Showing papers on "Gravitational field published in 1986"

Radiative gravitational fields in general relativity I. general structure of the field outside the source

Abstract: We present a well-defined formal framework, together with appropriate mathematical tools, which allow us to implement in a constructive way, and to investigate in full mathematical details, the Bonnor-Thorne approach to gravitational radiation theory. We show how to construct, within this framework, the general radiative (formal) solution of the Einstein vacuum equations, in harmonic coordinates, which is both past-stationary and past-asymptotically Minkowskian. We investigate the structure of the latter general radiative metric (including all tails and nonlinear effects) both in the near zone and in the far zone. As a side result it is proven that post-Newtonian expansions must be done by using the gauge functions (lg c)^p/c^n (p, n = positive integers).

Kinematic Resonance and Memory Effect in Free Mass Gravitational Antennas

Abstract: Detailed studies are made of two effects in the motion of free masses subject to the influence of gravitational waves: kinematic resonance and the memory effect. In the first of these, besides the oscillatory motion there is a systematic change in the distance between the bodies if they become free in an appropriate phase of the gravitational wave. The second effect takes the form that the distance between a pair of bodies will, in general, be different from the original distance after they have been influenced by a pulse of gravitational radiation. Possible practical applications of these effects in three different experimental programs are discussed. Allowance for these effects should lessen the requirements on the detection systems and ultimately raise the sensitivity of gravitational antennas.

Spinning cosmic strings and quantization of energy.

Abstract: It is shown that energy should be quantized if there exist cosmic spinning strings. Quantization of energy arises naturally from the fact that the wave function must be single valued in the gravitational field of a spinning string. This effect arises when the vortexlike vacuum configurations carry constant nonzero angular momentum per unit length. Spinning strings occur naturally in spontaneously broken grand unified theories. A limit on $J$ coming from the upper limit of the photon mass is presented. The analogy with quantization of energy in the presence of gravitational magnetic mass is established.

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.

Spherical harmonic expansions of the Earth's gravitational potential to degree 360 using 30' mean anomalies

Abstract: Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360.

Motion of particles and photons in the gravitational field of a rotating body (In memory of Vladimir Afanas'evich Ruban)

Abstract: A study is made of the trajectories of free motion of test particles and photons in the Kerr metric, which describes the gravitational field of a rotating massive body. The trajectories are classified on the basis of the integrals of the motion, which have a clear physical meaning. The cases of a strong gravitational field in the neighborhood of a rotating black hole as well as the weak-field approximation describing the motion of particles in the gravitational field of a rotating star or galaxy are considered. The review includes bound states (orbits) in the field of a rotating mass, scattering and gravitational capture of particles and photons by a rotating black hole, trajectories of falling into a black hole, and the bending of light rays and the gravitational time delay of signals in the gravitational field of a rotating body.

Ephemeris errors of GPS satellites

Abstract: Ephemeris errors are supposed to be a major factor limiting the usefulness ofGPS in high precision geodesy. Considerations of orbital mechanics suggest that, regardless of their complexity, the uncertainties in the solar radiation pressure model, the gravity field model, and the estimated initial state, may have simple effects on the ephemeris. This possibility has been tested by fitting linear combinations of simple functions—chosen on theoretical grounds—to simulated errors of three-day ephemerides. With a set of five functions for the across-track component, six for the radial, and seven for the along-track, it has been possible to fit the position errors to better than 1% of theirr.m.s values, in all the caces studied. The simulations included —besides solar radiation pressure errors—gravity field model and initial state uncertainties, as well as an unknown constant force along the axis of the solar panels. The solar radiation force was calculated taking into account the shape, orientation, and physical properties (reflectivity and specularity) of the main parts of the spacecraft, under various conditions of illumination (continuous sunlight, eclipses, etc.).

Multipole expansions of the general-relativistic gravitational field of the external universe

Abstract: The generic, vacuum, dynamical gravitational field in the vicinity of a freely falling observer is expanded in powers of distance away from the observer's spatial origin (i.e., in distance away from his timelike-geodesic world line). The expansion is determined fully, aside from coordinate freedom, by two families of time-dependent multipole moments: ''electric-type moments'' and ''magnetic-type moments'': which characterize the gravitational influence of the external universe. These ''external multipole moments'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives, evaluated on the observer's world line. The properties of these moments are discussed, and an analysis is given of the structure of the gravitational field's multipole expansion for the special case of de Donder coordinates. In de Donder coordinates the expansion involves only integral powers of distance from the origin; no logarithmic terms occur in this multiparameter expansion.

Two-fluid cosmological models

Abstract: Homogeneous and isotropic, relativistic two‐fluid cosmological models are investigated. In these models two separate fluids act as the source of the gravitational field, as represented by the FRW line element. The general theory of two‐fluid FRW models in which neither fluid need be comoving or perfect is developed. However, attention is focused on the physically interesting special class of flat FRW models in which one fluid is a comoving radiative perfect fluid and the second a noncomoving imperfect fluid. The first fluid is taken to model the cosmic microwave background and the second to model the observed material content of the universe. One of the motivations of the present work is to model the observed velocity of our galaxy relative to the cosmic microwave background that was recently discovered by G. F. Smoot, M. V. Gorenstein, and R. A. Muller [Phys. Rev. Lett. 39, 898 (1977)]. Several models within this special class are found and analyzed. The models obtained are theoretically satisfactory in ...

