scispace - formally typeset
Search or ask a question

Showing papers on "Gravitational field published in 2001"


Journal ArticleDOI
TL;DR: A spherical harmonic solution of the Mars gravity field to degree and order 80 was developed using X band tracking data of Mars Global Surveyor (MGS) from October 1997 to February 2000 and altimeter crossovers formed from the Mars Orbiter Laser Altimeter (MOLA) data between March and December 1999 as discussed by the authors.
Abstract: A spherical harmonic solution of the Mars gravity field to degree and order 80, Goddard Mars Model 2B (GMM-2B), has been developed using X band tracking data of Mars Global Surveyor (MGS) from October 1997 to February 2000 and altimeter crossovers formed from the Mars Orbiter Laser Altimeter (MOLA) data between March and December 1999. During the mapping mission, MGS was located in a near-polar (92.9° inclination) and near-circular orbit at a mean altitude of 400 km. The tracking data from this orbit provide a detailed, global, and high resolution view of the gravity field of Mars. Mars gravity solutions are stable to 60×60 even without application of a Kaula power law constraint. The Valles Marineris is resolved distinctly with lows reaching −450 mGals. Olympus Mons and its aureole are both separately resolved, and the volcano has a peak anomaly of 2950 mGals. The global correlation of the GMM-2B gravity coefficients with MOLA-derived topography is 0.78 through degree 60, and the correlation remains above 0.6 through degree 62. The global gravity anomaly error predicted from the GMM-2B error covariance through 60×60 is 11 mGal. The global geoid error from GMM-2B through 60×60 is 1.8 m. MGS orbit quality using GMM-2B, as measured by overlapping orbital arcs, is 1 m in the radial direction and 10 m in total position.

275 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate spacetimes in which the speed of light along flat 4D sections varies over the extra dimensions due to different warp factors for the space and the time coordinates (asymmetrically warped) and show that the cosmological constant may relax in such theories by the adjustment of the mass and the charge of the black hole.

251 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the precoalescing stage is presented, where a hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational.
Abstract: We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the precoalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multidomain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multidomain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in detail for a polytropic equation of state with $\ensuremath{\gamma}=2.$

201 citations


Journal ArticleDOI
TL;DR: In this paper, a 3D inversion program is developed to interpret gravity data using a selection of constraints, which includes minimum distance, flatness, smoothness and compactness constraints, combined using a Lagrangian formulation.
Abstract: A three-dimensional (3D) inversion program is developed to interpret gravity data using a selection of constraints. This selection includes minimum distance, flatness, smoothness and compactness constraints, which can be combined using a Lagrangian formulation. A multigrid technique is also implemented to resolve separately large and short gravity wavelengths. The subsurface in the survey area is divided into rectangular prismatic blocks and the problem is solved by calculating the model parameters, i.e. the densities of each block. Weights are given to each block depending on depth, a priori information on density and the density range allowed for the region under investigation. The present computer code is tested on modelled data for a dipping dike and multiple bodies. Results combining different constraints and a weight depending on depth are shown for the dipping dike. The advantages and behaviour of each method are compared in the 3D reconstruction. Recovery of geometry (depth, size) and density distribution of the original model is dependent on the set of constraints used. From experimentation, the best combination of constraints for multiple bodies seems to be flatness and a minimum volume for the multiple bodies. The inversion method is tested on real gravity data from the Rouyn-Noranda (Quebec) mining camp. The 3D inversion model for the first 10 km is in agreement with the known major lithological contacts at the surface; it enables the determination of the geometry of plutons and intrusive rocks at depth.

197 citations


Journal ArticleDOI
01 Sep 2001-Icarus
TL;DR: In this article, radio Doppler data generated by the Deep Space Network (DSN) from five encounters of the Galileo spacecraft with Callisto, Jupiter's outermost Galilean satellite, have been used to determine the quadrupole moments of the satellite's external gravitational field.

