Showing papers on "Gravitational field published in 2010"

f(R,L m ) gravity

Abstract: We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.

f(R,L_m) gravity

Abstract: We generalize the $f(R)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the matter Lagrangian $L_m$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy-density of the matter only. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert--Einstein Lagrange density are also derived.

Combined satellite gravity field model GOCO01S derived from GOCE and GRACE

Abstract: [1] The satellite-only gravity field model GOCO01S is a combination solution based on 61 days of GOCE gravity gradient data, and 7 years of GRACE GPS and K-band range rate data, resolved up to degree/order 224 of a harmonic series expansion. The combination was performed consistently by addition of full normal equations and stochastic modeling of GOCE and GRACE observations. The model has been validated against external global gravity models and regional GPS/leveling observations. While low to medium degrees are mainly determined by GRACE, significant contributions by the new measurement type of GOCE gradients can already be observed at degree 100. Beyond degree 150, GOCE becomes the dominant contributor. Correspondingly, with GOCO01S a global gravity field model with high performance for the complete spectral range up to degree/order 224 is now available. This new gravity model will be beneficial for many applications in geophysics, oceanography, and geodesy.

A precision measurement of the gravitational redshift by the interference of matter waves

Abstract: A central prediction of general relativity states that a gravitational field slows the running of a clock. Previous measurements of this effect, known as gravitational redshift, have involved clocks at different heights, and until now this has been the least accurately determined of the parameters supporting curved space-time theories. Now this prediction has been confirmed to unprecedented accuracy using the results of lab experiments performed more than 10 years ago in a study of the acceleration of free fall. Analysis of the data — on quantum interference of single caesium atoms bobbing up and down in an atomic fountain — provides a measurement based on matter-wave interference that improves accuracy by a factor of 10,000. One of the central predictions of general relativity is that a clock in a gravitational potential well runs more slowly than a similar clock outside the well. This effect, known as gravitational redshift, has been measured using clocks on a tower, an aircraft and a rocket, but here, laboratory experiments based on quantum interference of atoms are shown to produce a much more precise measurement. One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c2, where c is the velocity of light, as compared to a similar clock outside the potential1. This effect, known as gravitational redshift, is important to the operation of the global positioning system2, timekeeping3,4 and future experiments with ultra-precise, space-based clocks5 (such as searches for variations in fundamental constants). The gravitational redshift has been measured using clocks on a tower6, an aircraft7 and a rocket8, currently reaching an accuracy of 7 × 10-5. Here we show that laboratory experiments based on quantum interference of atoms9,10 enable a much more precise measurement, yielding an accuracy of 7 × 10-9. Our result supports the view that gravity is a manifestation of space-time curvature, an underlying principle of general relativity that has come under scrutiny in connection with the search for a theory of quantum gravity11. Improving the redshift measurement is particularly important because this test has been the least accurate among the experiments that are required to support curved space-time theories1.

Gravity Field, Shape, and Moment of Inertia of Titan

Abstract: Precise radio tracking of the spacecraft Cassini has provided a determination of Titan’s mass and gravity harmonics to degree 3. The quadrupole field is consistent with a hydrostatically relaxed body shaped by tidal and rotational effects. The inferred moment of inertia factor is about 0.34, implying incomplete differentiation, either in the sense of imperfect separation of rock from ice or a core in which a large amount of water remains chemically bound in silicates. The equilibrium figure is a triaxial ellipsoid whose semi-axes a, b, and c differ by 410 meters (a – c) and 103 meters (b – c). The nonhydrostatic geoid height variations (up to 19 meters) are small compared to the observed topographic anomalies of hundreds of meters, suggesting a high degree of compensation appropriate to a body that has warm ice at depth.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Abstract: Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach

