Showing papers on "Gravitational field published in 1991"

General-relativistic celestial mechanics. I. Method and definition of reference systems.

Abstract: We present a new formalism for treating the general-relativistic celestial mechanics of systems of $N$ arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such $N$-body systems ("external problem"), (ii) the local gravitational structure of each body ("internal problem"), and, (iii) the way the external and the internal problems fit together ("theory of reference systems"). This formalism uses in a complementary manner $N+1$ coordinate charts (or "reference systems"): one "global" chart for describing the overall dynamics of the $N$ bodies, and $N$ "local" charts adapted to the separate description of the structure and environment of each body. The main tool which allows us to develop, in an elegant manner, a constructive theory of these $N+1$ reference systems is a systematic use of a particular "exponential" parametrization of the metric tensor which has the effect of linearizing both the field equations, and the transformation laws under a change of reference system. This linearity allows a treatment of the first post-Newtonian relativistic celestial mechanics which is, from a structural point of view, nearly as simple and transparent as its Newtonian analogue. Our scheme differs from previous attempts in several other respects: the structure of the stress-energy tensor is left completely open; the spatial coordinate grid (in each system) is fixed by algebraic conditions while a convenient "gauge" flexibility is left open in the time coordinate [at the order $\ensuremath{\delta}t=O({c}^{\ensuremath{-}4})$]; the gravitational field locally generated by each body is skeletonized by particular relativistic multipole moments recently introduced by Blanchet and Damour, while the external gravitational field experienced by each body is expanded in terms of a particular new set of relativistic tidal moments. In this first paper we lay the foundations of our formalism, with special emphasis on the definition and properties of the $N$ local reference systems, and on the general structure and transformation properties of the gravitational field. As an illustration of our approach we treat in detail the simple case where each body can, in some approximation, be considered as generating a spherically symmetric gravitational field. This "monopole truncation" leads us to a new (and, in our opinion, improved) derivation of the Lorentz-Droste-Einstein-Infeld-Hoffmann equations of motion. The detailed treatment of the relativistic motion of bodies endowed with arbitrary multipole structure will be the subject of subsequent publications.

Exact scalar field cosmologies

Abstract: The authors consider exact cosmological solutions of the Einstein gravitational equations with a non-interacting combination of a classical scalar field and isotropic radiation as source. They show how a potential function for the scalar field can be found leading to desired volume behaviour of Robertson-Walker universes, and give a number of exact solutions of the coupled equations. These solutions in general do not obey the 'slow-rolling' approximation usually assumed in inflationary universe models.

The covariant phase space of asymptotically flat gravitational fields

Abstract: Publisher Summary This chapter discusses the covariant phase space of asymptotically flat gravitational fields and covariant constructions for field theories. In the case of general relativity, boundary conditions play a critical role and must be adjusted carefully for the symplectic structure to be finite and for the framework to be well-defined. The chapter presents a new application: the derivation of the expression of energy-momentum of an isolated gravitating system at null infinity. This derivation makes a crucial use of the covariant construction and cannot be carried out within the familiar, 3+1 phase space frameworks. The chapter presents a summarization of the basic ideas of the covariant procedure and the general framework for field theories on a background space-time. It reviews the covariant Hamiltonian description of gravitational fields in general relativity, which are asymptotically flat at spatial infinity. The chapter shows that the ADM 4-momentum is the generator of the asymptotic translation group, which arises from the boundary conditions. The chapter also discusses space-times that are asymptotically flat at null infinity.

Quantum gravitational corrections to the functional Schrodinger equation

Abstract: We derive corrections to the Schr\"odinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the gravitational constant. The correction terms fall into two classes: One describes the breakdown of the classical background picture while the other corresponds to quantum gravitational corrections for the matter fields themselves. The latter are independent of the factor ordering which is chosen for the gravitational kinetic term. If the total state evolves adiabatically, the only correction term that survives contains the square of the matter Hamiltonian. In the general case there are also smaller terms which describe a gravitationally induced violation of unitarity. The corrections are numerically extremely tiny except near the big bang and the final stages of a black hole. They are also of principle significance for quantum field theories near the Planck scale.

