Showing papers on "Gravitational field published in 1998"

Time variability of the Earth's gravity field: Hydrological and oceanic effects and their possible detection using GRACE

Abstract: The GRACE satellite mission, scheduled for launch in 2001, is designed to map out the Earth's gravity field to high accuracy every 2–4 weeks over a nominal lifetime of 5 years. Changes in the gravity field are caused by the redistribution of mass within the Earth and on or above its surface. GRACE will thus be able to constrain processes that involve mass redistribution. In this paper we use output from hydrological, oceanographic, and atmospheric models to estimate the variability in the gravity field (i.e., in the geoid) due to those sources. We develop a method for constructing surface mass estimates from the GRACE gravity coefficients. We show the results of simulations, where we use synthetic GRACE gravity data, constructed by combining estimated geophysical signals and simulated GRACE measurement errors, to attempt to recover hydrological and oceanographic signals. We show that GRACE may be able to recover changes in continental water storage and in seafloor pressure, at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer, with accuracies approaching 2 mm in water thickness over land, and 0.1 mbar or better in seafloor pressure.

The Search for Non-Newtonian Gravity

Abstract: 1 Introduction.- 2 Phenomenological Description of Non-Newtonian Gravity.- 3 Searches for Composition-Independent Effects.- 4 Searches for Composition-Dependent Effects.- 5 Gravitational Properties of Antimatter.- 6 Effects of External Forces in the Kaon System.- 7 Spin-Dependent Intermediate-Range Forces.- 8 Epilogue.- A Gravity-Gradient Couplings to Torsion Pendants.- B Luther-Towler Cavendish Experiment.- C The Earth's Gravity Field.- Author Index.

Precise orbit determination and gravity field improvement for the ERS satellites

Abstract: The radial orbit error has long been the major error source in ERS-1 altimetry, crippled by having only satellite laser ranging for precise tracking and relying on insufficiently accurate general-purpose gravity field models. Altimeter crossovers are used very effectively as additional tracking data to laser ranging. The ERS Tandem Mission even provides the unique possibility to simultaneously determine orbits of two similar satellites flying the same orbit. Altimeter crossovers between the two satellites then link the two orbits into a common reference frame. Tailoring of the Joint Gravity Model 3 (JGM 3) is another step to reduce orbit errors. This technique is aimed at the reduction of the geographically anticorrelated orbit error (observed in the crossover height differences) through the adjustment of selected gravity field parameters. The resulting Delft Gravity Model (DGM)-E04 has reduced this part of the orbit error by a factor of 2, performs even better with respect to the ESA-provided orbits, and also outperforms the recent Earth Geopotential Model EGM96 in this respect. ERS-1 and ERS-2 orbits for the entire Tandem Mission are computed and studied in detail, and orbit errors due to the gravity field and nonconservative forces are identified. Analyses systematically show that the orbits computed with JGM 3 have a radial root-mean-square orbit accuracy of 7 cm, with DGM-E04 5 cm.

Spherically symmetric solutions of the Schrodinger-Newton equations

Abstract: As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrodinger-Newton equations. For a single particle, this is a coupled system consisting of the Schrodinger equation for the particle moving in its own gravitational field, where this is generated by its own probability density via the Poisson equation. Restricting to the spherically-symmetric case, we find numerical evidence for a discrete family of solutions, everywhere regular, and with normalizable wavefunctions. The solutions are labelled by the non-negative integers, the nth solution having n zeros in the wavefunction. Furthermore, these are the only globally defined solutions. Analytical support is provided for some of the features found numerically.

Measurement of the Earth's Gravity Gradient with an Atom Interferometer-Based Gravity Gradiometer

Abstract: We report the demonstration of an atom interferometer-based gravity gradiometer. The gradiometer uses stimulated two-photon Raman transitions to measure the relative accelerations of two ensembles of laser cooled atoms. We have used this instrument to measure the gradient of the Earth's gravitational field.

