Showing papers on "Gravitational field published in 2002"

Methods for inferring regional surface‐mass anomalies from Gravity Recovery and Climate Experiment (GRACE) measurements of time‐variable gravity

Abstract: [1] The Gravity Recovery and Climate Experiment, GRACE, will deliver monthly averages of the spherical harmonic coefficients describing the Earth's gravity field, from which we expect to infer time-variable changes in mass, averaged over arbitrary regions having length scales of a few hundred kilometers and larger, to accuracies of better than 1 cm of equivalent water thickness. These data will be useful for examining changes in the distribution of water in the ocean, in snow and ice on polar ice sheets, and in continental water and snow storage. We describe methods of extracting regional mass anomalies from GRACE gravity coefficients. Spatial averaging kernels were created to isolate the gravity signal of individual regions while simultaneously minimizing the effects of GRACE observational errors and contamination from surrounding glacial, hydrological, and oceanic gravity signals. We then estimated the probable accuracy of averaging kernels for regions of arbitrary shape and size.

Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution

Abstract: From gravity and topography data collected by the Mars Global Surveyor spacecraft we calculate gravity/topography admittances and correlations in the spectral domain and compare them to those predicted from models of lithospheric flexure. On the basis of these comparisons we estimate the thickness of the Martian elastic lithosphere (T_e) required to support the observed topographic load since the time of loading. We convert T_e to estimates of heat flux and thermal gradient in the lithosphere through a consideration of the response of an elastic/plastic shell. In regions of high topography on Mars (e.g., the Tharsis rise and associated shield volcanoes), the mass-sheet (small-amplitude) approximation for the calculation of gravity from topography is inadequate. A correction that accounts for finite-amplitude topography tends to increase the amplitude of the predicted gravity signal at spacecraft altitudes. Proper implementation of this correction requires the use of radii from the center of mass (collectively known as the planetary “shape”) in lieu of “topography” referenced to a gravitational equipotential. Anomalously dense surface layers or buried excess masses are not required to explain the observed admittances for the Tharsis Montes or Olympus Mons volcanoes when this correction is applied. Derived T_e values generally decrease with increasing age of the lithospheric load, in a manner consistent with a rapid decline of mantle heat flux during the Noachian and more modest rates of decline during subsequent epochs.

A high‐quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN‐1S)

Abstract: [1] Using three months of GPS satellite-to-satellite tracking and accelerometer data of the CHAMP satellite mission, a new long-wavelength global gravity field model, called EIGEN-1S, has been prepared in a joint German-French effort. The solution is derived solely from analysis of satellite orbit perturbations, i.e. independent of oceanic and continental surface gravity data. EIGEN-1S results in a geoid with an approximation error of about 20 cm in terms of 5 × 5 degree block mean values, which is an improvement of more than a factor of 2 compared to pre-CHAMP satellite-only gravity field models. This impressive progress is a result of CHAMP's tailored orbit characteristics and dedicated instrumentation, providing continuous tracking and direct on-orbit measurements of non-gravitational satellite accelerations.

An Exact Anisotropic Quark Star Model

Abstract: We present an exact analytical solution of the gravitational field equa- tions describing a static spherically symmetric anisotropic quark matter distribution. The radial pressure inside the star is assumed to obey a linear equation of state, while the tangential pressure is a complicated function of the radial coordinate. In order to obtain the general solution of the field equations a particular density profile inside the star is also assumed. The anisotropic pressure distribution leads to an increase in the maximum radius and mass of the quark star, which in the present model is around three solar masses.

Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

Abstract: The propagation of light in the gravitational field of self-gravitating spinning bodies moving with arbitrary velocities is discussed The gravitational field is assumed to be ``weak'' everywhere The equations of motion of a light ray are solved in the first post-Minkowskian approximation which is linear with respect to the universal gravitational constant G We do not restrict ourselves to the approximation of a gravitational lens so that the solution of light geodesics is applicable for arbitrary locations of the source of light and the observer This formalism is applied for studying corrections to the Shapiro time delay in binary pulsars caused by the rotation of the pulsar and its companion We also derive the correction to the light deflection angle caused by the rotation of gravitating bodies in the solar system (Sun, planets) or a gravitational lens The gravitational shift of frequency due to the combined translational and rotational motions of light-ray-deflecting bodies is analyzed as well We give a general derivation of the formula describing the relativistic rotation of the plane of polarization of electromagnetic waves (Skrotskii effect) This formula is valid for arbitrary translational and rotational motion of gravitating bodies and greatly extends the results of previous researchers Finally, we discuss the Skrotskii effect for gravitational waves emitted by localized sources such as a binary system The theoretical results of this paper can be applied for studying various relativistic effects in microarcsecond space astrometry and developing corresponding algorithms for data processing in space astrometric missions such as FAME, SIM, and GAIA

