Showing papers on "Gravitational field published in 1983"

A modification of the newtonian dynamics as a possible alternative to the hidden mass hypothesis

Abstract: The author considers the possibility that there is not, in fact, much hidden mass in galaxies and galaxy systems. If a certain modified version of the Newtonian dynamics is used to describe the motion of bodies in a gravitational field (of a galaxy, say), the observational results are reproduced with no need to assume hidden mass in appreciable quantities. Various characteristics of galaxies result with no further assumptions. The basis of the modification is the assumption that in the limit of small acceleration a very low a0, the acceleration of a particle at distance r from a mass M satisfies approximately a2/a0 a MGr-2, where a0 is a constant of the dimensions of an acceleration.

Grand Unified Theories Based on Local Supersymmetry

Abstract: General features are discussed of grand unified theories with local supersymmetry broken at high energies by the super-Higgs effect. The low-energy effective Lagrangian is a globally supersymmetric one with all the explicit soft breakings. It is argued that the energy splittings among the vacua due to gravitational effects must be small in order to be able to pick out the correct vacuum. Also discussed are the mechanisms of breaking SU(2) by the gravitational effects and of suppressing monopole production in the early universe.

Cardiovascular Adjustments to Gravitational Stress

Abstract: The effects of gravity on the cardiovascular system must be taken into account whenever a hemodynamic assessment is made. All intravascular pressure have a gravity-dependent hydrostatic component. The interaction between the gravitational field, the position of the body, and the functional characteristics of the blood vessels determines the distribution of intravascular volume. In turn this distribution largely determines cardiac pump function. Multiple control mechanisms are activated to preserve optimal tissue perfusion when the magnitude of the gravitational field or its direction relative to the body changes. Humans are particularly sensitive to such changes because of the combination of their normally erect posture and the large body mass and blood volume below the level of the heart. Current aerospace technology also exposes human subjects to extreme variations in the gravitational forces that range from zero during space travel to as much an nine-times normal during operation of high-performance military aircraft. This chapter therefore emphasizes human physiology.

The relationship between surface topography, gravity anomalies, and temperature structure of convection

Abstract: Consideration is given to the relationship between the temperature structure of mantle convection and the resulting surface topography and gravity anomalies, which are used in its investigation. Integral expressions relating the three variables as a function of wavelength are obtained with the use of Green's function solutions to the equations of motion for the case of constant-viscosity convection in a plane layer subject to a uniform gravitational field. The influence of the boundary conditions, particularly at large wavelengths, is pointed out, and surface topographies and gravity produced by convection are illustrated for a number of simple temperature distributions. It is shown that the upper thermal boundary layer plays an important role in determining the surface observables, while temperatures near the bottom of the layer affect mainly that boundary. This result is consistent with an explanation of geoid anomalies over mid-ocean swells in terms of convection beneath the lithosphere.

Test of the principle of equivalence by a null gravitational red-shift experiment

Abstract: A test of the Einstein equivalence principle (EEP) was performed by carrying out a 'null' gravitational red-shift experiment. The experiment compared the rates of a pair of hydrogen maser clocks with those of a set of three superconducting-cavity stabilized oscillator clocks as a function of the solar gravitational potential. If EEP were not valid, the relative rates could vary with potential. During the experiment, the solar potential in the laboratory varied approximately linearly at 3 parts in 10 to the 12th per day because of the earth's orbital motion, and diurnally with an amplitude of 3 parts in 10 to the 13th because of the earth's rotation. An upper limit on the relative frequency variation of 1.7 parts in 100 of the external potential was set. The accuracy was limited by the frequency stability of the clocks and by unmodeled environmental effects. The result is consistent with the EEP at the 2 percent level. The experiment can also be viewed as setting a limit on a possible spatial variation of the fine-structure constant.