Global marine gravity field from the ERS-1 and Geosat geodetic mission altimetry

Abstract: Satellite altimetry from the Geosat and the ERS-I Geodetic Missions provide altimeter data with very dense spatial coverage. Therefore the gravity field may be recovered in great detail. As neighboring ground tracks are very closely distributed, cross-track variations in the sea surface heights are extremely sensitive to sea surface variability. To avoid errors in the gravity field caused by such effects, sea surface variability needs to be carefully eliminated from the observations. Initially, a careful removal of gross errors and outliers was performed, and the tracks were fitted individually to a geoid model and crossover adjusted using bias and tilt. Subsequently, sea surface heights were gridded using local collocation in which residual ocean variability was considered. The conversion of the heights into gravity anomalies was carried out using the fast Fourier transform (FFT). In this process, filtering was done in the spectral domain to avoid the so-called “orange skin” characteristics. Comparison with marine gravity was finally carried out in three different regions of the Earth to evaluate the accuracy of the global marine gravity field from ERS-1 and Geosat.

Gravitational waves from inspiraling compact binaries: The quadrupole-moment term

Abstract: A rotating star's oblateness creates a deformation in the gravitational field outside the star, which is measured by the quadrupole-moment tensor. We consider the effect of the quadrupole moment on the orbital motion and rate of inspiral of a compact binary system, composed of neutron stars and/or black holes. We find that in the case of circular orbits, the quadrupole-monopole interaction affects the relation between orbital radius and angular velocity, and also the rate of inspiral, by a quantity of order ${(v/c)}^{4}$, where $v$ is the orbital velocity and $c$ the speed of light.

Gravitational wave versus binary - pulsar tests of strong field gravity

Abstract: Binary systems comprising at least one neutron star contain strong gravitational field regions and thereby provide a testing ground for strong-field gravity. Two types of data can be used to test the law of gravity in compact binaries: binary pulsar observations, or forthcoming gravitational-wave observations of inspiralling binaries. We compare the probing power of these two types of observations within a generic two-parameter family of tensor-scalar gravitational theories. Our analysis generalizes previous work (by us) on binary-pulsar tests by using a sample of realistic equations of state for nuclear matter (instead of a polytrope), and goes beyond a previous study (by C.M. Will) of gravitational-wave tests by considering more general tensor-scalar theories than the one-parameter Jordan-Fierz-Brans-Dicke one. Finite-size effects in tensor-scalar gravity are also discussed.

Quantum theory of gravitation

Abstract: It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2) There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation

Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order

Abstract: We derive the gravitational field and equations of motion of compact binary systems up to the 5/2 post-Newtonian approximation of general relativity (where radiation-reaction effects first appear). The approximate post-Newtonian gravitational field might be used in the problem of initial conditions for the numerical evolution of binary black-hole space-times. On the other hand we recover the Damour-Deruelle 2.5PN equations of motion of compact binary systems. Our method is based on an expression of the post-Newtonian metric valid for general (continuous) fluids. We substitute into the fluid metric the standard stress-energy tensor appropriate for a system of two point-like particles. We remove systematically the infinite self-field of each particle by means of the Hadamard partie finie regularization.

On the multipole expansion of the gravitational field

Abstract: The multipole expansion (in general relativity) of the gravitational field generated by a slowly-moving isolated source is constructed. We introduce some definitions for the source multipole moments, valid to all orders in a post-Newtonian expansion, and depending in a well defined way on the total stress-energy pseudo-tensor of the material and gravitational fields. The source moments parametrize the linearized approximation of the gravitational field exterior to the source, as computed by means of a specific post-Minkowskian algorithm defined in a previous work. Since the radiative multipole moments parametrizing the radiation field far from the source can be obtained as nonlinear functionals of the source moments, the present paper allows one to relate the radiation field far from a slowly-moving source to the stress-energy pseudo-tensor of the source. This should be useful when comparing theory with the future observations of gravitational radiation by the LIGO and VIRGO experiments.

Effective Nonlocal Euclidean Gravity

Abstract: A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newtonian constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value Ω < 1 for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.

