Showing papers on "Gravitational field published in 1994"

Leading quantum correction to the Newtonian potential

Abstract: I argue that the leading quantum corrections, in powers of the energy or inverse powers of the distance, may be computed in quantum gravity through knowledge of only the low-energy structure of the theory. As an example, I calculate the leading quantum corrections to the Newtonian gravitational potential.

Bathymetric prediction from dense satellite altimetry and sparse shipboard bathymetry

Abstract: The southern oceans (south of 30°S) are densely covered with satellite-derived gravity data (track spacing 2–4 km) and sparsely covered with shipboard depth soundings (hundreds of kilometers between tracks in some areas). Flexural isostatic compensation theory suggests that bathymetry and downward continued gravity data may show linear correlation in a band of wave-lengths 15–160 km, if sediment cover is thin and seafloor relief is moderate. At shorter wave-lengths, the gravity field is insensitive to seafloor topography because of upward continuation from the seafloor to the sea surface; at longer wavelengths, isostatic compensation cancels out most of the gravity field due to the seafloor topography. We combine this theory with Wiener optimization theory and empirical evidence for gravity noise-to-signal ratios to design low-pass and band-pass filters to use in predicting bathymetry from gravity. The prediction combines long wavelengths (>160 km) from low-pass-filtered soundings with an intermediate-wavelength solution obtained from multiplying downward continued, band-pass-filtered (15–160 km) gravity data by a scaling factor S. S is empirically determined from the correlation between gravity data and existing soundings in the 15–160 km band by robust regression and varies at long wave-lengths. We find that areas with less than 200 m of sediment cover show correlation between gravity and bathymetry significant at the 99% level, and S may be related to the density of seafloor materials in these areas. The prediction has a horizontal resolution limit of 5–10 km in position and is within 100 m of actual soundings at 50% of grid points and within 240 m at 80% of these. In areas of very rugged topography the prediction underestimates the peak amplitudes of seafloor features. Images of the prediction reveal many tectonic features not seen on any existing bathymetrie charts. Because the prediction relies on the gravity field at wavelengths <160 km, it is insensitive to errors in the navigation of sounding lines but also cannot completely reproduce them. Therefore it may be used to locate tectonic features but should not be used to assess hazards to navigation. The prediction is available from the National Geophysical Data Center in both digital and printed form.

The Feynman path integral approach to atomic interferometry: A tutorial

Abstract: Many problems of current interest in atomic interferometry lend themselves to a path integral treatment. We present a practical guide to solving such problems, taking as examples the gravitational experiments of Kasevich and Chu, and the atomic equivalents of the Sagnac and Aharonov-Bohm effects. Atomic interferometry is a new and rapidly-developing field of research, concerned with physical phenomena in which the wave-nature of neutral atoms plays an important role ill. The wide variety of internal degrees of freedom of an atom opens up new possibilities for investigation which do not exist in the more traditional types of interferometry using photons, electrons and neutrons. The development of atomic interferometry has been aided by recent technical advances, particularly in the manipulation of atoms. New mechanisms for slowing, deflecting, cooling and trapping atoms allow control of both their position and momentum. Also important has been the birth of "atomic optics", a range of mechanisms providing the equivalent of mirrors, beamsplitters and lenses for atoms. Recently it has been pointed out that certain high-resolution spectroscopy techniques which avoid the Doppler effect amount to realizing an atomic interferometer (2). These methods have since been adapted to measure inertial fields (due to rotation and gravitation) by atomic interferometry. The situation encountered in atomic interferometry experiments is often close to the classical limit. When this is the case a path integral approach to the analysis is very appropriate since it reduces to a calculation of integrals along classical paths. Further simplifications can be made if the Lagrangian is quadratic, as is true for a particle in a gravitational field or a rotating (*) The Laboratoire Kastler Brossel is associated with the CNRS and the Universit4 Pierre et Marie

The gravitational potential of a homogeneous polyhedron or don't cut corners

Abstract: A polyhedron can model irregularly shaped objects such as asteroids, comet nuclei, and small planetary satellites. With minor effort, such a model can incorporate important surface features such as large craters. Here we develop closed-form expressions for the exterior gravitational potential and acceleration components due to a constant-density polyhedron. An equipotential surface of Phobos is illustrated.

