Showing papers on "Gravitational field published in 1989"

Gravitational Field of a Global Monopole

Abstract: We present an approximate solution of the Einstein equations for the metric outside a monopole resulting from the breaking of a global O(3) symmetry. The monopole exerts practically no gravitational force on nonrelativistic matter, but the space around it has a deficit solid angle, and all light rays are deflected by the same angle, independent of the impact parameter.

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

Abstract: The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

Gravitational phenomenology in higher-dimensional theories and strings

Abstract: We investigate gravitational phenomenology in compactified higher-dimensional theories, with particular emphasis on the consequences in string theory of tensor-induced spontaneous Lorentz-symmetry breaking. The role played by this mechanism in causing a gravitational version of the Higgs effect and in compactification is explored. The experimental viability of compactified theories with zero modes is considered by examining nonleading but observable gravitational effects. Additional constraints from the observed cosmological properties of the Universe are uncovered. Our investigations significantly constrain many theories involving extra dimensions in their perturbative regime. To resolve the phenomenological difficulties one must generate masses for the higher-dimensional components of the metric while leaving massless the physical spacetime components. Some possibilities for overcoming this metric-mass problem are suggested. An open issue is whether the metric-mass problem is resolved in string theory.

The GEM-T2 gravitational model.

Abstract: GEM-T2 is the latest in a series of Goddard Earth models of the terrestrial gravitational field. It is the second in a planned sequence of gravity models designed to improve both the modeling capabilities for determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10-cm RMS and for defining the long-wavelength geoid to support many oceanographic and geophysical applications. GEM-T2 includes more than 6OU coefficients above degree 36, the limit for GEM-T1, and provides a dynamically determined model of the major tidal components which contains 90 terms. Like GEM-T1, it was produced entirely from satellite tracking data. GEM-T2 however, now uses nearly twice as many satellites (31 versus 17), contains 3 times the number of observations (2.4 million), and has twice the number of data arcs (1130). GEM-T2 utilizes laser tracking from 11 satellites, Doppler data from four satellites, two- and three-way range rate data from Landsat-1, satellite-to-satellite tracking data between the geosynchronous ATS 6 and GEOS 3, and optical observations on 20 different orbits. This observation set effectively exhausts the inclination distribution available for gravitational field development from our historical data base. The recovery of the higher degree and order coefficients in GEM-T2 was made possible through the application of a constrained least squares technique using the known spectrum of the Earth's gravity field as a priori information. The error calibration of the model was performed concurrently with its generation by comparing the complete model against test solutions which omit each individually identifiable data set in turn. The differences between the solutions isolate the contribution of a given data set, and the magnitudes of these differences are compared for consistency against their expected values from the respective solution covariances. The process yields near optimal data weights and assures that the model will be both self-consistent and well calibrated. GEM-T2 has benefitted by its application as demonstrated through comparisons using independently derived gravity anomalies from altimelry. Results for the GEM-T2 error calibration indicate significant improvement over previous satellite-only GEM models. The accuracy assessment of the lower degree and order coefficients of GEM-T2 shows that their uncertainties have been reduced by 20% compared to GEM-T1. The commission error of the geoid has been reduced from 160 cm for GEM-T1 to 130 cm for GEM-T2 for the 36 × 36 portion of the field. The orbital accuracies achieved using GEM-T2 are likewise improved. This is especially true for the Starlette and GEOS 3 orbits where higher-order resonance terms not present in GEM-T1 (e.g., terms with m = 42,43) are now well represented in GEM-T2. The improvement in orbital accuracy of GEM-T2 over GEM-T1 extends across all orbit inclinations. This confirms our conclusion that GEM-T2 offers a significant advance in knowledge of the Earth's gravity field.

Evolution of cosmic string networks.

Abstract: A discussion of the evolution and observable consequences of a network of cosmic strings is given. A simple model for the evolution of the string network is presented, and related to the statistical mechanics of string networks. The model predicts the long string density throughout the history of the universe from a single parameter, which researchers calculate in radiation era simulations. The statistical mechanics arguments indicate a particular thermal form for the spectrum of loops chopped off the network. Detailed numerical simulations of string networks in expanding backgrounds are performed to test the model. Consequences for large scale structure, the microwave and gravity wave backgrounds, nucleosynthesis and gravitational lensing are calculated.