Cylindrical waves in general relativity

Abstract: A convenient framework is set up for constructing cylindrically symmetric solutions of the Einstein and the Einstein-Maxwell equations, and it is shown how a Hamiltonian density can be defined for space-times with cylindrical symmetry. Solutions are obtained that represent stationary monochromatic waves and satisfy all the requisite conditions of regularity. The case when the gravitational field is coupled with a perfect fluid in which the energy density is equal to the pressure is also briefly considered.

Choice of norm for the density distribution of the Earth

Abstract: Summary. The determination of the density distribution of the Earth from gravity data is called the inverse gravimetric problem. A unique solution to this problem may be obtained by introducing a priori data concerning the covariance of density anomalies. This is equivalent to requiring the density to fulfil a minimum norm condition. The generally used norm is the one equal to the integral of the square of the density distribution (L2-norm), the use of which implies that blocks of constant density are uncorrelated. It is shown that for harmonic anomalous density distributions this leads to an external gravity field with a power spectrum (degree-variances) which tends too slowly to zero, i.e. implying gravity anomalies much less correlated than actually observed. It is proposed to use a stronger norm, equal to the integral of the square sum of the derivatives of the density distribution. As a consequence of this, base functions which are constant within blocks, are no longer a natural choice when solving the inverse gravimetric problem. Instead a block with a linearly varying density may be used. A formula for the potential of such a block is derived.

The ADM Hamiltonian at the postlinear approximation

Abstract: The ADM Hamiltonian for a many-particle system is calculated up to the postlinear approximation, i.e., to the approximation that both the equations of motion for the particles and the equations of motion for the gravitational field in case of no-incoming radiation correctly result up to the postlinear approximation. The relation of this Hamiltonian to the ADM Hamiltonian obtained by a post-Newtonian approximation scheme which was applied up to the first radiation-reaction and radiation levels is discussed. From here the standard formulas for the mechanical angular momentum and energy losses as well as the radiated energy and angular momentum are deduced. Background logarithmic and logarithmic radiative terms are shown to be not present at our approximation if the condition of no-incoming radiation is fulfilled.

The Newtonian Limit of Fourth-Order Gravity

Abstract: The weak-field slow-motion limit of fourth-order gravity will be discussed. Let us consider the gravitational theory defined by the Lagrangian Lg = (8πG) −1 ( R/2 + (αRijR ij + βR)l ) . (1) G is Newton’s constant, l a coupling length and α and β numerical parameters. Rij and R are the Ricci tensor and its trace. Introducing the matter Lagrangian Lm and varying Lg + Lm one obtains the field equation Eij + αHij + βGij = 8πGTij . (2) For α = β = 0 this reduces to General Relativity Theory. The explicit expressions Hij and Gij can be found in STELLE (1978). In a well-defined sense, the weak-field slow-motion limit of Einstein’s theory is just Newton’s theory, cf. DAUTCOURT (1964). In the following we consider the analogous problem for fourth order gravity eqs. (1), (2). For the special cases α = 0 (PECHLANER, SEXL(1966), POLIJEVKTOVNIKOLADZE (1967)), α + 2β = 0 (HAVAS (1977), JANKIEWICZ (1981)) 1 and α+ 3β = 0 (BORZESZKOWSKI, TREDER, YOURGRAU (1978)) this has already been done in the past. Cf. also ANANDAN (1983), where torsion has been taken into account. The slow-motion limit can be equivalently described as the limit c→ ∞, where c is the velocity of light. In this sense we have to take the limit G→ 0 while G · c and l remain constants. Then the energy-momentum tensor Tij reduces to the rest mass density ρ: Tij = δ 0 i δ 0 j ρ , (3) x = t being the time coordinate. The metric can be written as ds = (1 − 2φ)dt − (1 + 2ψ)(dx + dy + dz) . (4) Now eqs. (3) and (4) will be inserted into eq. (2). In our approach, products and time derivatives of φ and ψ can be neglected, i.e., R = 4∆ψ − 2∆φ , where ∆f = f,xx + f,yy + f,zz . Further R00 = −∆φ, H00 = −2∆R00 − ∆R and G00 = −4∆R, where l = 1. Then it holds: The validity of the 00-component and of the trace of eq. (2), R00 −R/2 + αH00 + βG00 = 8πGρ (5) and − R− 4(α+ 3β)∆R = 8πGρ , (6) imply the validity of the full eq. (2). Now, let us discuss eqs. (5) and (6) in more details: Eq. (5) reads − ∆φ−R/2 + α(2∆∆φ− ∆R) − 4β∆R = 8πGρ . (7)

A plane symmetric cosmological model in Lyra manifold

Abstract: A non-static plane-symmetric cosmological model in Lyra's manifold is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some properties of the model have also been discussed.