Gravity model development for TOPEX/POSEIDON: Joint gravity models 1 and 2

Abstract: The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model-1 (JGM-1) and the postlaunch JGM-2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM-2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being +/- 25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3-4 cm root mean square (RMS), a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.

Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation

Abstract: We study the interior structure of a locally conformal invariant fourth order theory of gravity in the presence of a static, spherically symmetric gravitational source. We find, quite remarkably, that the associated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case. We present the solutions to this fourth order equation and find that we are able to recover all of the standard Newton-Euler gravitational phenomenology in the weak gravity limit, to thus establish the observational viability of the weak field limit of the fourth order theory. Additionally, we make a critical analysis of the second order Poisson equation, and find that the currently available experimental evidence for its validity is not as clearcut and definitive as is commonly believed, with there not apparently being any conclusive observational support for it at all either on the very largest distance scales far outside of fundamental sources, or on the very smallest ones within their interiors. Our study enables us to deduce that even though the familiar second order Poisson gravitational equation may be sufficient to yield Newton's Law of Gravity it is not in fact necessary.

Semiclassical equations for weakly inhomogeneous cosmologies

Abstract: The in-in effective action formalism is used to derive the semiclassical correction to Einstein's equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the back-reaction effect on the gravitational field of the string is discussed.

Fast Parallel Tree Codes for Gravitational and Fluid Dynamical N-Body Problems

Abstract: : We discuss two physical systems from separate disciplines that make use of the same algorithmic and mathematical structures to reduce the number of operations necessary to complete a realistic simulation. In the gravitational N- body problem, the acceleration of an object is given by the familiar Newtonian laws of motion and gravitation. The computational load is reduced by treating groups of bodies as single multipole sources rather than individual bodies. In the simulation of incompressible flows, the flow may be modeled by the dynamics of a set of N interacting vortices. Vortices are vector objects in three dimensions, but their interactions are mathematically similar to that of gravitating masses. The multipole approximation can be used to greatly reduce the time needed to compute the interactions between vortices. Both types of simulations were carried out on the Intel Touchstone Delta, a parallel MIMD computer with 512 processors. Timings are reported for systems of up to 10 million bodies, and demonstrate that the implementation scales well on massively parallel systems. The majority of the code is common between the two applications, which differ only in certain physics modules. In particular, the code for parallel tree construction and traversal is shared.

Fermi coordinates for weak gravitational fields.

Abstract: We derive the Fermi coordinate system of an observer in arbitrary motion in an arbitrary weak gravitational field valid to all orders in the geodesic distance from the world line of the observer. In flat space-time this leads to a generalization of Rindler space for arbitrary acceleration and rotation. The general approach is applied to the special case of an observer resting with respect to the weak gravitational field of a static mass distribution. This allows us to make the correspondence between general relativity and Newtonian gravity more precise.

Basic properties and gravity wave initiation of the midlatitude F region instability

Abstract: Observations of midlatitude spread F irregularities have shown that the most violent eruptions are often periodic and may be related to modulations of the F region bottomside. Similar aspects of equatorial spread F have been conclusively shown to be the result of seeding by atmospheric gravity waves. In this paper, we pursue a nonlinear description of the midlatitude F region instability first proposed by Perkins (1973) and show that, by itself, this instability saturates at approximately 1%. With gravity wave seeding, however, the growth of the instability is significantly enhanced and progresses until it is limited by third- or fourth-order nonlinearities. In the course of the analysis we expand the Perkins linear instability study, particularly with regard to the wave propagation angles suitable for stimulating linearly unstable, and eventually, nonlinear turbulent upwellings. Although gravity waves themselves have limited spatial extent, we also show that gravity waves which propagate perpendicular to the Earth's magnetic field create electric fields which map along the field lines to considerable distances. This transmission of electric fields is dependent on both the particular characteristics of the ionosphere along the field lines and the wavelength of the perturbation, but under certain circumstances, gravity wave-induced large-scale electric fields can map to the F region from either the E or conjugate F region and thus influence F region electrodynamics. Finally, we note that our results are consistent with observations of midlatitude spread F irregularities by the MU radar in Japan and large-scale perturbations of the F region over Arecibo.