186 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the evolution of large-scale curvature perturbations on the brane can be determined without solving the bulk perturbation equations, without the need to solve the bulk curvature equations.
Abstract: In brane-world cosmologies of Randall-Sundrum type, we show that the evolution of large-scale curvature perturbations may be determined on the brane, without solving the bulk perturbation equations. The influence of the bulk gravitational field on the brane is felt through a projected Weyl tensor which behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces for both the matter and Weyl fluids, and show that their evolution on large scales follows directly from the energy conservation equations for each fluid. The total curvature perturbation is not necessarily constant for adiabatic matter perturbations, but can change due to the Weyl entropy perturbation. To relate this curvature perturbation to the longitudinal gauge metric potentials requires knowledge of the Weyl anisotropic stress which is not determined by the equations on the brane. We discuss the implications for large-angle anisotropies on the cosmic microwave background sky.

137 citations


Posted Content
TL;DR: In this paper, the spectrum of the cosmological distribution of discrete gravitational wave sources, the total time-integrated energy spectrum of an individual source, and the present-day comoving number density of remnants are analyzed.
Abstract: There is an extremely simple relationship between the spectrum of the gravitational wave background produced by a cosmological distribution of discrete gravitational wave sources, the total time-integrated energy spectrum of an individual source, and the present-day comoving number density of remnants. Stated in this way, the background is entirely independent of the cosmology, and only weakly dependent on the evolutionary history of the sources. This relationship allows one easily to compute the amplitude and spectrum of cosmic gravitational wave backgrounds from a broad range of astrophysical sources, and to evaluate the uncertainties therein.

131 citations


Journal ArticleDOI
TL;DR: The MGS75D is a complete spherical harmonics model to degree and order 75 as mentioned in this paper, which is used to determine the gravity field of Mars, Phobos, and Deimos.
Abstract: Radiometric tracking data collected by NASA's Deep Space Network (DSN) for Mariner 9, Viking 1 and 2 orbiters, and Mars Global Surveyor (MGS) have been analyzed to determine the gravity field of Mars. The gravity solution (MGS75D) is a complete spherical harmonics model to degree and order 75. Also parts of the solution are the gravitational constants of Mars, Phobos, and Deimos. The significant improvement in the MGS75D Mars gravity model is mainly a consequence of globally distributed data set collected from the MGS mapping orbits, the use of optimal weighting and constrained least squares solution techniques, and improved force and measurement models in the orbit determination process. The gravity anomaly map reveals significantly more detail and larger amplitudes than any previous Mars gravity map over the major impact and volcanic areas on Mars. Olympus Mons remains the largest known gravity anomaly in our solar system and Isidis Planitia, the highest-amplitude mascon. There are mascons in the Hellas, Argyre, and Utopia basins. Valles Marineris has distinctive negative anomalies, and all volcanic features are positive. Gravity anomalies over several craters have also been resolved. The overall correlation of the MGS75D gravity anomaly map with topography derived from the Mars Orbiter Laser Altimeter (MOLA) is very high, while the polar regions display relatively poor correlation.

128 citations


Journal ArticleDOI
TL;DR: In this article, the authors used the 3.6-cm λ radio path of the Mars Global Surveyor (MGS) during periods of atmospheric occultation to estimate the vertical temperature-pressure structure T[p(r)] to accuracies at the surface of ΔT ≈ 0.4 K and Δp ≈ 2 Pa, and ∼10 K and ∼0.6 Pa at altitudes of 40-50 km; the error in radius is Δr ≈ 1 m at all levels.
Abstract: Mars Global Surveyor (MGS) radio science comprises studies of the atmosphere and gravity of the planet. Perturbations of the 3.6-cm λ radio path by the atmosphere during periods of atmospheric occultation provide the vertical temperature-pressure structure T[p(r)] to accuracies at the surface of ΔT ≈ 0.4 K and Δp ≈ 2 Pa, and ∼10 K and ∼0.6 Pa at altitudes of 40–50 km; the error in radius is Δr ≈ 1 m at all levels. Accurate knowledge of the radius permits fixing of the T-p structure to the geopotential and use of the gradient wind equation to calculate components of the wind. Systematic sampling of the atmosphere in combination with the accuracy of the MGS radio system supports studies of the large-scale dynamics of the atmosphere, including seasonal variations of the atmospheric fields and embedded waves such as Kelvin and Rossby waves. Terminator region ionospheric electron density profiles are obtained successfully much of the time but on occasion are undetectable with the MGS system. Two-way radio tracking of MGS with uncertainties in the line-of-sight velocity of several to tens of μm s−1 and less supports solution for spherical harmonic models of the gravity field of order and degree in the range of 75×75, although the degree and order of meaningful terms is limited by the ∼400 km spacecraft altitude to ∼62×62, corresponding to a resolution of a few degrees of arc on the surface. This resolution of gravity is sufficient to support geophysical studies of the planet's interior structure and history. Additional radio science investigations include the search for gravitational radiation and observation of very low grazing angle forward scattering by the surface of Mars.

