinematical parameters has been discussed.

General-relativistic kinetic theory of waves in a massive particle medium

Abstract: In this paper, we give a general-relativistic kinetic theory of waves propagating in a medium filled with massive particles. A major difficulty of this problem is to handle simultaneously dispersive and expansion effects. Matter itself is at the root of both phenomena, and in our treatment they are conveniently separated by using a two-time scale approximation. It turns out that the expansion modifies both the amplitude and the frequency of the waves. Dispersion effects give rise to proper modes, which are shown to be the 0, 1, and 2 helicity components of the total field. The dispersion equations for these different components are obtained in a general form. The propagation of gravitational modes is examined in more detail for the two extreme cases of cold and ultrarelativistic matter. A lower cutoff frequency appears, and no Landau damping is found in the case of a thermalized gas.

Zero-mass plane waves in nonzero gravitational backgrounds

Abstract: The mathematical definition of what is intuitively called a ''plane wave'' on the curved background of a black hole is clarified and discussed from the viewpoints of potentials and fields. Because of the long-range Newtonian part of the gravitational field the asymptotic wave fronts of an incident ''plane wave'' (describing a radiative perturbation for a scattering experiment) are distorted in a manner analogous to the wave fronts of an electron beam in the quantum-mechanical Coulomb scattering problem. In addition, the electromagnetic and gravitational fields can be described with either a potential formalism (i.e., the vector potential and the metric perturbation) or a field formalism (i.e., the electromagnetic field tensor and the Riemann tensor). In this paper we present a distorted ''plane wave'' prescription, necessary for the calculation of the scattering cross sections of electromagnetic and gravitational waves off of a black hole, which agrees with the accepted prescription for a massless scalar field and satisfies the intuitive notions of what constitutes a ''plane wave'' in terms of potentials and fields. (AIP)

The influence of the atmosphere on geoid and potential coefficient determinations from gravity data

Abstract: For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moritz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correction term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30 deg, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055 millionths at n = 2, m = 2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.

Anisotropic parametrized post-Newtonian gravitational metric field

Abstract: The anisotropic generalization of the parameterized post-Newtonian (PPN) gravitational metric field is made for the case of theories with energy and momentum conservation laws. Such an anisotropic metric field will generally result in two-tensor or bimetric theories of gravity in an anisotropic universe. New anisotropic 3 x 3 spatial PPN matrices are introduced into the general metric expansion. Earth gravimeter measurements strongly restrict some anisotropies, while anisotropic inertial and gravitational mass for celestial bodies result from other combinations of the PPN matrices.