Impact of altered gravity on aspects of cell biology

Abstract: Publisher Summary This chapter summarizes the progress that has been made in determining and understanding the effect of gravity on cell function. It describes the results from three general areas of spaceflight research, and within each area, focuses on specific cell systems for which sufficient data have been accumulated. Included are (1) cell physiology, with a focus on immune cell activation; (2) cell development, with a focus on plant cell differentiation; and (3) the physiology of unicellular organisms. In addition, the chapter describes the underlying principles that govern spaceflight research on the cell, and examines experimental approaches used to investigate the effects of altered gravity on cell function. One environmental factor that has remained constant throughout evolution is the force of earth's gravitational field. The cardiovascular system counteracts gravity when it pumps blood to the upper body, but also uses the pull of gravity when it distributes fluid to the lower extremities. These well-known adaptations to gravity become clearly evident during manned orbital spaceflight, where the inertial acceleration caused by gravitational force is virtually canceled and the gravity vector is no longer detectable. In this microgravity environment, where mass is nearly weightless, astronauts experience space motion sickness, muscle atrophy and bone demineralization, as well as cardiovascular deconditioning and the redistribution and pooling of body fluids in the upper body.

Edge states in Gravity and Black Hole Physics

Abstract: We show in the context of Einstein gravity that the removal of a spatial region leads to the appearance of an infinite set of observables and their associated edge states localized at its boundary. Such a boundary occurs in certain approaches to the physics of black holes like the one based on the membrane paradigm. The edge states can contribute to black hole entropy in these models. A ``complementarity principle" is also shown to emerge whereby certain ``edge" observables are accessible only to certain observers. The physical significance of edge observables and their states is discussed using their similarities to the corresponding quantities in the quantum Hall effect. The coupling of the edge states to the bulk gravitational field is demonstrated in the context of (2+1) dimensional gravity.

Striking property of the gravitational Hamiltonian.

Abstract: A Hamiltonian framework for (2+1)-dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically flat context. It is shown that the total energy of the system is non-negative, vanishing if and only if space-time is (globally) Minkowskian. Furthermore, contrary to one's experience with usual field theories, the Hamiltonian is bounded from above. This is a genuinely nonperturbative result. In the presence of a spacelike Killing field, (3+1)-dimensional vacuum general relativity is equivalent to (2+1)-dimensional general relativity coupled to certain matter fields. Therefore, our expression provides, in particular, a formula for energy per-unit length (along the symmetry direction) of gravitational waves with a spacelike symmetry in 3+1 dimensions. A special case is that of cylindrical waves which have two hypersurface orthogonal, spacelike Killing fields. In this case, our expression is related to the ``c energy'' in a nonpolynomial fashion. While in the weak field limit the two agree, in the strong field regime they differ significantly. By construction, our expression yields the generator of the time translation in the full theory, and therefore represents the physical energy in the gravitational field.