120 citations


Journal ArticleDOI
TL;DR: In this paper, radio Doppler data generated by the Deep Space Network (DSN) from four encounters of the Galileo spacecraft with Io, Jupiter's innermost Galilean satellite, are used to infer Io's gravitational quadrupole moments.
Abstract: Radio Doppler data generated by the Deep Space Network (DSN) from four encounters of the Galileo spacecraft with Io, Jupiter's innermost Galilean satellite, are used to infer Io's gravitational quadrupole moments. By combining the four flybys into a single solution for the gravity field, the response of Io to the second degree tidal and rotational potentials is accurately determined. This is characterized by the value of the second degree potential Love number k 2 = 1.2924 ± 0.0027. We construct interior models that satisfy constraints imposed by the mean radius R = 1821.6 ± 0.5 km, the mean density p = 3527.8 ± 2.9 kg/m 3 , and the normalized axial moment of inertia C/M R 2 = 0.37685 ± 0.00035. The gravitationally derived figure of Io has principal axes (c < b < a) a = 1830.0 ± 0.5 km, b = 1819.2 ± 0.5 km, and c = 1815.6 ± 0.5 km, consistent with the shape determined by imaging. Gravitational and other data strongly suggest that Io is in hydrostatic equilibrium. In this case, models of Io's interior density show that Io almost certainly has a metallic core with a radius between 550 and 900 km for an Fe-FeS core or between 350 and 650 km for an Fe core. Io is also likely to have a crust and a partially molten asthenosphere, but their thicknesses cannot be separately or uniquely determined from the gravitational data.

118 citations


Journal ArticleDOI
TL;DR: This paper derived spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in 2.5 post-Newtonian approximation to general relativity, one PN order beyond where spin effects first appear.
Abstract: We derive spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in the 2.5 post-Newtonian approximation to general relativity, one PN order beyond where spin effects first appear. Our method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian metric valid for general (continuous) fluids and represent pointlike compact objects with a $\ensuremath{\delta}$-function stress-energy tensor, regularizing divergent terms by taking the Hadamard finite part. To obtain post-Newtonian spin effects, we use a different $\ensuremath{\delta}$-function stress-energy tensor introduced by Bailey and Israel. In a future paper we will use the 2.5PN equations of motion for spinning bodies to derive the gravitational-wave luminosity and phase evolution of binary inspirals, which will be useful in constructing matched filters for signal analysis. The gravitational field derived here may help in posing initial data for numerical evolutions of binary black hole mergers.

Journal ArticleDOI
TL;DR: In this paper, the stability of the Vlasov-Poisson-Fokker-Planck system with respect to the physical constants is analyzed and the existence and uniqueness of solutions of the limit equation in L 1, global or local in time, according to the electrostatic or gravitational character of the field and to the space dimension.
Abstract: This paper is concerned with the analysis of the stability of the Vlasov-PoissonFokker-Planck system with respect to the physical constants. If the scaled thermal mean free path converges to zero and the scaled thermal velocity remains constant, then a hyperbolic limit or equivalently a high-field limit equation is obtained for the mass density. The passage to the limit as well as the existence and uniqueness of solutions of the limit equation in L 1 , global or local in time, are analyzed according to the electrostatic or gravitational character of the field and to the space dimension. In the one-dimensional case a new concept of global solution is introduced. For the gravitational field this concept is shown to be equivalent to the concept of entropy solutions of hyperbolic systems of conservation laws.