Atomic clocks and inertial sensors

Abstract: We show that the language of atom interferometry provides a unified picture for microwave and optical atomic clocks as well as for gravito-inertial sensors. The sensitivity and accuracy of these devices is now such that a new theoretical framework common to all these interferometers is required that includes: (a) a fully quantum mechanical treatment of the atomic motion in free space and in the presence of a gravitational field (most cold-atom interferometric devices use atoms in ``free fall'' in a fountain geometry); (b) an account of simultaneous actions of gravitational and electromagnetic fields in the interaction zones; (c) a second quantization of the matter fields to take into account their fermionic or bosonic character in order to discuss the role of coherent sources and their noise properties; (d) a covariant treatment including spin to evaluate general relativistic effects. A theoretical description of atomic clocks revisited along these lines is presented, using both an exact propagator of atom waves in gravito-inertial fields and a covariant Dirac equation in the presence of weak gravitational fields. Using this framework, recoil effects, spin-related effects, beam curvature effects, the sensitivity to gravito-inertial fields and the influence of the coherence of the atom source are discussed in the context of present and future atomic clocks and gravito-inertial sensors.

Energy and angular momentum of the gravitational field in the teleparallel geometry

Abstract: The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell.

Anisotropic relativistic stellar models

Abstract: We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations The solutions are obtained by assuming a particular form of the anisotropy factor The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars

Segregation in binary mixtures under gravity.

Abstract: We employ kinetic theory for a binary mixture to study segregation by size and/or mass in a gravitational field. Simple segregation criteria are obtained for spheres and disks that are supported by numerical simulations.

Theoretical estimates of intrinsic galaxy alignment

Abstract: ABSTRA C T It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity ‐ ellipticity correlation for widely separated galaxies. We present a new model relating ellipticity to angular momentum, which can be calculated in linear theory. We use this model to calculate the angular power spectrum of intrinsic galaxy shape correlations. We show that, for low-redshift galaxy surveys, our model predicts that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations. We find that our model produces ‘E-mode’ correlations enhanced by a factor of 3.5 over B-modes on small scales, making it harder to disentangle intrinsic correlations from those induced by weak gravitational lensing.

Essay: The Holography of Gravity Encoded in a Relation Between Entropy, Horizon Area, and Action for Gravity

Abstract: I provide a general proof of the conjecture that one can attribute an entropy to the area of any horizon. This is done by constructing a canonical ensemble of a subclass of spacetimes with a fixed value for the temperature T = β−1 and evaluating the exact partition function Z(β). For spherically symmetric spacetimes with a horizon at r = a, the partition function has the generic form Z ∝ exp[S − β E], where S = (1/4)4π a2 and |E| = (a/2). Both S and E are determined entirely by the properties of the metric near the horizon. This analysis reproduces the conventional result for the black-hole spacetimes and provides a simple and consistent interpretation of entropy and energy for De Sitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. Further, I show that the relationship between entropy and area allows one to construct the action for the gravitational field on the bulk and thus the full theory. In this sense, gravity is intrinsically holographic.

Regularization of gravity field estimation from satellite gravity gradients

Abstract: The performance of the L-curve criterion and of the generalized cross-validation (GCV) method for the Tikhonov regularization of the ill-conditioned normal equations associated with the determination of the gravity field from satellite gravity gradiometry is investigated. Special attention is devoted to the computation of the corner point of the L-curve, to the numerically efficient computation of the trace term in the GCV target function, and to the choice of the norm of the residuals, which is important for the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) in the presence of colored observation noise. The trace term in the GCV target function is estimated using an unbiased minimum-variance stochastic estimator. The performance analysis is based on a simulation of gravity gradients along a 60-day repeat circular orbit and a gravity field recovery complete up to degree and order 300. Randomized GCV yields the optimal regularization parameter in all the simulations if the colored noise is properly taken into account. Moreover, it seems to be quite robust against the choice of the norm of the residuals. It performs much better than the L-curve criterion, which always yields over-smooth solutions. The numerical costs for randomized GCV are limited provided that a reasonable first guess of the regularization parameter can be found.

Hydrogen atom in the gravitational fields of topological defects

Abstract: We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a pointlike global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the energy levels of the atom. We investigate how the geometric and topological features of these spacetimes lead to shifts in the energy levels as compared with the flat Minkowski spacetime.

Assessment of three numerical solution strategies for gravity field recovery from GOCE satellite gravity gradiometry implemented on a parallel platform

Abstract: The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth's gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies (preconditioned conjugate gradient method, semi-analytic approach, and distributed non-approximative adjustment), which are based on different concepts, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation regarding the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the coloured noise characteristics of the gradiometer. The numerical simulations show that the three methods deliver nearly identical results—even in the case of large data gaps in the observation time series. The newly proposed distributed non-approximative adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns out to be a feasible method for practical applications.