Abstract: We use an effective field theory (EFT) approach to calculate the next-to-leading order (NLO) gravitational spin-orbit interaction between two spinning compact objects. The NLO spin-orbit interaction provides the most computationally complex sector of the NLO spin effects, previously derived within the EFT approach. In particular, it requires the inclusion of nonstationary cubic self-gravitational interaction, as well as the implementation of a spin supplementary condition (SSC) at higher orders. The EFT calculation is carried out in terms of the nonrelativistic gravitational field parametrization, making the calculation more efficient with no need to rely on automated computations, and illustrating the coupling hierarchy of the different gravitational field components to the spin and mass sources. Finally, we show explicitly how to relate the EFT derived spin results to the canonical results obtained with the Arnowitt-Deser-Misner (ADM) Hamiltonian formalism. This is done using noncanonical transformations, required due to the implementation of covariant SSC, as well as canonical transformations at the level of the Hamiltonian, with no need to resort to the equations of motion or the Dirac brackets.

Global Mass Flux Solutions from GRACE: A Comparison of Parameter Estimation Strategies - Mass Concentrations Versus Stokes Coefficients

Abstract: The differences between mass concentration (mas con) parameters and standard Stokes coefficient parameters in the recovery of gravity infonnation from gravity recovery and climate experiment (GRACE) intersatellite K-band range rate data are investigated. First, mascons are decomposed into their Stokes coefficient representations to gauge the range of solutions available using each of the two types of parameters. Next, a direct comparison is made between two time series of unconstrained gravity solutions, one based on a set of global equal area mascon parameters (equivalent to 4deg x 4deg at the equator), and the other based on standard Stokes coefficients with each time series using the same fundamental processing of the GRACE tracking data. It is shown that in unconstrained solutions, the type of gravity parameter being estimated does not qualitatively affect the estimated gravity field. It is also shown that many of the differences in mass flux derivations from GRACE gravity solutions arise from the type of smoothing being used and that the type of smoothing that can be embedded in mas con solutions has distinct advantages over postsolution smoothing. Finally, a 1 year time series based on global 2deg equal area mascons estimated every 10 days is presented.

Off-equatorial orbits in strong gravitational fields near compact objects -- II: halo motion around magnetic compact stars and magnetized black holes

Abstract: Off-equatorial circular orbits with constant latitudes (halo orbits) of electrically charged particles exist near compact objects. In the previous paper, we discussed this kind of motion and demonstrated the existence of minima of the two-dimensional effective potential which correspond to the stable halo orbits. Here, we relax previous assumptions of the pseudo-Newtonian approach for the gravitational field of the central body and study properties of the halo orbits in detail. Within the general relativistic approach, we carry out our calculations in two cases. Firstly, we examine the case of a rotating magnetic compact star. Assuming that the magnetic field axis and the rotation axis are aligned with each other, we study the orientation of motion along the stable halo orbits. In the poloidal plane, we also discuss shapes of the related effective potential halo lobes where the general off-equatorial motion can be bound. Then we focus on the halo orbits near a Kerr black hole immersed in an asymptotically uniform magnetic field of external origin. We demonstrate that, in both the cases considered, the lobes exhibit two different regimes, namely, one where completely disjoint lobes occur symmetrically above and below the equatorial plane, and another where the lobes are joined across the plane. A possible application of the model concerns the structure of putative circumpulsar discs consisting of dust particles. We suggest that the particles can acquire a small (but non-zero) net electric charge, and this drives them to form the halo lobes.

Diffusion of Magnetic Field and Removal of Magnetic Flux from Clouds Via Turbulent Reconnection