Gravitational Signature of Jupiter's Deep Zonal Flows

Abstract: Calculations predict that, if Jupiter's observed zonal flows persist to a depth ∼1000 km below the cloud layers (corresponding to a pressure ∼10 kbar), they will produce gravity anomalies on the order of a few mgal in high-degree zonal components of the gravitational field, referenced to the field expanded to tenth degree. This signature would be detectable by a low-periapse Jupiter orbiter with a sensitivity to accelerations at the same level as the Galileo orbiter.

Superluminal censorship

Abstract: We argue that ``effective'' superluminal travel, potentially caused by the tipping over of light cones in Einstein gravity, is always associated with violations of the null energy condition (NEC) This is most easily seen by working perturbatively around Minkowski spacetime, where we use linearized Einstein gravity to show that the NEC forces the light cones to contract (narrow) Given the NEC, the Shapiro time delay in any weak gravitational field is always a delay relative to the Minkowski background, and never an advance Furthermore, any object travelling within the lightcones of the weak gravitational field is similarly delayed with respect to the minimum traversal time possible in the background Minkowski geometry

Equations of motion of a spinning relativistic particle in external fields

Abstract: We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields to first order in the external field but to arbitrary order in the spin. The influence of the spin on the particle trajectory is properly accounted for by describing the spin noncovariantly. Specific calculations are performed through second order in the spin. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a particular spin effect in general relativity. We show that for a Kerr black hole the gravimagnetic ratio, i.e., the coefficient of the GM, equals unity (just as the gyromagnetic ratio equals 2 for a charged Kerr hole). The equations of motion obtained for a spinning relativistic particle in an external gravitational field differ substantially from the Papapetrou equations.

Performance of three types of Stokes's kernel in the combined solution for the geoid

Abstract: When regional gravity data are used to compute a gravimetric geoid in conjunction with a geopotential model, it is sometimes implied that the terrestrial gravity data correct any erroneous wavelengths present in the geopotential model. This assertion is investigated. The propagation of errors from the low-frequency terrestrial gravity field into the geoid is derived for the spherical Stokes integral, the spheroidal Stokes integral and the Molodensky-modified spheroidal Stokes integral. It is shown that error-free terrestrial gravity data, if used in a spherical cap of limited extent, cannot completely correct the geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer a preferable approach. This is because they can filter out a large amount of the low-frequency errors expected to exist in terrestrial gravity anomalies and thus rely more on the low-frequency geopotential model, which currently offers the best source of this information.

Weighted Euler deconvolution of gravity data

Abstract: Euler deconvolution is used for rapid interpretation of magnetic and gravity data. It is particularly good at delineating contacts and rapid depth estimation. The quality of the depth estimation depends mostly on the choice of the proper structural index and adequate sampling of the data. The structural index is a function of the geometry of the causative bodies. For gravity surveys, station distribution is in general irregular, and the gravity field is aliased. This results in erroneous depth estimates. By weighting the Euler equations by an error function proportional to station accuracies and the interstation distance, it is possible to reject solutions resulting from aliasing of the field and less accurate measurements. The technique is demonstrated on Bouguer anomaly data from the Charlevoix region in eastern Canada.

Relevance of Newtonian seismic noise for the VIRGO interferometer sensitivity

Abstract: In this paper we analyse the noise level induced by changes in the mass density distribution around the Virgo interferometric antenna. These stochastic mass density fluctuations generate a gravitational field which couples directly to the mirrors of the optical apparatus, and it could be relevant if the planned final sensitivity of the Virgo interferometer is to be reached.

Optimum expression for computation of the gravity field of a polyhedral body with linearly increasing density

Abstract: The formula for the computation of the gravity field of a polyhedral body whose density is linearly dependent on some coordinate is derived and transformed into the optimum form for numerical calculation.

Anisotropic stresses in inhomogeneous universes

Abstract: Anisotropic stress contributions to the gravitational field can arise from magnetic fields, collisionless relativistic particles, hydrodynamic shear viscosity, gravitational waves, skew axion fields in low-energy string cosmologies, or topological defects. We investigate the effects of such stresses on cosmological evolution, and in particular on the dissipation of shear anisotropy. We generalize some previous results that were given for homogeneous anisotropic universes, by including small inhomogeneity in the universe. This generalization is facilitated by a covariant approach. We find that anisotropic stress dominates the evolution of shear, slowing its decay. The effect is strongest in radiation-dominated universes, where there is slow logarithmic decay of shear. ©1998 The American Physical Society.