Superfluid hydrodynamics in rotating neutron stars. I : Nondissipative equations

Abstract: Newtonian hydrodynamic equations are developed which describe the outer-core regions of neutron stars composed of superfluid neutrons, superconducting protons, and degenerate electrons and muons. The equations include couplings to the gravitational and electromagnetic fields. They also include the effects of rotation and forces due to the elastic properties of the neutron and proton vortices. The set of equations is closed by constructing a model of the total energy density and using it to express the dependent variables in terms of the independent variables. The low-frequency-long-wavelength limit of the equations is determined.

Holonomy and path structures in general relativity and Yang-Mills theory

Abstract: This article is about a different representation of the geometry of the gravitational field, one in which the paths of test bodies play a crucial role. The primary concept is the geometry of the motion of a test body, and the relation between different such possible motions. Space-time as a Lorentzian manifold is regarded as a secondary construct, and it is shown how to construct it from the primary data. Some technical problems remain. Yang-Mills fields are defined by their holonomy in an analogous construction. I detail the development of this idea in the literature, and give a new version of the construction of a bundle and connection from holonomy data. The field equations of general relativity are discussed briefly in this context.

Einstein equivalence principle and the polarization of radio galaxies.

Abstract: The theoretical foundations of metric theories of gravitation rest largely on the Einstein equivalence principle (EEP). Schiff has conjectured that no consistent Lorentz-invariant theory can obey the weak equivalence principle and not obey the EEP. However, a counterexample has been proposed by Ni in a theoretical framework for studying electromagnetism coupled to gravity. Under the assumption that gravitational fields vary smoothly over a Hubble time, we show that Ni's counterexample would lead to a rotation in the plane of polarization of radiation from distant ratio sources

New measurement of solar gravitational deflection of radio signals using VLBI

Abstract: RADIO observations using very-long-baseline interferometry (VLBI) can measure the deflection of electromagnetic radiation by the Sun's gravitational field with an accuracy of better than 1 milliarcsecond, and can thus be used to test General Relativity For an object at an angle a from the centre of the Sun, the expected deflection is1 (1 + γ) (Ms/re)((l + cos α)/(l-cos α))1/2, where Ms is the mass of the Sun in geometrized units2 (1477 × 105 cm), re is the distance from the Earth to the Sun in cm, and y is a parameter whose value is 1 if General Relativity is correct but which takes on different values in other theories of gravity For γ = 1, the deflection is 1,750 mas at the Sun's limb, 4 mas at α =90° and 0 at α = 180° Our analysis of ten years of VLBI data, including observations of objects in the range 25° < a< 178°, yields an estimate γ = 10002 with a formal standard error of 000096 and an estimated standard error of 0002 This determination is comparable in accuracy and in good agreement with the determination from Mars–Viking time-delay measurements3

Two Lectures on Fermions and Gravity

Abstract: In these two lectures we want to provide information on the behavior of elementary particles in special relativity (SR), such as electrons, protons, or neutrons, in order to get ideas of the underlying principles of the gravitational interaction of fermions. For tangible matter and for the electromagnetic field, Einstein’s gravitational theory, general relativity (GR), describes all phenomena very well and has been verified experimentally with ever increasing accuracy. In contrast therefrom, not too much is known experimentally for fermions and their gravitational interaction, apart from the celebrated Colella-Overhauser-Werner (or COW) experiment [21] using a neutron interferometer in a gravitational field.

The gravitational field of a global monopole

Abstract: The authors present an exact solution to the non-linear equation which describes a global monopole in the flat space. They re-examine the metric and the geodesics outside the global monopole. They show that a global monopole produces a repulsive gravitational field outside the core in addition to a solid anglar deficit. The lensing property of the global monopole and the global monopole-antimonopole annihilation mechanism are studied.

Semiclassical gravity in 1+1 dimensions.