Abstract: The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology via reconnection in highly conducting media. Recent progress in understanding fast magnetic reconnection in the presence of turbulence reassures that the magnetic field behavior in computer simulations and turbulent astrophysical environments is similar, as far as magnetic reconnection is concerned. This makes it meaningful to perform MHD simulations of turbulent flows in order to understand the diffusion of magnetic field in astrophysical environments. Our studies of magnetic field diffusion in turbulent medium reveal interesting new phenomena. First of all, our three-dimensional MHD simulations initiated with anti-correlating magnetic field and gaseous density exhibit at later times a de-correlation of the magnetic field and density, which corresponds well to the observations of the interstellar media. While earlier studies stressed the role of either ambipolar diffusion or time-dependent turbulent fluctuations for de-correlating magnetic field and density, we get the effect of permanent de-correlation with one fluid code, i.e., without invoking ambipolar diffusion. In addition, in the presence of gravity and turbulence, our three-dimensional simulations show the decrease of the magnetic flux-to-mass ratio as the gaseous density at the center of the gravitational potential increases. We observe this effect both in the situations when we start with equilibrium distributions of gas and magnetic field and when we follow the evolution of collapsing dynamically unstable configurations. Thus, the process of turbulent magnetic field removal should be applicable both to quasi-static subcritical molecular clouds and cores and violently collapsing supercritical entities. The increase of the gravitational potential as well as the magnetization of the gas increases the segregation of the mass and magnetic flux in the saturated final state of the simulations, supporting the notion that the reconnection-enabled diffusivity relaxes the magnetic field + gas system in the gravitational field to its minimal energy state. This effect is expected to play an important role in star formation, from its initial stages of concentrating interstellar gas to the final stages of the accretion to the forming protostar. In addition, we benchmark our codes by studying the heat transfer in magnetized compressible fluids and confirm the high rates of turbulent advection of heat obtained in an earlier study.

Notes on wormhole existence in scalar-tensor and F(R) gravity

Abstract: Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω > −3/2, except for the case ω = 0; in the latter case, G eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G eff changes its sign.

An improved lunar gravity field model from SELENE and historical tracking data: Revealing the farside gravity features

Abstract: [1] A new spherical harmonic solution of the lunar gravity field to degree and order 100, called SGM100h, has been developed using historical tracking data and 14.2 months of SELENE tracking data (from 20 October 2007 to 26 December 2008 plus 30 January 2009). The latter includes all usable 4-way Doppler data collected which allowed direct observations of the farside gravity field for the first time. The new model successfully reveals farside features in free-air gravity anomalies which are characterized by ring-shaped structures for large impact basins and negative spots for large craters. SGM100h produces a correlation with SELENE-derived topography as high as about 0.9, through degree 70. Comparison between SGM100h and LP100K (one of the pre-SELENE models) shows that the large gravity errors which existed in LP100K are drastically reduced and the asymmetric error distribution between the nearside and the farside almost disappears. The gravity anomaly errors predicted from the error covariance, through degree and order 100, are 26 mGal and 35 mGal for the nearside and the farside, respectively. Owing to the 4-way Doppler measurements the gravity coefficients below degree and order 70 are now determined by real observations with contribution factors larger than 80 percent. With the SELENE farside data coverage, it is possible to estimate the gravity field to degree and order 70 without applying any a priori constraint or regularization. SGM100h can be used for global geophysical interpretation through degree and order 70.

Modified Entropic Force

Abstract: The theory of statistical thermodynamics tells us the equipartition law of energy does not hold in the limit of very low temperatures. It is found the Debye model is very successful in explaining the experimental results for most of the solid objects. Motivated by this fact, we modify the entropic force formula which is proposed very recently. Since the Unruh temperature is proportional to the strength of the gravitational field, so the modified entropic force formula is an extension of the Newtonian gravity to the weak field. On the contrary, general relativity extends Newtonian gravity to the strong field case. Corresponding to Debye temperature, there exists a Debye acceleration g{sub D}. It is found the Debye acceleration is g{sub D}=10{sup -15} N kg{sup -1}. This acceleration is very much smaller than the gravitational acceleration 10{sup -4} N kg{sup -1} which is felt by Neptune and the gravitational acceleration 10{sup -10} N kg{sup -1} felt by the Sun. Therefore, the modified entropic force can be very well approximated by the Newtonian gravity in the Solar System and in the Galaxy. With this Debye acceleration, we find the current cosmic speeding up can be explained without invoking any kind of dark energy.