A Free-Fall Determination of the Newtonian Constant of Gravity

Abstract: Recent determinations of the Newtonian constant of gravity have produced values that differ by nearly 40 times their individual error estimates (more than 0.5%). In an attempt to help resolve this situation, an experiment that uses the gravity field of a one-half metric ton source mass to perturb the trajectory of a free-falling mass and laser interferometry to track the falling object was performed. This experiment does not suspend the test mass from a support system. It is therefore free of many systematic errors associated with supports. The measured value was G = (6.6873 +/- 0. 0094) x 10(-11) m3 kg-1 sec-2.

General Relativistic Effects of Gravity in Quantum Mechanics A Case of Ultra-Relativistic, Spin 1/2 Particles

Abstract: We present a general relativistic framework for studying gravitational effects in quantum mechanical phenomena. We concentrate our attention on the case of ultra-relativistic, spin-1/2 particles propagating in Kerr spacetime. The two-component Weyl equation with general relativistic corrections is obtained in the case of a slowly rotating, weak gravitational field. Our approach is also applied to neutrino oscillations in the presence of a gravitational field. The relative phase of two different mass eigenstates is calculated in radial propagation, and the result is compared with those of previous works.

Continuous gravity recording with Scintrex CG‐3M meters:a promising tool for monitoring active zones

Abstract: We acquired continuous series of microgravity measurements using several Scintrex CG-3M gravity meters for several weeks in 1997. The meters with 1 mGal resolution were installed side by side in a stable reference station at the ORSTOM research centre to perform identical data acquisition. We present and compare the instrumental responses obtained for the various gravity meters (measurement series of gravity field, standard deviation, internal temperature, tilts) and analyse their correlation with simultaneous recordings of meteorological parameters. The data have been processed in order to (1) establish the mid-to long-term relative stability and the accuracy of the instruments, (2) estimate the contribution of instrumental effects to gravity data measurements and (3) quantify the amplitude of the time variations of the gravity field that might be detected with such instruments. This study emphasizes the sensitivity of some instrumental responses of the Scintrex CG-3M gravity meters (such as internal temperature or tilt) to local atmospheric-pressure variations. This sensitivity can lead to non-negligible perturbations of the gravity measurements through automatic corrections applied in real-time mode by the integrated software. We show that most of these instrumental artefacts can be easily removed in data post-processing by using simultaneous atmospheric-pressure data. After removal of an accurate Earth tide model, the instrumental drift and the instrumental effects, the temporal series are compared by computing differential signals. These residual signals obtained over a period of several weeks exhibit the following characteristics: (1) the gravity residuals have a maximum amplitude ranging from 5 to 10 mGal and from 10 to 15 μGal for filtered and unfiltered data, respectively; and (2) the standard error, tilts and internal temperature measurements of the various gravity meters are very consistent; their respective residual amplitudes are ±2 mGal, ±3 arcsec and ±0.05 mK. In order to calibrate the gravity meters precisely in the measurement range used in this study, we have measured a calibration line established in the framework of the fourth intercomparison of absolute and relative gravity meters. This calibration was achieved with an accuracy of 5 μGal. This result is consistent with other field tests already performed with such gravity meters. In addition, we also checked the accuracy of the tilt sensors by increasing the electronic read-out by a factor of 10. The tilt response of the whole gravity meter to a small induced inclinometric variation indicates that the precision of the tilt measurements is about a few tenths of an arc second. This study reveals that temporal variations of the gravity field could potentially be detected in the field with an accuracy of about 5–15 mGal by permanent networks of Scintrex CG-3M gravity meters set up a few kilometres apart. This result is of particular interest in field surveys of temporal gravity changes related to some environmental or geodynamical processes, where the expected gravity variations are greater than a few tens of mGal. In particular, in volcanological applications, the continuous monitoring of active volcanoes with such permanent networks of gravity meters co-located with subcentimetre-accuracy GPS receivers should be very helpful to understand internal magmatic processes better and to detect possible gravity and inclinometric signals occurring during pre-eruptive phases. In this field, continuous microgravity recordings associated with classical reiteration networks will probably improve hazard mitigation in the near future

Gravitational wave extraction and outer boundary conditions by perturbative matching

Abstract: We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three-dimensional numerical relativity code.