Gravity as a zero-point-fluctuation force

Abstract: Sakharov has proposed a suggestive model in which gravity is not a separately existing fundamental force, but rather an induced effect associated with zero-point fluctuations (ZPF's) of the vacuum, in much the same manner as the van der Waals and Casimir forces. In the spirit of this proposal we develop a point-particle\char21{}ZPF interaction model that accords with and fulfills this hypothesis. In the model gravitational mass and its associated gravitational effects are shown to derive in a fully self-consistent way from electromagnetic-ZPF-induced particle motion (Zitterbewegung). Because of its electromagnetic-ZPF underpinning, gravitational theory in this form constitutes an ``already unified'' theory.

Relativistic reference systems and motion of test bodies in the vicinity of the earth

Abstract: Relativistic theory of constructing nonrotating harmonic reference systems (RS) is developed. The theory enables one to produce the celestial RS for solar-system dynamics neglecting the gravitational field of the Galaxy. Particular attention is focused on the barycentric RS (BRS) with the origin at the solar-system barycentre and the geocentric RS (GRS) with the origin at the geocentre. It is assumed therewith that the velocities of bodies are small as compared with the light velocity and the gravitational field is weak everywhere. The specific RS and the gravitational field are described by the metric tensor to be found by Newtonian approximations from the Einstein field equations with given boundary conditions. The BRS coordinates cover all the solar-system space. The GRS coordinates are initially restricted in space by the orbit of the Moon. The relationship between BRS and GRS is established by the asymptotic matching technique. The explicit transformation formulae permit to prolonge the GRS coordinates beyond the lunar orbit to cover actually all the solar-system space. The GRS equations of the Earth satellite motion have been deduced. The relativistic right-hand members of these equations contain Schwarzschild, Lense-Thirring and quadrupole terrestrial perturbations as well as tidal perturbations due to the Sun, the Moon and the major planets. The equations are derived by two different techniques. The first one implies the application of the geodesic principle to the GRS metric. The second one is based on the transformation of the BRS satellite equations of motion into the GRS equations. Both techniques result in the same final expressions.

General static axisymmetric solution of Einstein's vacuum field equations in prolate spheroidal coordinates.

Abstract: A solution of Einstein's vacuum field equations is presented explicitly in Eqs. (22), (28), and (43). This completes our stationary metric presented previously and therefore gives the exact solution to the problem of describing the exterior field of rotating deformed bodies. The metric given here is equivalent to the general Weyl metric; however, we use prolate spheroidal coordinates for conve- nience. We investigate the Newtonian and the relativistic (Geroch-Hansen) multipole moments of the solution and conclude that it describes the exterior gravitational field of a static axisymmetric mass distribution.

Relativistic theory of gravitation

Abstract: In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday--Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly fulfilled for the energy-moment and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just ''flat.'' This suggests that in the universe a ''missing mass'' should exist in a form of matter.

Quadratic Poincaré gauge theory of gravity: A comparison with the general relativity theory

Abstract: The classical dynamics of the gravitational field in the Poincare gauge theory is studied. The most general Lagrangian quadratic in curvature and torsion is considered. The relevant field equations and their solutions are analyzed in detail, with particular emphasis on the comparison of the Poincare gauge models with the general relativity theory. We investigate correspondence between the spaces of exact solutions of these theories, both in the presence and absence of material sources, and with or without torsion. Some new exact solutions are obtained without the use of the double duality ansatz. The weak-field approximation is discussed, and gravitational radiation is considered.

On the equilibrium statistical mechanics of isothermal classical self-gravitating matter

Abstract: The canonical ensemble is investigated for classical self-gravitating matter in a finite containerΛ [d]⊂ℝ d ,d=3 and 2. Starting with modified gravitational interactions (smoothed-out singularity), it is proven by explicit construction that, in thew *-topology, the canonical equilibrium measure converges to a superposition of Dirac measures when the limit of exact Newtonian gravitational interactions between classical point particles is taken. The consequences of this result for more realistic classical systems are evaluated, and the existence of a gravitational phase transition is proven. The results are discussed with view toward applications in astrophysics and space science. Some attention is paid also to the problem of founding thermodynamics by means of statistical mechanics.