Dark spinor models in gravitation and cosmology

Abstract: We introduce and carefully define an entire class of field theories based on non-standard spinors. Their dominant interaction is via the gravitational field which makes them naturally dark; we refer to them as Dark Spinors. We provide a critical analysis of previous proposals for dark spinors noting that they violate Lorentz invariance. As a working assumption we restrict our analysis to non-standard spinors which preserve Lorentz invariance, whilst being non-local and explicitly construct such a theory. We construct the complete energy-momentum tensor and derive its components explicitly by assuming a specific projection operator. It is natural to next consider dark spinors in a cosmological setting. We find various interesting solutions where the spinor field leads to slow roll and fast roll de Sitter solutions. We also analyse models where the spinor is coupled conformally to gravity, and consider the perturbations and stability of the spinor.

Off-equatorial orbits in strong gravitational fields near compact objects—II: halo motion around magnetic compact stars and magnetized black holes

Abstract: Off-equatorial circular orbits with constant latitudes (halo orbits) of electrically charged particles exist near compact objects. In the previous paper, we discussed this kind of motion and demonstrated the existence of minima of the two-dimensional effective potential which correspond to the stable halo orbits. Here, we relax previous assumptions of the pseudo-Newtonian approach for the gravitational field of the central body and study properties of the halo orbits in detail. Within the general relativistic approach, we carry out our calculations in two cases. Firstly, we examine the case of a rotating magnetic compact star. Assuming that the magnetic field axis and the rotation axis are aligned with each other, we study the orientation of motion along the stable halo orbits. In the poloidal plane, we also discuss shapes of the related effective potential halo lobes where the general off-equatorial motion can be bound. Then we focus on the halo orbits near a Kerr black hole immersed in an asymptotically uniform magnetic field of external origin. We demonstrate that, in both the cases considered, the lobes exhibit two different regimes, namely one where completely disjoint lobes occur symmetrically above and below the equatorial plane, and another where the lobes are joined across the plane. A possible application of the model concerns the structure of putative circumpulsar discs consisting of dust particles. We suggest that the particles can acquire a small (but non-zero) net electric charge, and this drives them to form the halo lobes.

GOCE gravity field model derived from orbit and gradiometry data applying the time-wise method

Abstract: A first GOCE gravity field model based on two months of GOCE orbit and gradiometry data has been computed applying the time-wise method. The paper gives an overview of the software system, and discusses the key features of the solution strategy. The resulting global gravity field model, resolved complete to degree/order 224, is GOCE-only in a strict sense, i.e., no a priori gravity field information entered the solution. Realistic stochastic models for both the orbit and gradiometer observations have been included. Thus, the coefficient error information, provided as full variance-covariance matrix, reflects the true error behaviour of the solution. The resulting GOCE model is assessed and validated against state-of-the art gravity field models. Since the model is independent of any gravity prior information, it can be used to assess the additional information content of GOCE, and can be combined with complementary satellite and terrestrial gravity field information.

Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects

Abstract: Accretion onto black holes and compact stars brings material in a zone of strong gravitational and electromagnetic fields. We study dynamical properties of motion of electrically charged particles forming a highly diluted medium (a corona) in the regime of strong gravity and large-scale (ordered) magnetic field. We start our work from a system that allows regular motion, then we focus on the onset of chaos. To this end, we investigate the case of a rotating black hole immersed in a weak, asymptotically uniform magnetic field. We also consider a magnetic star, approximated by the Schwarzschild metric and a test magnetic field of a rotating dipole. These are two model examples of systems permitting energetically bound, off-equatorial motion of matter confined to the halo lobes that encircle the central body. Our approach allows us to address the question of whether the spin parameter of the black hole plays any major role in determining the degree of the chaoticness. To characterize the motion, we construct the recurrence plots (RPs) and we compare them with Poincare surfaces of section. We describe the RPs in terms of the recurrence quantification analysis, which allows us to identify the transition between different dynamical regimes. We demonstrate that this new technique is able to detect the chaos onset very efficiently and provide its quantitative measure. The chaos typically occurs when the conserved energy is raised to a sufficiently high level that allows the particles to traverse the equatorial plane. We find that the role of the black hole spin in setting the chaos is more complicated than initially thought.

