Showing papers on "Gravitational field published in 1979"

Gravity model improvement using Geos 3 (GEM 9 and 10)

Abstract: Although errors in previous gravity models have produced large uncertainties in the orbital position of GEOS 3, significant improvement has been obtained with new geopotential solutions, Goddard Earth Model (GEM) 9 and 10. The GEM 9 and 10 solutions for the potential coefficients and station coordinates are presented along with a discussion of the new techniques employed. Also presented and discussed are solutions for three fundamental geodetic reference parameters, viz. the mean radius of the earth, the gravitational constant, and mean equatorial gravity. Evaluation of the gravity field is examined together with evaluation of GEM 9 and 10 for orbit determination accuracy. The major objectives of GEM 9 and 10 are achieved. GEOS 3 orbital accuracies from these models are about 1 m in their radial components for 5-day arc lengths. Both models yield significantly improved results over GEM solutions when compared to surface gravimetry, Skylab and GEOS 3 altimetry, and highly accurate BE-C (Beacon Explorer-C) laser ranges. The new values of the parameters discussed are given.

Gravity effects in fluids near the gas--liquid critical point

Abstract: The presence of a gravitational field leads to both practical and fundamental limits of the resolution in critical phenomena experiments in fluids near the gas-liquid critical point. We present equations that yield estimates of the gravitational limitations in a variety of critical phenomena experiments for a large number of fluids and as a function of the magnitude of the gravitational field. Various strategies for improving the resolution of such experiments are discussed, including procedures that remove a fluid from thermodynamic equilibrium (e.g., stirring). A comparison is made between the gravitational limitations in earth-bound experiments and those at the microgravitational levels that may become accessible in an orbiting laboratory.

Constructive procedure for perturbations of spacetimes

Abstract: The method of Debye scalar superpotentials has previously been extended by the authors to curved spaces to yield a constructive procedure for neutrino, electromagnetic, and gravitational perturbations of algebraically special spacetimes. The solution of a decoupled scalar wave equation is differentiated to give the solution of the corresponding spinor or tensor perturbation field equations. In this paper covariant formulations and proofs are given. The results are derived in a general spinor formalism framework which extends earlier exterior differential form and tensor treatments of the electromagnetic case.

Backlund transformations of axially symmetric stationary gravitational fields

Abstract: A generation theorem for solutions of Einstein's equations is presented. It consists mainly of algebraic steps. With its aid, one obtained from an 'old' solution (e.g. from the Minkowski space) 'new' solutions with an arbitrary number of constants. The method of repeated application of potential and coordinate transformations considered by Geroch (1972) and Kinnerley (1977) is included.

Matter and Light Wave Interferometry in Gravitational Fields

Abstract: We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism∫ ds. In weak fieldsh μυ this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 ∫h μυ P υ dx μ whereP υ is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the “dragging of the ether frame” by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 ∫h μυ K υ dx μ , whereK υ is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.

Shear‐free gravitational collapse

Abstract: Spherically symmetric perfect fluids are studied under the restriction of shear‐free motion. All solutions of the field equations are found by solving a single second order nonlinear equation containing an arbitrary function. It is shown that this arbitrary function is a geometric invariant, E, which measures the gravitational field energy, and it is shown that E=const generates all the homogeneous density solutions. An improved proof is given for the nonexistence of any one‐parameter equation of state. A number of exact solutions are presented and discussed.

Gravitational Lens of the Sun: Its Potential for Observations and Communications over Interstellar Distances

Abstract: The gravitational field of the sun acts as a spherical lens to magnify the intensity of radiation from a distant source along a semi-infinite focal line. A spacecraft anywhere on that line in principle could observe, eavesdrop, and communicate over interstellar distances, using equipment comparable in size and power with what is now used for interplanetary distances. If one neglects coronal effects, the maximum magnification factor for coherent radiation is inversely proportional to the wavelength, being 100 million at 1 millimeter. The principal difficulties are that the nearest point on the focal half-line is about 550 times the sun-earth distance, separate spacecraft would be needed to work with each stellar system of interest, and the solar corona would severely limit the intensity of coherent radiation while also restricting operations to relatively short wavelengths.