Similarity considerations and conservation laws for magneto-static atmospheres

Abstract: The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

Instability of De Sitter Space on Short Time Scales

Abstract: We consider the Einstein gravitational field equations coupled to the expectation value of the stress tensor in a real scalar field theory with arbitrary mass and coupling to curvature. We consider small oscillations of the metric and linearize the response of the quantum wave functional and the stress-tensor expectation value. In a small-time approximation we find unstable oscillations for a minimally coupled field and stable oscillations in the case of conformal coupling.

Seasat‐derived gravity over the Musicians Seamounts

Abstract: The two-dimensional gravity field over the Musicians seamount province in the Pacific Ocean has been derived from Seasat altimetry. Geoid maps were produced by fitting a minimum curvature surface to the sea surface height measurements. As a check on the quality of this interpolation method, we also gridded the data using weighted grid point averages. Fourier transforms of both the geoid and geoid gradient were used to determine the gravity field. We have compared gravity maps produced these different ways in order to identify the problems involved in pushing Seasat data to the limits of its spatial resolution and accuracy. Our minimum-curvature interpolation scheme was determined to be the more accurate and cost effective mapping method, while gravity obtained by transforming the geoid produced more reliable gravity maps. The bathymetry of this area was used to predict the gravity field by filtering the bathymetry under the assumption that it is regionally compensated by a thin elastic plate. Gravity fields predicted for a variety of effective elastic thicknesses were compared to the Seasat-derived gravity, particularly in areas with good track coverage. The derived gravity tends to favor a thin plate with an effective elastic thickness of ∼5 km, though the east-west ridges in the south display a smaller signal more consistent with Airy compensation. This variation may be indicative of early fracturing of the lithosphere in the south, or it may be a manifestation of the age difference and early thermal structure across the Murray fracture zone, which separates the seamount province into northern and southern sections. Neighboring seamounts with different flexural signatures, particularly in the south, may indicate that volcanism occurred in the same location over an extended period of time.

Geometrical structures for cosmological applications

Abstract: A set of conditions for selecting geometrical structures appropriate for cosmological applications is suggested. These conditions are being applied to two geometrical structures constructed mainly for cosmological applications. The algebraic manipulation language REDUCE 2 has been used to carry out the relevant calculations. Without the help of a computer, the calculations involved are very tedious. The results obtained show that one of the two structures should be ruled out as a model for cosmological applications. The combination of the results of the present paper and those of a previous one support the procedure known as ‘The Type Analysis’.

Exact power law metrics in cosmology

Abstract: Spatially homogeneous and non-exceptional spatially self-similar spacetime metrics which are 'exact power law metrics' are defined, explicitly parametrised and shown to have fixed conformal 3-geometry in the natural slicing of the spacetime by the orbits of the symmetry group and to admit a homothetic Killing vector field not tangent to that slicing. In fact the exact power metrics are exactly those spatially homogeneous and spatially self-similar metrics which admit a homothetic Killing vector field not tangent to the spacelike orbits of the homogeneity or self-similarity group. Such metrics arise as 'singular point solutions' of gravitational field equations when formulated as a certain system of first order differential equations. These special exact solutions play an important role in the qualitative behaviour of the general solution of a given set of field equations and sources with these symmetries.

The Representation of the Earth's Gravitational Potential in a Spherical Harmonic Expansion to Degree 250,

Abstract: : The gravitational potential of the earth has been presented in a spherical harmonic series that is complete to degree and order 250. This solution has been obtained by first carrying out a combination of satellite derived potential coefficients (GEML2') with a set of 1 deg by 1 deg mean free air anomalies. These anomalies were formed from a merger of a June 1986 terrestrial set and a set derived from Geos-3/Sesat altimeter data. The combination solution was carried out after making downward continuation corrections to the surface anomalies and ellipsoidal corrections to the a priori potential coefficients. The adjustment yielded 582 potential coefficients and 64800 1 deg by 1 deg anomalies. Two combination solutions were made, one (OSU86C) that excluded geophysically predicted anomalies and one (OSU86D) that included 5547 such anomalies. The potential coefficients are determined through an optimal estimation procedure where, primarily, sampling error was minimized. Tests of the new solution were made by comparing undulation residuals at Doppler stations, and by using the field, up to degree 36, in orbit calculations. In North American the root mean square undulation difference was + or - 1.55 m. The undulation residuals are found to correlated with elevation although it is not clear why.

Possible anisotropic phases in the early universe and gravitational wave background

Abstract: We discuss possible anisotropic and inhomogeneous phases in the early Universe at relatively late epochs corresponding to the temperatures 1 GeV–10 TeV. The anisotropy and inhomogeneity of the energy-momentum tensor at the horizon scale gives rise to the generation of a stochastic gravitational wave background. It is shown that the present amplitudes and frequencies of this background may be well within the access of planned gravitational wave detectors.