Gravitational signature of Jupiter's internal dynamics

Abstract: Telescopic observations and space missions to Jupiter have provided vast information about Jupiter's cloud level winds, but the depth to which these winds penetrate has remained an ongoing mystery. Scheduled to be launched in 2011, the Jupiter orbiter Juno will make high-resolution observations of Jupiter's gravity field. In this paper we show that these measurements are sensitive to the depth of the internal winds. We use dynamical models ranging from an idealized thermal wind balance analysis, using the observed cloud-top winds, to a full general circulation model (GCM). We relate the depth of the dynamics to the external gravity spectrum for different internal wind structure scenarios. In particular, we predict that substantial Jovian winds below a depth of 500 km would lead to detectable (milligal-level) gravity anomalies with respect to the expected gravity for a planet in solid body rotation.

Einstein's unification

Abstract: Introduction 1. Formulating the gravitational field equations 2. On the method of theoretical physics 3. Unification and field theory 4. Experiment and experience 5. The method as directive: semivectors 6. Unification in five dimensions 7. The method and the quantum Conclusion Bibliography Index.

Handbook of geomathematics

Abstract: Part 1: General Issues, Historical Background, and Future Perspectives - Geomathematics: Its Role, Its Aim, and Its Potential - Navigation on Sea: Topics in the History of Geomathematics- Gauss and Weber's "Atlas des Erdmagnetismus" (1840) Was Not the First: History of the Geomagnetic Atlases - Part 2: Observational and Measurement Key Technologies- Earth Observation Satellite Missions and Data Access- Satellite-to-Satellite Tracking (Low-Low/High-Low SST)- GOCE: Gravitational Gradiometry in a Satellite- Sources of the Geomagnetic Field and the Modern Data That Enable Their Investigation- Part 3: Modeling of the System Earth (Geosphere, Cryosphere, Hydrosphere, Atmosphere, Biosphere, Anthroposphere)- Classical Physical Geodesy - Geodetic Boundary Value Problem - Time-Variable Gravity Field and Global Deformation of the Earth- Satellite Gravity Gradiometry (SGG): From Scalar to Tensorial Solution- Spacetime Modelling of the Earth's Gravity Field by Ellipsoidal Harmonics- Multiresolution Analysis of Hydrology and Satellite Gravitational Data Time Varying Mean Sea Level- Self-Attraction and Loading of Oceanic Masses - Unstructured Meshes in Large-Scale Ocean Modeling- Numerical Methods in Support of Advanced Tsunami Early Warning- Gravitational Viscoelastodynamics- Elastic and Viscoelastic Reaction of the Lithosphere to Loads- Use of Multiscale Methods in Geomathematics- Efficient Modeling of Flow and Transport in Porous Media Using- Multiphysics and Multiscale Approaches- Convection Structures of Binary Fluid Mixtures in Porous Media- Numerical Dynamo Simulations: From Basic Concepts to Realistic Models- Mathematical Properties Relevant to Geomagnetic Field Modeling- Multiscale Modeling of the Geomagnetic Field and Ionospheric Currents- Toroidal - Poloidal Decompositions of Electromagnetic Green's Functions in Geomagnetic Induction- Using B-Spline Expansions for Ionosphere Modeling- The Forward and Adjoint Methods of Global Electromagnetic Induction for CHAMP Magnetic Data- Climate Dynamics- Modern Techniques for Numerical Weather Prediction: A Picture Drawn from Kyrill- Radio Occultation via Satellites- Asymptotic Models for Atmospheric Flows- Stokes Problem, Layer Potentials and Regularizations, Multiscale