Cosmological perturbations in the early universe

Abstract: We elucidate and somewhat extend Bardeen's gauge-invariant formalism for calculating the growth of linear gravitational perturbations in a Friedmann-Robertson-Walker cosmological background. We show that the formalism can be derived from the usual gravitational Lagrangian, by variation with respect to a restricted set of metric perturbation functions. This approach produces a natural decomposition of an arbitrary matter field (whose constitutive equations need not resemble the usual cosmological perfect fluid) into a spatially homogeneous piece, which couples to the background metric, plus a spatially inhomogeneous piece, which is not necessarily small and which is the source term in a second-order differential equation which evolves the gauge-invariant metric perturbation potential. We show how the complete perturbed metric can be reconstructed in arbitrary gauge from the single gauge-independent metric potential, so that the evolution of the matter fields can be concurrently calculated in the usual manner (i.e., in a perturbed coordinate frame). The approach of this paper is designed to be particularly suited to the study of fluctuations generated by classical scalar or gauge fields in "inflationary" cosmological models.

Proper-time gauge in the quantum theory of gravitation

Abstract: The proper-time gauge appears to be the simplest one consistent with the invariance properties of the gravitational action. It also permits one to implement in a direct manner the requirement of causality in the quantum theory of gravitation. In this paper the measure for the path integral over gravitational fields in the proper-time gauge is explicitly worked out. The corresponding propagation amplitude results after the following steps: (i) evaluating the amplitude for a transition between two three-geometries for which one specifies the relative pointwise proper-time separation and relative spatial coordinate system, (ii) integrating over all positive proper-time separations with a logarithmic measure, (iii) averaging over all possible choices of the relative coordinate system. (An explicit expression for the measure over the diffeomorphism group in terms of a set of ghost fields emerges from the path integral.)

Causality Versus Gauge Invariance in Quantum Gravity and Supergravity

Abstract: It is proposed that one should admit in the path integral for the quantized gravitational field only those space-times for which the final three-geometry is located in the future of the initial one. As a consequence, and unlike the situation for the Yang-Mills field, the resulting causal amplitude is not annihilated by all the gauge (surface deformation) generators. In supergravity the causal amplitude turns out not to be annihilated by the local supersymmetry generators either.

Null cone computation of gravitational radiation

Abstract: The production of gravitational waves is explored, both analytically and numerically, using a null cone formulation of axially symmetric gravitational and matter fields. The coupled field equations are written in an integral form, on a single conformally compactified patch, which is well suited for numerical computation. Some analytic and numerical solutions of the initial value problem are given. The total mass and radiation flux is studied in detail for a special class of collapsing dust configurations.

The Gravitational Potential Due to Uniform Disks and Rings

Abstract: The gravitational potential of bodies possessing axial symmetry can be expressed as a power series in distance, with the Legendre polynomials as coefficients. Such series, however, converge so slowly in the neighborhood of thin, uniform disks and rings that too many series terms must be summed in order to obtain an accurate field measure. A gravitational potential expression is presently obtained in closed form, in terms of complete elliptic integrals.

The Earth's shape and gravity field: a report of progress from 1958 to 1982

Abstract: Summary. A major step forward in geophysics during the last 25 years has been the progress in the determination of the Earth’s shape and gravity field, from the halting steps of the first satellite orbit analyses to the global solutions expanded in spherical harmonics up to degree 36, and from painstaking gravity surveys on land to the detailed regional geoids derived from altimeter observations. No other geophysical quantity pertaining to lateral variations in the structure of the crust and mantle is now known with a comparable accuracy and spatial resolution. An increasingly acute problem has been to find ways to validate the global results since differences between individual solutions remain substantial. Absolute tests are not available but statistical comparisons produce some useful insight into the status of the recent gravity field models. A number of recent models are evaluated in this paper. A primary conclusion is that the gravity or geoid anomalies are frequently not as well determined as stated by the autbors. We estimate, for example, that the root mean square errors of the geoid heights deduced from models by Lerch et al. and Gaposchkin are about 3m and that maximum errors may exceed 10m in some places. A considerable part of this comes from uncertainties in the low degree harmonics, in particular the degree and order 3 coefficients and more generally the odd degree coefficients, for while the signal-to-noise ratio of these coefficients is high the power in the spectrum is also high. Most tests developed for evaluating the gravity fields are insensitive to the long wavelength components in the spatial spectrum. Future projects call particular attention to improving the high degree part of the geopotential spectrum but thought should also be given to these low degree harmonics. Considerable progress in determining the gravity field can still be made by using data already available.