The Constraint equations

Abstract: Initial data for solutions of Einstein’s gravitational field equations cannot be chosen freely: the data must satisfy the four Einstein constraint equations. We first discuss the geometric origins of the Einstein constraints and the role the constraint equations play in generating solutions of the full system. We then discuss various ways of obtaining solutions of the Einstein constraint equations, and the nature of the space of solutions.

Nested braneworlds and strong brane gravity

Abstract: We find the gravitational field of a ‘‘nested’’ domain wall living entirely within a brane-universe, or, a localized vortex within a wall. Using two illustrative examples, a vortex living on a critical Randall-Sundrum brane universe and a nested Randall-Sundrum scenario, we show that the induced gravitational field on the brane is identical to that of an (n21)-dimensional Einstein domain wall. We comment on the absence of any ‘‘nonconventional’’ interactions and the definition of the braneworld Newton constant.

The Holography of Gravity encoded in a relation between Entropy, Horizon area and Action for gravity

Abstract: I provide a general proof of the conjecture that one can attribute an entropy to the area of {\it any} horizon. This is done by constructing a canonical ensemble of a subclass of spacetimes with a fixed value for the temperature $T=\beta^{-1}$ and evaluating the {\it exact} partition function $Z(\beta)$. For spherically symmetric spacetimes with a horizon at $r=a$, the partition function has the generic form $Z\propto \exp[S-\beta E]$, where $S= (1/4) 4\pi a^2$ and $|E|=(a/2)$. Both $S$ and $E$ are determined entirely by the properties of the metric near the horizon. This analysis reproduces the conventional result for the black-hole spacetimes and provides a simple and consistent interpretation of entropy and energy for De Sitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be $(1/4)$ while the energy is zero. Further, I show that the relationship between entropy and area allows one to construct the action for the gravitational field on the bulk and thus the full theory. In this sense, gravity is intrinsically holographic.

Astrod–an overview

Abstract: The objectives of the Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) Mission concept are threefold. The first objective is to discover and explore fundamental physical laws governing matter, space and time via testing relativistic gravity with 3-6 orders of magnitude improvement. Relativistic gravity is an important cornerstone of physics, astronomy and cosmology. Its improved test is crucial to cosmology and modern theories of gravitation including superstring theories. Included in this objective is the precise determination of the relativistic parameters β and γ, the improved measurement of Ġ and a precise determination of an anomalous, constant acceleration directed towards the Sun. The second objective of the ASTROD mission is the high-precision measurement of the solar-system parameter. This includes: (i) a measurements of solar angular momentum via Lense-Thirring effect and the detection of solar g-mode oscillations via their changing gravity field, thus, providing a new eye to see inside the Sun; (ii) precise determination of the planetary orbit elements and masses; (iii) better determination of the orbits and masses of major asteroids. These measurements give better solar dynamics and probe the origin of our solar system. The third objective is to detect and observe gravitational waves from massive black holes and galactic binary stars in the frequency range 50 μHz to 5 mHz. Background gravitational -waves will also be explored. A desirable implementation is to have two spacecraft in separate solar orbit carrying a payload of a proof mass, two telescopes, two 1-2 W lasers, a clock and a drag-free system, together with an Earth reference system. the two spacecraft range coherently with the Earth reference system using lasers. When they are near, they range coherently to each other. The Earth reference system could be ground stations, Earth satellites and/or spacecraft near Earth-Sun Lagrange points. In this overview, we discuss the payload concept, the technological requirements, technological developments, orbit design, orbit simulation, the measurement of solar angular momentum, the gravitational-wave detection sensitivity, and the solar g-mode detection possibility for this mission concept. A simplified mission, Mini-ASTROD with one spacecraft ranging optically with ground stations, together with Super-ASTROD with four spacecraft of 5 AU (Jupiter-like) orbits, will be mentioned in the end. Super-ASTROD is a dedicated low-frequency gravitational-wave detection concept. For Mini-ASTROD, the first objective of ASTROD will be largely achieved; the second objective will be partially achieved; for gravitational wave detection, the sensitivity will be better than the present-day sensitivity using Doppler tracking by radio waves.

Exact models for anisotropic relativistic stars

Abstract: We present a class of exact solutions of the Einstein gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solution is represented in a closed integral form. The energy density and both radial and tangential pressure are finite and positive inside the anisotropic star. The energy density, radial pressure, pressure-density ratio and the adiabatic speed of sound are monotonically decreasing functions. Several stellar models with the anisotropy coefficient proportional to r2 are discussed, the values of the basic physical parameters of the star (radius, mass and red shift) and bound on anisotropy parameter is obtained.