Journal ArticleDOI
TL;DR: In this article, the authors present analytic solutions of the Maxwell equations in the internal and external background spacetime of a slowly rotating magnetized neutron star, where the star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation.
Abstract: We present analytic solutions of Maxwell equations in the internal and external background spacetime of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat spacetime solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections due to the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections due both to the spacetime curvature and to the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.

Posted Content
TL;DR: In this article, a practical model for relativistic reduction of positional observations with an accuracy of 1 \muas which is expected to be attained in the future space astrometry missions is presented.
Abstract: This paper is devoted to a practical model for relativistic reduction of positional observations with an accuracy of 1 \muas which is expected to be attained in the future space astrometry missions. All relativistic effects which are caused by the gravitational field of the Solar system and which are of practical importance for this accuracy level are thoroughly calculated and discussed. The model includes relativistic modeling of the motion of observer, modeling of relativistic aberration and gravitational light deflection as well as a relativistic treatment of parallax and proper motion suitable for the accuracy of 1 \muas. The model is formulated both for remote sources (stars, quasars, etc.) and for Solar system objects (asteroids, etc.). The suggested model is formulated within the framework of Parametrized Post-Newtonian Formalism with parameters $\beta$ and $\gamma$. However, for general relativity ($\beta=\gamma=1$) the model is fully compatible with the IAU Resolutions (2000) on relativity in celestial mechanics, astrometry and metrology. The model is presented in a form suitable for implementation in a software system for data processing or simulation. The changes which should be applied to the model to attain the accuracy of 0.1 \muas are reviewed. Potentially important relativistic effects caused by additional gravitational fields which are generated outside of the Solar system are also briefly discussed.

Journal ArticleDOI
TL;DR: In this article, a full cycle numerical simulation of the Radio Science Experiments of the BepiColombo mission has been tested with simulated tracking and accelerometer data, and the determination, by least squares fit, of a long list of variables including the initial conditions for each observed arc, calibration parameters, gravity field harmonic coefficients, and corrections to the orbit of Mercury.

Proceedings ArticleDOI
16 Jan 2001
TL;DR: A review of the classical geometry and dynamics of these braneworld models can be found in this article, where the authors introduce local and non-local effects on the brane.
Abstract: Recent developments in string theory have led to 5-dimensional warped spacetime models in which standard-model fields are confined to a 3-brane (the observed universe), while gravity can propagate in the fifth dimension. Gravity is localized near the brane at low energies, even if the extra dimension is noncompact. A review is given of the classical geometry and dynamics of these braneworld models. The field equations on the brane modify the general relativity equations in two ways: local 5-D effects are imprinted on the brane as a result of its embedding, and are significant at high energies; nonlocal effects arise from the 5-D Weyl tensor. The Weyl tensor transmits tidal (Coulomb), gravitomagnetic and gravitational wave effects to the brane from the 5-D nonlocal gravitational field. Local high-energy effects modify the dynamics of inflation, and increase the amplitude of scalar and tensor perturbations generated by inflation. Nonlocal effects introduce new features in cosmological perturbations. They induce a non-adiabatic mode in scalar perturbations and massive modes in vector and tensor perturbations, and they can support vector perturbations even in the absence of matter vorticity. In astrophysics, local and nonlocal effects introduce fundamental changes to gravitational collapse and black hole solutions.

Journal ArticleDOI
TL;DR: In this article, the authors compare these data with traditional large scale structure surveys to provide us with a test of gravity at such scales, which is of great importance in the framework of higher dimensional cosmological models.
Abstract: Recent developments in gravitational lensing astronomy have paved the way to genuine mappings of the gravitational potential at cosmological scales. We stress that comparing these data with traditional large scale structure surveys will provide us with a test of gravity at such scales. These constraints could be of great importance in the framework of higher dimensional cosmological models.