On calculation of magnetic-type gravitation and experiments

Abstract: The linearized Einstein equations are written in the same form as the Maxwell equation. In the case of a weak stationary field and low velocity, the geodesic equations are written in the form of the Lorentz equation of motion. We suggest that the existence of the magnetic-type gravitation predicted by GR is equivalent to the existence of the gravitational wave predicted by GR. The Schiff effect is explained as one of the magnetic-type gravitation and the new effect is given. The Hall-type gravitational experiment is studied.

Rotating black hole in asymptotic de sitter space: perturbation of the space-time with spin fields

Abstract: The Newman-Penrose formalism is used to work with gravitational, electromagnetic, and Dirac field perturbations of the Kerr---de Sitter space. It is shown that the resulting equations are separable, and the radial parts (for the massless fields) combine into a master equation resembling that of Teukolsky. This master equation includes the Teukolsky equation and the equation arising from the de Sitter-Schwarzschild universe, and can be reduced to these cases under appropriate limiting conditions. Finally, the radial parts of the electromagnetic and neutrino fields are transformed to the form of the one-dimensional barrier-penetration equation.

The inner edge of Saturn's B ring

Abstract: The sharp, 90-km wide transition from an optical depth of 0.2 in the C ring to 1 in the B ring begins at 91,970 km from Saturn's center. This radius is found to be almost exactly at the inward stability limit of charged particles launched in the ring plane at the local Kepler velocity, provided these particles have large charge to mass ratio. The zonal harmonic models of Saturn's magnetic field from the Voyager data and the gravitational field model from Pioneer data are essential to get the very close agreement between theory and observation. The theoretical stability limits are 91,973 + or - 145 km from Voyager 1 magnetic field data and 91,991 + or 145 km from Voyager 2 magnetic data. The zonal harmonic magnetic field lines are not perpendicular to the ring plane. Therefore, in addition to the magnetic mirror, gravitational, and centrifugal forces, an unknown force must be postulated to produce equilibrium in the ring plane and make the stability calculation meaningful.

Inflation and time asymmetry in the Universe

Abstract: The recently proposed inflationary Universe scenario1–4 explains several of the mysteries of modern cosmology. I argue here that it also provides a natural explanation for the origin of time asymmetry (‘time's arrow’) in the Universe. The new feature which inflation injects into this long-standing problem is the temporary dominance of the cosmological term in the gravitational field equations, which acts as a sort of repulsive gravity. This term generates huge quantities of energy and radiation (or matter) entropy, while drastically reducing the entropy density of the gravitational field. It thus establishes a large gap between the radiation entropy and the gravitational entropy, which gravity is now trying to close.

Direct determination of gravitational harmonics from low‐low GRAVSAT data

Abstract: An efficient method is developed to compute gravitational harmonics from low-low satellite-satellite range rate measurements. The satellites are assumed to be in nearly the same low eccentricity orbits. The residual range rate signal is modeled with frequencies derived from linear perturbation theory to an accuracy of about 99%. Significant nonlinear effects involving J2, not currently modeled, require both J2 and J3 to be known in the reference trajectories. Each harmonic (l, m) generates l+ 1 principal frequencies, but they are not unique. Yet it appears possible to design a low-altitude mission which keeps the pair at nearly constant separation and where the frequencies for all terms to (180,180) are separable after only about 4 weeks. A simple demonstration of the method is shown to recover (in two iterations) a complete (4,4) model (less J2 and J3) from 1 day of “perfect” measurements (every 7 min) generated by numerical integration. In this result, the effects of orbit determination are included in a crude way, but no other gravitational effects (of higher degree or from luni-solar attraction) are present. Nevertheless, the method is easily extended to high degree with rapid new techniques (which are described) for calculating the required inclination functions of the orbits.