M2, S2, K1 models of the global ocean tide

Abstract: Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and Kl. The resulting representations of the global tide are stable over at least a ?5% variation in the mean depth of the model basin, and they conserve mass. Maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each contituent are presented.

Coupled inertial and gravitational effects in the proper reference frame of an accelerated, rotating observer

Abstract: To the second order in metric and the first order in equations of motion in the local coordinates of an accelerated rotating observer, the inertial effects and gravitational effects are simply additive. To look into the coupled inertial and gravitational effects, we derive the third‐order expansion of the metric and the second‐order expansion of the equations of motion in local coordinates. Besides purely gravitational (purely curvature) effects, the equations of motion contain, in this order, the following coupled inertial and gravitational effects: redshift corrections to electric, magnetic, and double‐magnetic type curvature forces; velocity‐induced special relativistic corrections; and electric, magnetic, and double‐magnetic type coupled inertial and gravitational forces. An example is provided with a static observer in the Schwarzchild spacetime.

Self-interaction of charged particles in the gravitational field

Abstract: The gravitationally induced self-interaction force is calculated at a large distance from a Schwarzschild black hole. If, instead of the electromagnetic field, the particle is coupled to a vector-meson field of vanishingly small, but nonzero, mass, then it is shown that the self-force has the same magnitude but opposite direction. A sharp difference between massive and massless vector fields is a result of different boundary conditions at the horizon surface.

Final state of the evolution of the interior of a charged black hole

Abstract: We describe the dynamical evolution of scalar, electromagnetic, and gravitational test fields on the interior of a Reissner-Nordstr\"om (spherically symmetric and electrically charged) black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the divergences of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. The late-time development of the fields is discussed and a picture of the final state for the interior (in terms of classical fields) is developed. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstr\"om solution is highly unstable and not a physical feature of a realistic gravitational collapse.

Development and analysis of a twelfth degree and order gravity model for Mars

Abstract: Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

Quantum effects and regular cosmological models

Abstract: Allowance for the quantum nature of matter fields and weak gravitational waves on the background of the classical metric of a cosmological model leads to two main effects: vacuum polarization and particle production. The first of these effects can be taken into account qualitatively by the introduction into the Lagrangian density of the gravitational field of corrections of the type A+BR/sup 2/+CR/sup 2/lnvertical-barR/R/sub 0/vertical-bar; the second, by the specification of a local rate of production of particles (gravitons) proportional to the square of the scalar curvature R/sup 2/. It is shown that simultaneous allowance for the influence of these effects on the evolution of a homogeneous anisotropic metric of the first Bianchi type eliminates the Einstein singularities. Asymptotic approach to the classical model, however, is attained only if additional assumptions are made. In the contraction stage the solution is close to the anisotropic vacuum Kasner solution; in the expansion stage it tends to the isotropic Friedmann solution, in which matter is produced by the gravitational field.

Aspects of Quantum Field Theory in Curved Space-Time: Effective Action and Energy-Momentum Tensor

Abstract: The theory of quantized fields in curved spacetime has reached a high level of development, and a number of important physical consequences have been predicted. By treating the metric of the gravitational field classically, one avoids the nonrenormalizability problems of quantized gravity, but nevertheless retains a wide domain of applicability. I have already given a recent review of quantized fields in curved spacetime [L. Parker, 1977], in which the creation of elementary particles by strong gravitational fields (as in cosmology and near black holes) was emphasized. The present lectures will emphasize material which was not covered in the previous review.

Gravitational collapse of a charged fluid sphere

Abstract: A class of solutions of Einstein's gravitational field equations is discussed which describes the collapse or expansion of a charged, perfect-fluid spherical distribution of matter. These solutions reduce in the appropriate limits to certain charged Newtonian polytropes. A physical interpretation of the collapsing configurations is given, and it is shown that these solutions can describe the gravitational collapse of a bounded, charged fluid around a charged black hole. In all these configurations the singular region is either a spacelike or a null hypersurface. Therefore, the final state of collapse cannot be described by the complete analytic extension of the Reissner-Nordstr\"om spacetime. The special case of uniform density models is investigated in detail and it is shown that they describe the accretion of neutral matter by a charged black hole. On the basis of this analysis, it is suggested that for the realistic collapse of charged matter the singular region formed within the matter is either spacelike or null.