Journal ArticleDOI
TL;DR: In this article, a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background is presented.
Abstract: The development of high sensitivity and high accuracy atom interferometers requires new theoretical tools for their modelization: in this article we emphasize specifically a generalized Fresnel–Kirchhoff formula for atom optics in the form of ABCD matrices and covariant wave equations in the form of a Dirac equation for atom optics in the presence of gravito-inertial fields. As examples, we derive the phase shift for the atom gravimeter and the output of an atom laser. Some of the physics of the beam splitters is described. We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background. This theory is used to calculate and discuss relativistic phase shifts in the context of matter-wave interferometry (especially atom or antiatom interferometry). In this way, many effects are introduced in a unified relativistic framework, including spin-gravitation terms: gravitational red shift, Thomas precession, Sagnac effect, spin-rotation effect, orbital and spin Lense–Thirring effects, de Sitter geodetic precession and finally the effect of gravitational waves.

Journal ArticleDOI
TL;DR: In this paper, a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations are presented by assuming a particular form of the anisotropy factor.
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.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the possibility of brane-world inflation driven not by an inflaton field on the brane, but by a bulk, dilaton-like gravitational field.
Abstract: Inspired by the Randall-Sundrum brane-world scenario, we investigate the possibility of brane-world inflation driven not by an inflaton field on the brane, but by a bulk, dilaton-like gravitational field. As a toy model for the dilaton-like gravitational field, we consider a minimally coupled massive scalar field in the bulk five-dimensional space-time, and look for a perturbative solution in the anti--de Sitter (AdS) background. For an adequate range of the scalar field mass, we find a unique solution that has a nontrivial dependence on the fifth dimensional coordinate, and that induces slow-roll inflation on the brane.

Journal ArticleDOI
TL;DR: In this article, the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime were obtained in the context of the teleparallel equivalent of general relativity.
Abstract: In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime It is shown that, in the slow rotation and weak-field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus responsible for the Lense-Thirring effect

Journal ArticleDOI
TL;DR: In this article, the authors proposed an architecture of the onboard and ground radio frequency subsystems which combines minimization of mass and power, technological feasibility, and adequate phase stability and ranging accuracy.

Journal ArticleDOI
TL;DR: The quantum gravity program seeks a theory that handles quantum matter fields and gravity consistently, but is such a theory really required and must it involve quantizing the gravitational field? as mentioned in this paper give reasons for a positive answer to the first question, but dispute a widespread contention that it is inconsistent for the gravitational force to be classical while matter is quantum.
Abstract: The quantum gravity program seeks a theory that handles quantum matter fields and gravity consistently. But is such a theory really required and must it involve quantizing the gravitational field? We give reasons for a positive answer to the first question, but dispute a widespread contention that it is inconsistent for the gravitational field to be classical while matter is quantum. In particular, we show how a popular argument (Eppley and Hannah 1997) falls short of a no-go theorem, and discuss possible counterexamples. Important issues in the foundations of physics are shown to bear crucially on all these considerations.

Journal ArticleDOI
TL;DR: The study of the gravity field of arbitrary polyhedral bodies of homogeneous density has provoked a series of publications over the last decades as discussed by the authors, which represented an arbitrary three dimensional body in terms of contours obtained by the intersection of horizontal planes with the body.
Abstract: The study of the gravity field of arbitrary polyhedral bodies of homogeneous density has provoked a series of publications over the last decades. Some of the researchers represented an arbitrary three dimensional body in terms of contours obtained by the intersection of horizontal planes with the body.

Journal ArticleDOI
TL;DR: In this paper, the angular power spectrum of intrinsic galaxy shape correlations was calculated in linear theory and it was shown that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this paper, it was shown that at any point the gravity field from a solid body bounded by plane surfaces and having uniform density can be computed as a force from a fictitious distribution of surface mass density on the same body.
Abstract: We show that at any point the gravity field from a solid body bounded by plane surfaces and having uniform density can be computed as a field from a fictitious distribution of surface mass‐density on the same body. The surface mass density at every surface element is equal to the product of the volume density of the body and the scalar product of (1) the unit outward vector normal to that surface element and (2) the position vector of the surface element with respect to the point of observation. Accordingly, the contribution to the gravity field from any plane surface of the body vanishes if the observation point lies in the plane of that surface. As a result, we can compute the gravity field everywhere, including points inside, on the surface, on an edge, or at a corner of the body where more than two surfaces meet. This new result lets us compute the gravity field using exactly the same simple procedure as for the magnetic field of a uniformly magnetized object, computed from an equivalent surface distr...