Gravitational effects in bubble collisions

Abstract: We investigate the effects of gravitation in the collision of two bubbles in the very early universe, using the thin-wall approximation. In general, the collision of two bubbles gives rise to modulus wall and a phase wave. The space-time metric and all physical quantities possess hyperbolic O(2,1) symmetry. We derive a generalized Birkhoff's theorem to show that the space-time in different regions must therefore be flat, de Sitter, pseudo-Schwarzschild, and pseudo-Schwarzschild-de Sitter, respectively. As in the spherically symmetric O(3) case, the space-time is Petrov type $D$, and so there is no gravitational radiation. Owing to the special symmetry of the space-time, the concentration of matter does not suffice to cause any gravitational collapse to a singularity no matter how severely the two bubbles collide. The modulus walls, viewed from the real vacuum region, eventually propagate outwards with kinks due to a series of collisions, in contrast to the situation in the absence of gravity.

Dynamical friction in a mean field approximation

Abstract: An exact formula is derived for the average frictional force acting upon a ‘test’ star which moves along a prescribed trajectory amongst a collection of ‘field’ stars which are characterized by a Maxwellian distribution of velocities. In the limit that the actual stellar trajectories may be approximated by their average forms, as determined by the mean gravitational field, one obtains a relatively simple expression which establishes an important connection with the fluctuation-dissipation theorem. For the case of an infinite, homogeneous system, one recovers Chandrasekhar's classical result. Alternatively, by allowing for the possibility of nearly periodic motion, one is led to new and intriguing phenomena.

Modeling in chaotic relativity

Abstract: The chaotic behavior of solutions to Einstein's equations has recently been studied by Barrow within the framework of the dynamical systems theory. Barrow's program of gravitational turbulence is implemented in part by considering the solutions of type VII/sub 0/ and IX as well as some intermediate types. Quantitative measures of chaos, such as the power spectrum and Lyapunov characteristic exponent, are computed. By converting the equations of motion for the cosmic scale factors to stochastic Langevin's equations, the Mixmaster cosmology in the presence of driving noise terms is investigated. Possible sources of noise can be attributed to an imperfect cancellation of the effective vacuum energy density and the energy density associated with the Higgs field. An ensemble average over random trajectories leads to the suppression of chaotic behavior for type-IX cosmology.

On spacelike congruences in general relativity

Abstract: The theory of spacelike congruences in general relativity is briefly reviewed and the physical interpretation of the rotation tensorR a b , the expansion E, and the shear tensorS a b , of the curves is discussed. It is proved that if the unit tangent vector to any curve of the congruence is everywhere orthogonal to the 4‐velocity field u a of a self‐gravitating fluid, then observers comoving with the fluid can be employed along a curve of the congruence if and only if the curves are material curves in the fluid. A congruence of vortex lines is studied in detail. Starting from the Ricci identity for u a and using Einstein’s equations, general expressions in terms of the kinematic quantities and fluid variables are derived for R a b , C, and S a b for a vortex congruence. It is found that E and S a b depend explicitly on the gravitational field only through the magnetic part of the Weyl tensor, and R a b only through a term proportional to the total energy flux q a derived from Einstein’s equations. With the aid of Maxwell’sequations, properties of congruences of magnetic field lines, electric field lines, and a certain combination of vortex and magnetic field lines are determined. For a congruence of magnetic field lines in an electrically conducting fluid and assuming the magnetohydrodynamic approximation of vanishing electric field, it is proved that for a comoving observer, R a b =0 if and only if the conduction current in the fluid is orthogonal to the magnetic field. The propagation equations for R a b , E, and S a b along a curve of a spacelike congruence are considered. These equations are developed in full for the special case of a congruence of material curves in a fluid. The divergence, or constraint, equation for the rotation vector is also derived. Where appropriate, corresponding results in Newtonian gravitation theory are given for comparison.