Abstract: Relativistic wave equations are solved exactly in the classical space-time background of a two-dimensional gravitational theory. In the simplest nontrivial geometry without horizons, the solutions are necessarily bound states and the constraints on the energy eigenvalues are determined. Aspects of quantum field theory in the background of the (1+1)-dimensional black hole are also examined.

Reformulation of Stokes's theory for higher than second‐degree reference field and modification of integration kernels

Abstract: An argument is put forward in favor of using a model gravity field of a degree and order higher than 2 as a reference in gravity field studies. Stokes's approach to the evaluation of the geoid from gravity anomalies is then generalized to be applicable to a higher than second-order reference spheroid. The effects of truncating Stokes's integration and of modifying the integration kernels are investigated in the context of the generalized approach. Several different modification schemes, starting with a Molodenskij-like modification and ending with the least squares modification, are studied. Particular attention is devoted to looking at both global and local biases and mean square errors of the individual schemes.

Potential and gravity changes raised by point dislocations

Abstract: SUMMARY We derive expressions in closed form which give the gravity potential changes caused by point dislocations. They enable us to evaluate coseismic changes in surface gravity and geoid height. Numerical simulation shows that a great earthquake could cause a geoid height change of order 1 m.

Automatic interpretation of gravity gradiometric data in two dimensions: vertical gradient1

Abstract: The magnetic and gravity field produced by a given homogeneous source are related through Poisson's equation. Starting from this consideration, it is shown that some 2D interpretation tools, widely applied in the analysis of aeromagnetic data, can also be used for the interpretation of gravity gradiometric data (vertical gradient). This paper deals specifically with the Werner deconvolution, analytic signal and Euler's equation methods. After a short outline of the mathematical development, synthesized examples have been used to discuss the efficiency and limits of these interpretation methods. These tools could be applied directly to airborne gravity gradiometric data as well as ground gravity surveys after transformation of the Bouguer anomalies into vertical gradient anomalies. An example is given of the application of the Werner deconvolution and Euler's equation methods to a microgravity survey.

Neutrino helicity flip from gravity-spin coupling.

Abstract: It is suggested that the rotation-spin coupling predicted by Mashhoon may lead, in the case of neutrinos, to a helicity flip that has implications for astrophysical objects such as rotating neutron stars and supernovae. The coupling is generalized here to include gravitational fields and total angular momentum and is derived by solving the covariant Dirac and Maxwell-Proca equations exactly to first order in the metric deviation ${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\mu}}\ensuremath{ u}}$. For fermions the spin part of the effect also applies to gravitational fields of arbitrary strength.

Seismic tomography constrained by bouguer gravity anomalies: Applications in western Washington

Abstract: Tomographic inversions for velocity variations in western Washington indicate a high correlation with surface geology and geophysical measurements, including gravity observations. By assuming a simple linear relationship between density and velocity (Birch's law) it is possible to calculate the gravity field predicted from the velocity perturbations obtained by local tomographic inversion. While the predicted gravity matches observations in parts of the model, the overall correlation is not satisfactory. In this paper we suggest a method of constraining the tomographic inversion to fit the gravity observations simultaneously with the seismic travel time data. The method is shown to work well with synthetic data in 3 dimensions where the assumption of Birch's law holds strictly. If the sources of the gravity anomalies are assumed to be spatially localized, integration can be carried out over a relatively small volume below the observation points and sparse matrix techniques can be applied. We have applied the constrained inversion method to western Washington using 4,387 shallow earthquakes, to depths of 40.0 km, (36,865 raypaths) convering a 150×250 km region and found that the gravitational constraints may be satisfied with minor effect on the degree of misfit to the seismic data.

General Structure of the Gravitational Equations of Motion in Conformal Weyl Gravity

Abstract: A general method for determining the structure of the gravitational equations of motion is presented in the fourth-order theory of gravity based on local conformal Weyl invariance of the gravitational action. The explicit structure for these equations is given for a time-dependent, spherically symmetric geometry.