Journal ArticleDOI
TL;DR: In this article, a new method of construction of integral varieties of Einstein equations in 3D and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with associated nonlinear connections, the structure of gravity field equations is substantially simplified.
Abstract: A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with associated nonlinear connections, the structure of gravity field equations is substantially simplified. It is shown that there are 4D solutions of Einstein equations which are constructed as nonlinear superpositions of soliton solutions of 2D (pseudo) euclidean sine-Gordon equations (or of lorentzian black holes in Jackiw-Teitelboim dilaton gravity). The Belinski-Zakharov-Meison solitons for vacuum gravitational field equations are generalized to various cases of two and three coordinate dependencies, local anisotropy and matter sources. The general framework of this study is based on investigation of anholonomic soliton-dilaton black hole structures in general relativity. We prove that there are possible static and dynamical black hole, black torus and disk-cylinder like solutions (of non-vacuum gravitational field equations) with horizons being parametrized by hypersurface equations of rotation ellipsoid, torus, cylinder and another type configurations. Solutions describing locally anisotropic variants of the Schwarzschild-Kerr (black hole), Weyl (cylindrical symmetry) and Neugebauer-Meinel (disk) solutions with anisotropic variable masses, distributions of matter and interaction constants are shown to be contained in Einstein's gravity. It is demonstrated in which manner locally anisotropic multi-soliton-dilaton-black hole type solutions can be generated.