Applications- On High Reynolds Number Aerodynamics - Separated Flows-Turbulence Theory- Analysis of Forest Fire Spreading Theory- Phosphorus Cycles in Lakes and Rivers: Modeling, Analysis, and Simulation- Model-based Visualization of Instationary Geo-Data with Application to Volcano Ash Data- Modeling of Fluid Transport in Geothermal Research- Fractional Diffusion and Wave Propagation- Modeling Deep Geothermal Reservoirs: Recent Advances and Future Problems- Part 4: Analytic, Algebraic, and Operator Theoretical Methods- Noise Models for Ill-Posed Problems- Sparsity in Inverse Geophysical Problems- Multiparameter Regularization in Downward Continuation of Satellite Data- Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics- Quantitative Remote Sensing Inversion in Earth Science: Theory and Numerical Treatment- Correlation Modeling of the Gravity Field in Classical Geodesy- Inverse Resistivity Problems in Computational Geoscience- Identification of Current Sources in 3D Electrostatics- Numerical Simulation and Inversion for Geo-Electromagnetic Methods- Transmission Tomography in Seismology- Numerical Algorithms for Non-Smooth Optimization Applicable to Seismic Recovery- Strategies in Adjoint Tomography- Potential-field Estimation using Scalar and Vector Slepian Functions at Satellite Altitude- Multidimensional Seismic Compression by Hybrid Transform with Multiscale Based Coding Tomography: Problems and Multiscale Solutions- RFMP: An Iterative Best Basis Algorithm for Inverse Problems in the Geosciences- Material Behavior: Texture and Anisotropy- Rayleigh Wave Dispersive Properties of a Vector Displacement as a Tool for P- and S-wave Velocities Near Surface Profiling- Dynamic Simulation of Land Use Change and Management Effects on Soil N2O Emissions- Part 5: Statistical and Stochastic Methods- Selected Statistical Methods - Statistical Analysis of Climate Series- Oblique Stochastic Boundary-Value Problem- Geodetic Deformation Analysis with Respect to an Extended Uncertainty Budget)- It's All About Statistics Global Gravity Field Modeling from GOCE and Complementary Data- Mixed Integer Estimation and Validation for Next Generation GNSS- Mixed Integer Linear Models- Part 6: Special Function Systems and Methods- Special Functions in Mathematical Geosciences: An Attempt at a Categorization- Clifford Analysis and Harmonic Polynomials- Splines and Wavelets on Geophysically Relevant Manifolds- Slepian Functions and Their Use in Signal Estimation and Spectral Analysis- Dimension Reduction and Remote Sensing Using Modern Harmonic Analysis- Low Discrepancy Methods- Part 7: Computational and Numerical Methods- Radial Basis Function-generated Finite Differences: A Mesh-free Method for Computational Geosciences- Numerical Integration on the Sphere- Fast Spherical/Harmonic Spline Modeling- Multiscale Approximation- Sparse Solutions of Underdetermined Linear Systems- Nonlinear Methods for Dimensionality Reduction- Part 8: Cartographic, Photogrammetric, Information Systems and Methods- Cartography- Map Projections: Cartographic Information Systems- Modeling Uncertainty of Complex Earth Systems in Metric Space- Geometrical Reference System- Analysis of Data from Multi-Satellite Geospace Missions- Geodetic World Height System Unification- Mathematical Foundations of Photogrammetry- Potential Methods and Geoinformation Systems- Geoinformatics

Notes on entropy force in general spherically symmetric spacetimes

Abstract: In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einstein's equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.