Can the Sun shed light on neutrino gravitational interactions

Abstract: We have examined the effects of a large gravitational field on the phenomenon of neutrino oscillations as contemplated in the Mikheyev-Smirnov-Wolfenstein mechanism. We find that the Sun's gravitational field would amplify any small breakdown in the universality of the gravitational coupling by many orders of magnitude. A breakdown of only 1 part in 10{sup 14} would still make the gravitational effect comparable to the conventional weak interaction. The differing energy dependences of the two level-crossing mechanisms can therefore be used as a very sensitive tool to test the conventional universality hypothesis.

Gravitational field of a hedgehog and the evolution of vacuum bubbles.

Abstract: The gravitational field produced by a spherically symmetric hedgehog'' configuration in scalar field theories with global SO(3) symmetry (or higher) is studied in the limit in which these models become nonlinear {sigma} models. The same gravitational effect can be generated by a set of cosmic strings intersecting at a point, in the limit that one considers a continuous distribution of such intersecting strings in a spherically symmetric configuration (to be referred to as the string hedgehog''). When the energy densities associated with the hedgehog are small, we obtain a static geometry, but for higher values, the resulting geometry is that of an anisotropic cosmology. The evolution of bubbles joining two phases, one of which contains a hedgehog (as defined above) is investigated. The role of such configurations in processes that lead to classical false-vacuum destabilization and in the evolution of inflationary bubbles is discussed. The generalization of our results to the gauged case, i.e., to magnetic-monopole hedgehogs, is discussed.

Temporal variation of the Earth's low‐degree zonal gravitational field caused by atmospheric mass redistribution: 1980–1988

Abstract: Temporal variations in the low-degree zonal harmonics of the earth's gravitational field have recently been observed by satellite laser ranging. A host of geophysical processes contribute to these variations. The present paper studies quantitatively a prime contributor, atmospheric mass redistribution, using ECMWF global surface pressure data for the period of 1980-1988. The annual and semiannual amplitudes and phases of the zonal J(l) coefficient with degree l = 2-6 with and without the oceanic inverted-barometer (IB) effect are computed to obtain the predicted effects on the orbit nodal residuals of Lageos and Starlette. These predicted values are then compared with observations. It is found that the atmospheric influence, combined with the hydrological influence agree well with the Lageos observation for the annual term. The corresponding match appears poorer for Starlette.

Analysis of gravity-induced particle motion and fluid perfusion flow in the NASA-designed rotating zero-head-space tissue culture vessel

Abstract: The gravity induced motions, through the culture media, is calculated of living tissue segments cultured in the NASA rotating zero head space culture vessels. This is then compared with the media perfusion speed which is independent of gravity. The results may be interpreted as a change in the physical environment which will occur by operating the NASA tissue culture systems in actual microgravity (versus unit gravity). The equations governing particle motions which induce flows at the surface of tissues contain g terms. This allows calculation of the fluid flow speed, with respect to a cultured particle, as a function of the external gravitational field strength. The analysis is approached from a flow field perspective. Flow is proportional to the shear exerted on a structure which maintains position within the field. The equations are solved for the deviation of a particle from its original position in a circular streamline as a function of time. The radial deviation is important for defining the operating limits and dimensions of the vessel because of the finite radius at which particles necessarily intercept the wall. This analysis uses a rotating reference frame concept.

Optimum data weighting and error calibration for estimation of gravitational parameters

Abstract: A new approach has been developed for determining consistent satellite-tracking data weights in solutions for the satellite-only gravitational models. The method employs subset least-squares solutions of the satellite data contained within the complete solution and requires that the differences of the parameters of subset solutions and the complete solution to be in agreement with their error estimates by adjusting the data weights. GEM-T2 model was recently computed and adjusted through a direct application of this method. The estimated data weights are markedly smaller than the weights implied by the formal uncertainties of the measurements. Orbital arc tests as well as surface gravity comparisons show significant improvements for solutions when more realistic data weighting is achieved.