Experimental constraints on a minimal and nonminimal violation of the equivalence principle in the oscillations of massive neutrinos.

Abstract: The negative results of the oscillations experiments are discussed with thehypothesis that the various neutrino types are not universally coupled togravity. In this case the transition probabiltiy between two different flavoreigenstates may be affected by the local gravitational field present in aterrestrial laboratory, and the contribution of gravity can interfere, ingeneral, with the mass contribution to the oscillation process. In particularit is shown that even a strong violation of the equivalence principle could becompatible with the experimental data, provided the gravity-induced energysplitting is balanced by a suitable neutrino mass difference.

Gravitational analogs of the Aharonov-Bohm effect

Abstract: A quantum scalar particle is considered in the following background gravitational fields due to (a) a tubular matter source with axial interior magnetic field and vanishing exterior magnetic field; (b) slowly moving mass currents (weak approximation); and (c) a spinning cosmic string. It is shown that in the flat space‐time around these sources, the energy spectrum and wave function of the particle depend on the amount of matter and magnetic field (tubular matter source case), on the velocity of the moving mass currents, and on the angular momentum in the spinning cosmic string case. These represent gravitational analogs of the Aharonov–Bohm effect in electrodynamics and are due to global (topological) features of the background space‐times under consideration.

Theory of satellite geodesy and gravity field determination

Abstract: to classical mechanics.- Lectures in celestial mechanics.- Four lectures on special and general relativity.- Reference coordinate systems: An update.- Gravity field recovery from satellite tracking data.- Fundamentals of orbit determination.- Combination of Satellite, Altimetric and Terrestrial Gravity Data.- Summer school lectures on satellite altimetry.- Advanced techniques for high-resolution mapping of the gravitational field.- The integrated approach to satellite geodesy.- Determination of a local geodetic network by multi-arc processing of satellite laser ranges.- Boundary value problems and invariants of the gravitational tensor in satellite gradiometry.- A possible application of the space VLBI observations for establishment of a new connection of reference frames.- Optimization of the reordering algorithm for least squares problems relevant to space geodesy.

Gravity interpretation using correlation factors between successive least‐squares residual anomalies

Abstract: The correlation factors between successive least‐squares residual (or regional) gravity anomalies from a buried sphere, a two‐dimensional (2‐D) horizontal cylinder, and a vertical cylinder and the first horizontal derivative of the gravity from a 2‐D thin faulted layer are computed. Correlation values are used to determine the depth to the center of the buried structure, and the radius of the sphere or the cylinder and the thickness of the fault are estimated. The method can be applied not only to residuals but also to the Bouguer‐anomaly profile consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of any order. The method is easy to apply and may be automated if desired. It can also be applied to the derivative anomalies of the gravity field. The validity of the method is tested on two field examples from the United States and Denmark.

Positive energy via the teleparallel hamiltonian

Abstract: The canonical analysis of the teleparallel form of Einstein’s gravitational theory is discussed. For teleparallel theories of gravity the Hamiltonian density is mostly quadratic and the flux integrand at spatial infinity for the conserved total energy-momentum is quite naturally fully 4-covariant. These features plus a rotational gauge condition allow us to obtain a new, strictly tensorial, proof of the positivity of total energy for Einstein gravity from its teleparallel formulation. The Schwarzschild solution is used to provide insight into the proof and its various allowed positive “localizations” of gravitational energy.

Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer. Theoretical principles.