Inference of variations in the gravity field from satellite-to-satellite range rate

Abstract: An analytic scheme for inferring variations of the gravity field from satellite-to-satellite range rate (low-low) is developed. As a test, it is applied to a pair of satellites in polar orbit, at altitude 160 km and spacing 100 km, with 72 data points per revolution. An assumed gravity field of tesseral spherical harmonics up to the eighth degree is completely recovered in three iterations over 64 revolutions. It is apparent that data points at regular intervals enable the use of data analysis techniques that avoid massive matrix inversions.

The asymptotic near-tip solution for mode-III crack in steady growth in power hardening media

Abstract: Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.

Consequences of a New Experimental Determination of the Quadrupole Moment of the Sun for Gravitation Theory

Abstract: A preliminary experimental determination by Hill, Bos and Goode of the interior rotation of the sun leads to a nonzero value for the quadrupole-moment coefficient J/sub 2/ This produces a deviation of 16% from Einstein's prediction of the precession of the perihelion of Mercury A nonsymmetric gravitational theory can fit the measured precession with this J/sub 2/ and all other solar-system relativity experiments for one value of a post-Newtonian parameter in the theory A prediction is made for the perihelion precession of Icarus

GRM: observing the terrestrial gravity and magnetic fields in the 1990's.

Abstract: NASA is proposing to launch a new geopotential fields exploration system called the Geopotential Research Mission (GRM). Two spacecraft will be placed in a circular polar orbit at 160 km altitude. Distances between these satellites will vary from 100 to 600 km. Both scalar and vector magnetic fields will be measured by magnetometers mounted on a boom positioned in the forward direction on the lead satellite. Gravity data will be computed from the measured change in distance between the two spacecraft. This quantity, called the range-rate, will be determined from the varying frequency (Doppler shift) between transmitter and receiver on each satellite. Expected accuracies (at the one-sigma level) are: gravity field, 1.0 milliGal, 5 cm geoid height; magnetics, scalar field 2 nT, vector to 20 arcsec, both resolved to less than 100 km. With these more accurate and higher resolution data, it will be possible to investigate the earth's structure from the crust (with the shorter wavelength gravity and magnetic anomalies) through the mantle (from the intermediate wavelength gravity field) and into the core (using the longer wavelength gravity and magnetic fields).

A numerical study of the divergence of spherical harmonic series of the gravity and height anomalies at the earth's surface

Abstract: The problem of the divergence of the geopotential spherical harmonic series at the earth's surface is investigated from a numerical, rather than a theoretical, approach. A representative model of the earth's potential is devised on the basis of a density layer, which, in the spherical approximation, generates a gravity field whose harmonic constituents decay according to an accepted degree variance model. This field, expanded to degree 300, and a topographic surface specified to a corresponding resolution of 67 km are used to compute the differences between truncated inner and outer series of the gravity and height anomalies at the surface of the earth model. Up to degree 300, these differences attain RMS values from 0.33 μgal to 86 μgal for the gravity anomaly and from 0.32 μm to 410 μm for the height anomaly, in areas ranging respectively from near the equator to the vicinity of the pole. In addition to these values, there is an expected truncation effect, caused by the neglect of higher degree components of the inner series, of about 30 mgal and 36 cm, respectively. The field is then subjected to a Gaussian filter which effectively cuts off information at degree 300 (at the 5% level). The RMS error to degree 300 is thereby reduced by factors of 10 to 20, with a concomitant reduction in the truncation effect to about 0.3 mgal and 0.7 cm.

Equilibrium shapes of crystals in a gravitational field: Crystals on a table

Abstract: We consider the variational problem associated with the equilibrium shape of crystals resting on a table in a gravitational field. For two-dimensional crystals the shape can be calculated explicitly, i.e., reduced to quadrature. In three dimensions only qualitative results are available. The most interesting new result is that for large crystals, under suitable conditions, the top may be a corrugated facet or curved surface. The motivation for this work comes from lowtemperature experiments on helium crystals in equilibrium with the superfluid.