General solution to two-scalar field cosmologies with exponential potentials

Abstract: We find the exact general solution for cosmological models arising from the interaction of the gravitational field with two scalar fields in both flat Robertson - Walker and the locally rotationally symmetric Bianchi I spacetime filled with an exponential potential. One scalar field self-interacts with this potential and the other is a free massless scalar field. The solutions have a singularity and a set of these exhibit the transition to power-law inflation for both metrics.

Relativistic Theory of Gravity

Abstract: This paper presents a brief critical analysis of General Relativity Theory (GRT). It is shown that the theory, if accepted, leads to repudiation of a number of fundamental principles underlying physics. The article also presents the construction of Relativistic Theory of Gravitation (RTG) in which the gravitational field possesses all the attributes of physical fields and which concurs completely with the fundamental physical principles as well as with the available experimental and observational facts. It also considers the consequences of RTG, dealing, in particular, with the development of collapse and Universe evolution.

Gravitational waves from collapsing vacuum domains

Abstract: Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA(DART-HEP-98/03 February 5, 2008)The breaking of an approximate discrete symmetry, thefinal stages of a first order phase transition, or a post-inflationary biased probability distribution for scalar fields arepossible cosmological scenarios characterized by the presenceof unstable domain wall networks. Combining analytical andnumerical techniques, we show that the non-spherical collapseof these domains can be a powerful source of gravitationalwaves. We compute their contribution to the stochastic back-ground of gravitational radiation and explore their observabil-ity by present and future gravitational wave detectors.04.30.Db, 98.80.Cq

A weakly nonlinear theory for the dynamical rayleigh-taylor instability

Abstract: The dynamics of an interface between two incompressible, inviscid, irrotational, and immiscible liquids with densities ρ1 and ρ2 under the influence of a time-dependent gravitational field g(t) is investigated. A Hamiltonian formulation of the system is adopted leading to a perturbative expansion of the equations of motion for the canonical variables. Equations, accurate up to third order in the perturbation amplitude are derived. They are able to describe the initial stage of instability “saturation.” The latter equations are integrated iteratively for two standard limiting cases: constant gravity (classical Rayleigh–Taylor instability), g(t)≡g0, and impulsive Richtmyer–Meshkov loading, g(t)=v0δ(t−t0). The comparative growth of various two-dimensional structures and rectangular and hexagonal cells is evaluated. Surface tension effects are considered.

Effect of gravity on contact angle: A theoretical investigation

Abstract: Using the Gibbs description of an interphase, the necessary conditions for equilibrium of a closed, two-phase fluid system in the presence of gravity are the Laplace and Young equations and a condition on the chemical potentials. The last condition has been neglected in all previous examinations of contact angles in a gravitational field. After introducing explicit expressions for the chemical potentials, we find that the condition on the chemical potentials can be used to determine the pressure profile within the system. In a “two-interface” system in which a liquid phase is both above and below a vapor phase and the vapor phase forms a solid–vapor interphase in one region, the pressure profile in the liquid phases is the same as it would have been if the vapor phase were not there; thus in a gravitational field, the pressure is smaller in the liquid phase above the vapor phase than it is in the liquid phase below the vapor phase. This results in the contact angle at the upper three-phase line necessarily being smaller than that at the lower three-phase line. This difference in contact angles is conventionally referred to as contact angle hysteresis; however, we show that it is simply an equilibrium property of a capillary system in a gravitational field. The contact angle difference predicted to exist in the presence of gravity does not violate the Young equation, but the Young equation does impose a restriction on the equilibrium adsorption isotherms at the solid–vapor and solid–liquid interfaces.