Abstract: The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of ${10}^{\mathrm{\ensuremath{-}}10}$ of the Newtonian tidal terms arising from the mass of the Earth. These components could be detected in principle by sensitive superconducting gravity gradiometers currently under development. We lay out the theoretical principles of such an experiment by using the parametrized post-Newtonian formalism to derive the locally measured Riemann tensor in an orbiting proper reference frame, in a class of metric theories of gravity that includes general relativity. A gradiometer assembly consisting of three gradiometers with axes at mutually right angles measures three diagonal components of a 3\ifmmode\times\else\texttimes\fi{}3 ``tidal tensor,'' related to the Riemann tensor. We find that, by choosing a particular assembly orientation relative to the orbit and taking a sum and difference of two of the three gradiometer outputs, one can isolate the gravitomagnetic relativistic effect from the large Newtonian background.

Cosmological deductions from the alignment of local gravity and motion

Abstract: L'alignement du mouvement du Groupe Local au travers du fond microonde cosmique et du flux optique net determine a partir de catalogues de galaxies est considere. Le rapport du dipole optique au taux d'accroissement du monopole optique est utilise pour determiner le parametre Ω directement sur l'echelle 1 pour cent du rayon de Hubble

Test of Newton's inverse-square law in the Greenland ice cap.

Abstract: An Airy-type geophysical experiment was conducted in a 2-km-deep hole in the Greenland ice cap at depths between 213 and 1673 m to test for possible violations of Newton's inverse-square law. An anomalous gravity gradient was observed. We cannot unambiguously attribute it to a breakdown of Newtonian gravity because we have shown that it might be due to unexpected geological features in the rock below the ice.

Nonequivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field

Abstract: A general expression is obtained for the space‐time interval between neighboring events in a one‐dimensional space in which it is possible to set up a rigid reference frame. Particular expressions are then obtained for the interval for the special cases of a rigid frame at rest in a uniform gravitational field and a rigid frame uniformly accelerating in field‐free space. The two expressions are not equivalent and are used to show why, how, and to what extent observations made in a rigid enclosure at rest in a gravitational field are not equivalent to observations made in a rigid enclosure that is uniformly accelerating in field‐free space. Two facts of particular interest that are demonstrated in the course of the analysis are the following: (i) Two spatially separated particles that are simultaneously released from rest and allowed to fall freely in a uniform gravitational field will not remain at rest with respect to one another. (ii) Uniformly accelerating reference frames and inertial frames are the only possible one‐dimensional rigid frames in flat space‐time.

Gravitational fields of straight and circular cosmic strings: Relation between gravitational mass, angular deficit, and internal structure.

Abstract: The first part of the paper formulates general conditions (independent of a particular gauge-theoretic model) under which a cylindrical distribution of matter can be joined to a vacuum exterior with a conical geometry and exhibits the relation between angular deficit and internal structure. To bring out the relation to gravitational mass, the second part is devoted to a detailed study of solutions of the initial-value problem for circular loops of string at a moment of time symmetry.

The decay of the spectrum of the gravitational potential and the topography for the Earth

Abstract: The spectrum of the earth's gravitational potential and topography, as represented by spherical harmonic expansions to degree 180, have been computed. Modeling the decay in the form of (A x l) exp-Beta, values of A and Beta for several degree (l) ranges were computed. For degree range 5-180, Beta was 2.54 for the potential and 2.16 for equivalent rock topography. The potential decay was somewhat slower than that implied by Kaula's rule. However, at high degree ranges, the Beta values were larger agreeing better with recent determinations from terrestrial gravity data and geoid undulations implied by satellite altimetric data. The values imply that the potential decays faster at higher l values.

Curvature-singularity-free solutions for colliding plane gravitational waves with broken u - v symmetry

Abstract: We discuss the most general solution describing the collision of plane gravitational waves with constant polarization. Among these solutions there is an infinite-dimensional family of metrics free of curvature singularities and analytically extendable across the ``focusing'' hypersurface. These regular solutions describe collisions between two incoming plane waves with different amplitudes for which u-v symmetry is broken. Boundary conditions on the null hypersurfaces u=0, v=0 are discussed and it is shown that any solution describing the scattering of plane gravitational waves with constant polarization has to include at least two solitary terms each of which stabilizes the behavior of the gravitational field on the null boundaries.

The Vaidya Solution in Higher Dimensions

Abstract: The Vaidya metric representing the gravitational field of a radiating star is generalized to spacetimes of dimensions greater than four.