Gravitational instability of cold matter

Abstract: We solve the nonlinear evolution of pressureless, irrotational density fluctuations in a perturbed Robertson-Walker spacetime using a new Lagrangian method based on the velocity gradient and gravity gradient tensors. Borrowing results from general relativity, we obtain a set of Newtonian ordinary differential equations for these quantities following a given mass element. Using these Lagrangian fluid equations we prove the following results: (1) The spherical tophat perturbation, having zero shear, is the slowest configuration to collapse for a given initial density and growth rate. (2) Initial density maxima are not generally the sites where collapse first occurs. (3) Initially underdense regions may undergo collapse if the shear is not too small. If the magnetic part of the Weyl tensor vanishes, the nonlinear evolution is described purely locally by our equations; this condition holds for spherical, cylindrical, and planar perturbations and may be a good approximation in other circumstances. Assuming the vanishing of the magnetic part of the Weyl tensor, we compute the exact nonlinear gravitational evolution of cold matter. We find that 56\% of initially underdense regions collapse in an Einstein-de Sitter universe for a homogeneous and isotropic random field. We also show that, given this assumption, the final stage of collapse is generically two-dimensional, leading to strongly prolate filaments rather than Zel'dovich pancakes. While this result may explain the prevalence of filamentary collapses in N-body simulations, it is not true in general, suggesting that the magnetic part of the Weyl tensor need not vanish in the Newtonian limit.

Is the gravitational action additive

Abstract: The gravitational action is not always additive in the usual sense. We provide a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified. We discuss possible implications for the superposition law of quantum gravity. We present a definition of ``generalized additivity'' which does hold for arbitrary spacetime composition.

Gravity changes and deformation due to a magmatic intrusion in a two-layered crustal model

Abstract: We develop and extend theoretical and computational methods for the calculation of the deformation, gravity and potential change due to a point source of magma injection into a multilayered, elastic-gravitational earth model. In our calculations, which are based upon the method outlined by Rundle, two distinct layers overlying a half-space may be incorporated. The source can be located in either of the layers or the half-space. The method is quite general, and can be readily adapted to calculations in which stresses in either the layers or the half-space relax by viscoelastic flow. The results obtained indicate that the use of homogeneous half-space to represent the Earth may in some cases be too simple a model and that variations in elastic moduli have a more significant effect than variation in reference density on both the surface displacements and gravity changes. As an example, we calculate the displacement and gravity changes due to a subsurface mass injection in a crust-mantle model appropriate to the volcanic island of Lanzarote, which is presently the subject of numerous geophysical experiments. Both historical and recent data indicate that Lanzarote may be subject to some risk of volcanic eruption in the future, thus our calculations may be useful in interpreting observations of preemption phenomena. The results are discussed in terms of prediction versus measurement capabilities.

Some special orbits in the two-body problem with radiation pressure

Abstract: The motion has been studied of a particle in a gravitational field perturbed by radiation pressure By combining the formulation in the physical space variables with the KS variables we obtained explicit evidence for the existence of a surface of stable circular orbits with centers on an axis through the primary body Furthermore, the effects of a sharp shadow on the two-dimensional unstable parabolic orbits were investigated It was found that they do not survive the introduction of a shadow

An active vertical-direction gravity compensation system

Abstract: To perform simulations of partial or microgravity environments on Earth requires some method of compensation for the Earth's gravitational field. This paper discusses an active compensation system that modulates the tension in a counterweight support cable in order to minimize state deviation between the compensated body and the ideal weightless body. The system effectively compensates for inertial effects of the counterweight mass, viscous damping of all pulleys, and static friction in all parts of the gravity compensation (GC) system using a hybrid PI (proportional plus integral)/fuzzy control algorithm. The dynamic compensation of inertia and viscous damping is performed by PI control, while static friction compensation is performed by the fuzzy system. The system provides a very precise gravity compensation force, and is capable of nonconstant gravity force compensation in the case that the payload mass is not constant. >

General Relativistic Hydrodynamics with a Roe solver

Abstract: We present a numerical method to solve the equations of general relativistic hydrodynamics in a given external gravitational field. The method is based on a generalization of Roe's approximate Riemann solver for the non relativistic Euler equations in Cartesian coordinates. The new method is applied to a set of standard test problems for general relativistic hydrodynamics, and is shown to perform well in comparison to existing numerical schemes. In contrast to existing explicit methods the present method can cope with strong relativistic shocks. By-products are: the characteristic form of the general relativistic Euler equations, a numerical method for special relativity that can deal with strong discontinuities, a numerical scheme for the integration of the Euler equations in an arbitrary coordinate system, possibly under the influence of (external) gravity, and a novel method to incorporate source terms in numerical schemes.