Book
01 Jan 2001
TL;DR: In this paper, the authors considered the problem of placing two masses at a purely imaginary distance from one another, and the connection between the two problems was discussed. But the authors focused on the unperturbed and perturbed motion of a satellite, with a digression on asymptotic methods of nonlinear mechanics.
Abstract: First Essay. On the unperturbed and perturbed motion of a satellite, with a digression on asymptotic methods of nonlinear mechanics.- 1. Lucky us!.- 2. Keplerian motion.- 3. Perturbed motion. Osculating elements.- 4. Osculating orbit of an equatorial satellite.- 5. The equations in osculating elements. Delaunay elements.- 6. Digression on asymptotic methods of nonlinear mechanics. Oscillations of a satellite about its center of mass. Averaging of canonical equations.- 7. Satellite in the gravitational field of Earth.- Second Essay. On the rebirth of an old problem, or what happens if two masses are placed at a purely imaginary distance from one another.- 1. From Euler to our days.- 2. The connection between the two problems.- 3. Integration. Coordinate system.- 4. The Hamilton-Jacobi method.- 5. Integration.- 6. The region of motion of a satellite.- 7. Jacobi's elliptic functions.- 8. The motion of a polar Earth satellite.- Third Essay. Yet another reincarnation of an old problem.- 1. And what sort of problem is that?.- 2. Briefly on the equations of motion and their integration.- 3. Plane motion.- 4. Description of the trajectories of plane motion.- 5. A few words about the influence of radiation pressure on the motion of Earth satellites.- Fourth Essay. Motion of the worlds.- 1. One more time about the "Laplace Theorem" and other [Serious] "Things".- 2. Wouldn't you like to see the Moon fall on Earth?.- 3. The region of weakly-perturbed motion.- 4. Stability of the Solar System.- 5. Is the Solar System resonant?.- Fifth Essay. The restricted three-body problem, flight to the Moon, and galactic evolution.- 1. The Hill surfaces.- 2. Digression on libration points.- 3. Moon intercept trajectories and a method for their investigation.- 4. Galactic evolution.- Sixth Essay. They are waltzing in orbits.- 1. Gravitational potential.- 2. Rotation of the Moon. Background material on stability theory.- 3. Stability of relative equilibrium in a gravitational field.- 4. Rhinogradentia in orbit 151.- 5. Passive stabilization of artificial satellites.- 6. Nonlinear oscillations.- 7. Fast rotations.- 8. Where the author slightly frightens the reader.- 9. Explicit form of the perturbed motion.- 10. Pegasus.- 11. Moon, Mercury, resonances.- 12. Schiaparelli and others.- 13. Resonant rotations of celestial bodies and the generalized Cassini laws.- 14. Tendency toward synchronization of rotational motion in complex gravitational fields. Lunar-solar precession and nutation of the Earth's axis.- 15. A model of tidal phenomena and capture into resonant rotation.- 16. Magnetic and magneto-gravitational stabilization.- Seventh Essay. In a spiral to space.- 1. Low thrust.- 2. Escape parameters and paradoxes.- 3. A monotone escape spiral.- 4. Arbitrary trajectories with small eccentricities.- Eighth Essay. The full force of the sun blows in the sails.- Ninth Essay. The gravity flyer.- 1. Force of attraction on a body of non-negligible dimensions.- 2. A pulsating spaceship.- 3. Left behind by your spaceship? Swim breaststroke!.- 4. The gravity flyer and the reader.- 5. The gravity flyer as a resonance phenomenon.- 6. The gravity flyer and writers.- Tenth Essay. Interplanetary flights: low trusts for high goals.- 1. Prelude.- 2. Larger payloads, less fuel.- 3. The Pontryagin maximum principle.- 4. The equation of optimal flight.- 5. No constraints.- 6. The method of carrier trajectories.- 7. The scheme for solving the boundary value problem.- 8. Integration.- 9. Some problems of relative motion.- 10. Computational results for optimal interplanetary trajectories.- 11. Presentation of results of the computation of series of trajectories.- 12. Correction of interplanetary trajectories.- Eleventh Essay. Relative motion of orbiting bodies.- 1. In orbit - two satellites.- 2. The equations of relative motion.- 3. Free motion of an astronaut relative to his spaceship.- 4. Leonov and the lens cap.- 5. Space probe.- 6. Boleadoras in space.- 7. The evolution of mixed motion.- 8. System of linked bodies in space.- 9. Cloud of particles in orbit and the PoincareFirst Essay. On the unperturbed and perturbed motion of a satellite, with a digression on asymptotic methods of nonlinear mechanics.- 1. Lucky us!.- 2. Keplerian motion.- 3. Perturbed motion. Osculating elements.- 4. Osculating orbit of an equatorial satellite.- 5. The equations in osculating elements. Delaunay elements.- 6. Digression on asymptotic methods of nonlinear mechanics. Oscillations of a satellite about its center of mass. Averaging of canonical equations.- 7. Satellite in the gravitational field of Earth.- Second Essay. On the rebirth of an old problem, or what happens if two masses are placed at a purely imaginary distance from one another.- 1. From Euler to our days.- 2. The connection between the two problems.- 3. Integration. Coordinate system.- 4. The Hamilton-Jacobi method.- 5. Integration.- 6. The region of motion of a satellite.- 7. Jacobi's elliptic functions.- 8. The motion of a polar Earth satellite.- Third Essay. Yet another reincarnation of an old problem.- 1. And what sort of problem is that?.- 2. Briefly on the equations of motion and their integration.- 3. Plane motion.- 4. Description of the trajectories of plane motion.- 5. A few words about the influence of radiation pressure on the motion of Earth satellites.- Fourth Essay. Motion of the worlds.- 1. One more time about the "Laplace Theorem" and other [Serious] "Things".- 2. Wouldn't you like to see the Moon fall on Earth?.- 3. The region of weakly-perturbed motion.- 4. Stability of the Solar System.- 5. Is the Solar System resonant?.- Fifth Essay. The restricted three-body problem, flight to the Moon, and galactic evolution.- 1. The Hill surfaces.- 2. Digression on libration points.- 3. Moon intercept trajectories and a method for their investigation.- 4. Galactic evolution.- Sixth Essay. They are waltzing in orbits.- 1. Gravitational potential.- 2. Rotation of the Moon. Background material on stability theory.- 3. Stability of relative equilibrium in a gravitational field.- 4. Rhinogradentia in orbit 151.- 5. Passive stabilization of artificial satellites.- 6. Nonlinear oscillations.- 7. Fast rotations.- 8. Where the author slightly frightens the reader.- 9. Explicit form of the perturbed motion.- 10. Pegasus.- 11. Moon, Mercury, resonances.- 12. Schiaparelli and others.- 13. Resonant rotations of celestial bodies and the generalized Cassini laws.- 14. Tendency toward synchronization of rotational motion in complex gravitational fields. Lunar-solar precession and nutation of the Earth's axis.- 15. A model of tidal phenomena and capture into resonant rotation.- 16. Magnetic and magneto-gravitational stabilization.- Seventh Essay. In a spiral to space.- 1. Low thrust.- 2. Escape parameters and paradoxes.- 3. A monotone escape spiral.- 4. Arbitrary trajectories with small eccentricities.- Eighth Essay. The full force of the sun blows in the sails.- Ninth Essay. The gravity flyer.- 1. Force of attraction on a body of non-negligible dimensions.- 2. A pulsating spaceship.- 3. Left behind by your spaceship? Swim breaststroke!.- 4. The gravity flyer and the reader.- 5. The gravity flyer as a resonance phenomenon.- 6. The gravity flyer and writers.- Tenth Essay. Interplanetary flights: low trusts for high goals.- 1. Prelude.- 2. Larger payloads, less fuel.- 3. The Pontryagin maximum principle.- 4. The equation of optimal flight.- 5. No constraints.- 6. The method of carrier trajectories.- 7. The scheme for solving the boundary value problem.- 8. Integration.- 9. Some problems of relative motion.- 10. Computational results for optimal interplanetary trajectories.- 11. Presentation of results of the computation of series of trajectories.- 12. Correction of interplanetary trajectories.- Eleventh Essay. Relative motion of orbiting bodies.- 1. In orbit - two satellites.- 2. The equations of relative motion.- 3. Free motion of an astronaut relative to his spaceship.- 4. Leonov and the lens cap.- 5. Space probe.- 6. Boleadoras in space.- 7. The evolution of mixed motion.- 8. System of linked bodies in space.- 9. Cloud of particles in orbit and the Poincare recurrence theorem.- Twelfth Essay. Cosmic pinwheel.- 1. The Proton satellites.- 2. Here is how all this was discovered.- 3. What was discovered.- 4. Here is how all this is explained.- References.- Author index.