The rotation of LAGEOS

Abstract: In view of the need of an accurate modelling of nongravitational forces on laser-tracked satellites, it is important to understand their rotational dynamics, which determines the temperature anisotropy and the ensuing radiation recoil effects. We propose a model of the torques acting on LAGEOS due to eddy currents and gravity gradient. The electromotive forces induced in the spacecraft by its rotation in the magnetic field of the Earth dissipate angular momentum and produce a precession of the spin axis; the oblate spacecraft will precess in the gravitational field of the Earth at a rate proportional to the rotation period. Therefore the gravitational torques become more and more important with time and eventually may produce a chaotic dynamics. The predicted evolution of the spin period agrees very well with the few experimental data available and corresponds to an approximately exponential growth rate of about 3 years.

Tensor-multi-scalar theories of gravitation

Abstract: A generic class of theories where gravity is mediated by one tensor field together with an arbitrary number of scalar fields is considered. The predictions of these theories are worked out in four different observationally relevant regimes: (i) quasi-stationary weak fields (solar system conditions); (ii) rapidly varying weak fields (gravitational wave experiments); (iii) quasi-stationary strong fields (motion of systems of compact bodies, i.e. neutron stars or black holes); and (iv) the mixing of strong and radiative field effects in the gravitational radiation of N-compact-body systems. Moreover, the authors derive several significant relations between the theoretical quantities entering these predictions. They show how strong-field-gravity effects in the motion and gravitational radiation of N-compact-body systems can be parametrized by a set of theory parameters that generalize the usual post-Newtonian parameters ( gamma , beta ,. . .) introduced in the context of quasi-stationary weak gravitational fields. These new parameters ( beta 2, beta ', beta 3, beta ",. . .) provide a chart for the yet essentially unexplored domain of strong-gravitational-field effects, and thereby suggest new directions for testing relativistic gravity. This is illustrated by studying in detail a specific two-parameter tensor-bi-scalar theory T( beta ', beta ") which has the same post-Newtonian limit as general relativity but leads to new nonEinsteinian predictions for the various observables that can be extracted from binary pulsar data.

Generalization of Kerr spacetime

Abstract: A class of exact solutions of the Einstein-Maxwell equations is presented It represents the exterior gravitational field of a charged rotating mass The class contains a generalization of the charged Kerr metric involving an infinite set of parameters that pertain to an axisymmetric deformation of the source

Scale‐invariant gravity in two dimensions

Abstract: The vacuum field equations are solved in a V 2 following from the scale‐invariant gravitational Lagrangian £=R k+1. For £=R 2, exactly six solutions exist. Just one of them breaks the scale‐invariance and has indefinite signature. For k→0, nontrivial results also arise. Their relation to two‐dimensional quantum gravity is discussed. For £=F(R) a Birkhoff‐type theorem holds.

Submarine measurement of the Newtonian gravitational constant.

Abstract: We have measured the Newtonian gravitational constant using the ocean as an attracting mass and a research submersible as a platform for gravity measurements. Gravitational acceleration was measured along four continuous profiles to depths of 5000 m with a resolution of 0.1 mGal. These data, combined with satellite altimetry, sea surface and seafloor gravity measurements, and seafloor bathymetry, yield an estimate of C=(6.677±0.013)×10 -11 m 3 s -2 kg -1 ; the fractional uncertainty is 2 parts in 1000

A Measurement of Planetary Relativistic Deflection

Abstract: The technique of differential VLBI, over two DSN California-Australia baselines, is used to measure the angular deflection of the ray path of P0201 + 113 when it passed within 200 arcsec of Jupiter on March 21, 1988. Its angular position was measured 10 times over 4 hr on that date, with a similar measurement set on April 2, 1988, to detect the differential angular deflection of the ray path. According to general relativity, the expected gravitational bend of the ray path averaged over the March experiment duration was approximately 300 microarcsec, projected onto the two California-Australia baselines over which it was measured. Measurement accuracies of the order of 160 microarcsec were obtained for each of the ten differential measurements. The chi(2) per degree of freedom of the data for the noise and tropospheric fluctuations fully accounted for the scatter in the measured angular deflections. The chi(2) per degree of freedom for the hypothesis of no gravitational deflection by Jupiter was 4.1, which rejects the no-deflection hypothesis with greater than 99.999-percent confidence.