Short-arc analysis of intersatellite tracking data in a gravity mapping mission

Abstract: A technique for the analysis of low-low intersatellite range-rate data in a gravity mapping mission is explored. The technique is based on standard tracking data analysis for orbit determination but uses a spherical coordinate representation of the 12 epoch state parameters describing the baseline between the two satellites. This representation of the state parameters is exploited to allow the intersatellite range-rate analysis to benefit from information provided by other tracking data types without large simultaneous multiple data type solutions. The technique appears especially valuable for estimating gravity from short arcs (e.g., less than 15 minutes) of data. Gravity recovery simulations which use short arcs are compared with those using arcs a day in length. For a high-inclination orbit, the short-arc analysis recovers low-order gravity coefficients remarkably well, although higher order terms, especially sectorial terms, are less accurate. Simulations suggest that either long or short arcs of GRACE data are likely to improve parts of the geopotential spectrum by orders of magnitude.

GOCE: The Earth Gravity Field by Space Gradiometry

Abstract: An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by a very accurate orbit determination, would allow a perfect estimation of the field A true satellite experiences a number of perturbational, non-gravitational forces acting on the shell of the spacecraft; these can be revealed and accurately measured by a spaceborne accelerometer If more accelerometers are flown in the same satellite, they naturally eliminate (to some extent) the common perturbational accelerations and their differences are affected by the second derivatives of the gravity fields only (gradiometry) The mission GOCE is based on this principle Its peculiar dynamical observation equations are reviewed The possibility of estimating the gravity field up to some harmonic degree (∼200) is illustrated

Energy-momentum current for coframe gravity

Abstract: The obstruction for the existence of an energy-momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. This must not be valid for alternative geometrical structures. A teleparallel manifold is defined as a parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields related by global Lorentz, i.e. SO(1, 3) transformations. In this paper a general free parametric class of teleparallel models is considered. It includes a 1-parameter subclass of viable models with the Schwarzschild coframe solution. A new form of the coframe field equation is derived from the general teleparallel Lagrangian by introducing the notion of a 3-parameter conjugate field strength a. The field equation turns out to have a form completely similar to the Maxwell field equation d * a = a. By applying the Noether procedure, the source 3-form a is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source a of the coframe field is interpreted as the total conserved energy–momentum current. The energy–momentum tensor for the coframe is defined. The total energy–momentum current of a system of a coframe and a material field is conserved. Thus a redistribution of the energy–momentum current between material and coframe (gravity) fields is possible in principle, unlike in the standard GR. For special values of parameters, when the GR is reinstated, the energy–momentum tensor gives up the invariant sense, i.e. becomes a pseudo-tensor. Thus even a small-parametric change of GR turns it into a well-defined Lagrangian theory.

Modeling of the Eros gravity field as an ellipsoidal harmonic expansion from the NEAR Doppler tracking data

Abstract: [1] The gravity field for asteroid 433 Eros has been determined in terms of ellipsoidal harmonic functions by processing the Doppler tracking data of the NEAR spacecraft while it was in orbit about the asteroid. Using the same set of NEAR spacecraft Doppler tracking data, comparative descriptions of the Eros gravity field are provided for both the ellipsoidal and the traditional spherical harmonic models. It is shown that for elongated bodies, like the asteroid Eros, the ellipsoidal harmonics model permits a better representation of the gravity signature than does the spherical harmonics model. Eros has a nearly uniform density but there are negative gravity anomalies near the ends of Eros and positive gravity anomalies near the Psyche crater and the Himeros depression.

Dynamics of brane-world cosmological models

Abstract: Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or brane embedded in a higher-dimensional bulk spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, and it is not necessary for the extra dimensions to be small, or even compact, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall–Sundrum-type models are relatively simple phenomenological models that capture some of the essential features of the dimensional reduction of eleven-dimensional supergravity introduced by Hořava and Witten. These curved (or warped) models are self-consistent and simple and allow for an investigation of the essential nonlinear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in t...

General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes

Abstract: We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein's equations for the gravitational field, and the equations of relativistic MHD for a perfectly conducting ideal gas. The adopted form of the equations is suitable for evolving numerically a relativistic MHD fluid in a dynamical spacetime characterized by a strong gravitational field.

Gravimagnetic similarity in anomaly formulas for uniform polyhedra

Abstract: Gravitational and magnetic anomalies of an arbitrary target body are linked through Poisson's differential relation. For a uniform polyhedral target, Poisson's relation reduces to an algebraic link between gravity and magnetic anomaly formulas.The derivation is given in tensor form. It identifies for each target facet edge a vector function, in terms of which the gravitational and magnetic potential and field anomaly formulas are similarly expressed as appropriately weighted linear combinations. This similarity unifies the theory of uniform polyhedral anomalies. It benefits analysis and construction of software that naturally embraces all anomalies in a single code.The analysis is exemplified by a discussion of singularities and by the adaptation of three gravity‐field algorithms to the remaining gravitational and magnetic cases, while retaining the respective computational advantages of the former gravity‐field algorithms.