Journal ArticleDOI
TL;DR: In this article, the authors discuss the non-linear stability of convection in a horizontal porous layer subjected to an inclined temperature gradient and a variable gravity field and show that a decrease in gravity variation has a stabilizing effect on the system.

Journal ArticleDOI
TL;DR: In this paper, the effect of the bulk gravitational field on the cosmological perturbations on a brane embedded in 5D anti-de Sitter (AdS) spacetime is investigated.
Abstract: We investigate the effect of the bulk gravitational field on the cosmological perturbations on a brane embedded in 5D anti--de Sitter (AdS) spacetime. The effective 4D Einstein equations for the scalar cosmological perturbations on the brane are obtained by solving the perturbations in the bulk. Then the behavior of the corrections caused by the bulk gravitational field to the conventional 4D Einstein equation is determined. Two types of correction are found. First we investigate the corrections that become significant at scales below the AdS curvature scales and in the high energy universe with an energy density larger than the tension of the brane. The evolution equation for the perturbations on the brane is found and solved. Another type of correction is induced on the brane if we consider the bulk perturbations, which do not contribute to the metric perturbations but do contribute to matter perturbations. At low energy, they have an imaginary mass ${m}^{2}=\ensuremath{-}(2/3){\mathbf{k}}^{2}$ in the bulk where $\mathbf{k}$ is the 3D comoving wave number of the perturbations. They diverge at the horizon of the AdS spacetime. The induced density perturbations behave as sound waves with a sound velocity of $1/\sqrt{3}$ in the low energy universe. At large scales, they are homogeneous perturbations that depend only on time and decay like radiation. They can be identified as the perturbations of dark radiation. They produce isocurvature perturbations in the matter dominated era. Their effects can be observed as shifts of the location and the height of the acoustic peak in the cosmic microwave background spectrum.