Gravitational lensing in a non-uniform plasma

Abstract: We develop a model of gravitational lensing in a non-uniform plasma. When a gravitating body is surrounded by a plasma, the lensing angle depends on the frequency of the electromagnetic wave, due to the dispersion properties of the plasma, in the presence of a plasma inhomogeneity, and of gravity. The second effect leads, even in a uniform plasma, to a difference of the gravitational photon deflection angle from the vacuum case, and to its dependence on the photon frequency. We take into account both effects, and derive the expression for the lensing angle in the case of a strongly non-uniform plasma in the presence of gravitation. The dependence of the lensing angle on the photon frequency in a homogeneous plasma resembles the properties of a refractive prism spectrometer, the strongest action of which is for very long radio waves. We discuss the observational appearance of this effect for the gravitational lens with a Schwarzschild metric, surrounded by a uniform plasma. We obtain formulae for the lensing angle and the magnification factors in this case and discuss the possibility of observation of this effect by the planned very long baseline interferometry space project RadioAstron. We also consider models with a non-uniform plasma distribution. For different gravitational lens models we compare the corrections to the vacuum lensing due to the gravitational effect in the plasma, and due to the plasma inhomogeneity. We show that the gravitational effect could be detected in the case of a hot gas in the gravitational field of a galaxy cluster.

Regional gravity decrease after the 2010 Maule (Chile) earthquake indicates large-scale mass redistribution

Abstract: [1] We report small but detectable changes in the GRACE satellites' relative trajectory after the M8.8 Maule, Chile earthquake on 27 February 2010 that can be used to delineate the shift in the gravity field. A gravity anomaly of −5 μGal with a spatial scale of 500 km was found east of the epicenter after the earthquake. Based on coseismic models, the long-wavelength negative gravity change is primarily the result of crustal dilatation as well as surface subsidence in the onland region. The offshore positive gravity anomaly predicted from finite fault coseismic models is considerably smaller because the gravity changes due to surface uplift and interior deformation are opposite in polarity. Our study suggests a role for large-scale gravity observations in deciphering changes of the Earth's interior during great earthquakes by filling in the seldom-observed long-wavelength spectrum of earthquake deformations as a complement to surface geodetic measurements and seismic data.

Testing gravitational parity violation with coincident gravitational waves and short gamma-ray bursts

Abstract: Gravitational parity violation is a possibility motivated by particle physics, string theory, and loop quantum gravity. One effect of it is amplitude birefringence of gravitational waves, whereby left and right circularly polarized waves propagate at the same speed but with different amplitude evolution. Here we propose a test of this effect through coincident observations of gravitational waves and short gamma-ray bursts from binary mergers involving neutron stars. Such gravitational waves are highly left or right circularly polarized due to the geometry of the merger. Using localization information from the gamma-ray burst, ground-based gravitational wave detectors can measure the distance to the source with reasonable accuracy. An electromagnetic determination of the redshift from an afterglow or host galaxy yields an independent measure of this distance. Gravitational parity violation would manifest itself as a discrepancy between these two distance measurements. We exemplify such a test by considering one specific effective theory that leads to such gravitational parity violation, Chern-Simons gravity. We show that the advanced LIGO-Virgo network and all-sky gamma-ray telescopes can be sensitive to the propagating sector of Chern-Simons gravitational parity violation to a level roughly 2 orders of magnitude better than current stationary constraints from the LAGEOS satellites.

Minimal length and bouncing-particle spectrum

Abstract: In this paper we study the effects of the Generalized Uncertainty Principle (GUP) on the spectrum of a particle that is bouncing vertically and elastically on a smooth reflecting floor in the Earth's gravitational field (a quantum bouncer). We calculate energy levels and corresponding wave functions of this system in terms of the GUP parameter. We compare the outcomes of our study with the results obtained from elementary quantum mechanics. A potential application of the present study is discussed finally.

ITG-GRACE: Global Static and Temporal Gravity Field Models from GRACE Data

Abstract: More than 4 years of GRACE data were used to determine the gravity field model ITG-Grace03 s. The solution consists of three parts: a static high resolution model up to a spherical harmonic degree of 180, temporal variations up to degree 40 and the full variance-covariance matrix for the static solution. The temporal gravity field variations are parameterized by continuous basis functions in the time domain. The physical model of the gravity field recovery technique is based on Newton’s equation of motion, formulated as a boundary value problem in the form of a Fredholm type integral equation. The principal characteristic of this method is the use of short arcs of the satellite’s orbit in order to avoid the accumulation of modeling errors and a rigorous consideration of correlations between the range observations in the subsequent adjustment procedure.