Gravitational spectra from direct measurements

Abstract: A simple rapid method is described for determining the spectrum of a surface field (in spherical harmonics) from harmonic analysis of direct (in situ) measurements along great circle arcs. The method is shown to give excellent overall trends (smoothed spectra) to very high degree from even a few short arcs of satellite data. Three examples are taken with perfect measurements of satellite tracking over a planet made up of hundreds of point masses using (1) altimetric heights from a low-orbiting spacecraft, (2) velocity (range rate) residuals between a low and a high satellite in circular orbits, and (3) range rate data between a station at infinity and a satellite in a highly eccentric orbit. In particular, the smoothed spectrum of the earth's gravitational field is determined to about degree 400(50-km half wavelength) from 1° × 1° gravimetry and the equivalent of 11 revolutions of Geos 3 and Skylab altimetry. This measurement shows there is about 46 cm of geoid height (rms worldwide) remaining in the field beyond degree 180.

Scalar field and gravitational instability

Abstract: We study monopole perturbations of spherically symmetric scalar-vacuum and scalar-electrovacuum fields in general relativity and reduce the problem to a one-dimensional Schrodinger-like equation with a certain effective potential. Imposing certain boundary conditions, we select physically meaningful perturbations. Some of them grow exponentially and we conclude that the background system is unstable.

General Perturbations Theories Derived from the 1965 Lane Drag Theory

Abstract: : The Air Force General Perturbation theory (AFGP4) based on the analytic satellite theory of Lane (1965) and Lane and Cranford (1969) which models the gravitational zonal harmonics through J5 and models the atmosphere with a spherically symmetric power density function is given here in its complete form. All equations needed for satellite prediction are given and the reader is referred to the original publications for theoretical background. Two simplified equation subsets (IGP4 and SGP4) of AFGP4 are also given and the procedure by which they were obtained is outlined.

Gravitational radiation and the ultimate speed in Rosen's Bimetric theory of gravity

Abstract: Emission of gravitational radiation was shown to prevent particles of nonzero rest mass from exceeding the speed of gravitational radiation.

General-relativistic treatment of the gravitational coupling between laser beams

Abstract: The present paper is an extension of the earlier work of Tolman, Ehrenfest, and Podolsky who investigated the gravitational interaction between ''thin pencils of light.'' We calculate the gravitational field produced by a laser pulse traveling with a velocity v < c, and the trajectory of a probe pulse propagating through this field. The amplitude and phase variations of the probe pulse due to the presence of the laser pulse are calculated via the Einstein-Maxwell equations.

Static spherically symmetric solution for the field of a charged particle in a theory of gravity

Abstract: The field equations for a new theory of gravity are derived from a variational principle when electromagnetic fields are included in the Lagrangian density L. A static spherically symmetric solution to the field equations is obtained, which reduces to the Reissner-Nordstroem solution when a new gravitational coupling constant l equals zero. For l > m + (m/sup 2/ - 4..pi..Q/sup 2/)/sup 1/2/ black-hole event horizons are excluded from physical space-time.

Euclidean Quantum Gravity

Abstract: In these lectures I am going to describe an approach to Quantum Gravity using path integrals in the Euclidean regime ie over positive definite metrics (Strictly speaking, Riemannian would be more appropriate but it has the wrong connotations) The motivation for this is the belief that the topological properties of the gravitational fields play an essential role in Quantum Theory Attempts to quantize gravity ignoring the topological possibilities and simply drawing Feynman diagrams corresponding to perturbations around flat space have not been very successful: there seem to be an infinite sequence of undetermined renormalization parameters The situation is slightly better with supergravity theories; the undetermined renormalization parameters seem to come in only at the third and higher loops around flat space but perturbations around metrics that are topologically non-trivial introduce undetermined parameters even at the one loop level [1] [27] as I shall show later on