Showing papers on "Gravitational field published in 1971"
TL;DR: In this article, the exact solution from the Schwarzschild metric was obtained by means of a singular Lorentz transformation, and the result was identical with the exact solutions obtained from the singular Langevin transformation.
Abstract: The gravitational field of a massless point particle is first calculated using the linearized field equations. The result is identical with the exact solution, obtained from the Schwarzschild metric by means of a singular Lorentz transformation. The gravitational field of the particle is nonvanishing only on a plane containing the particle and orthogonal to the direction of motion. On this plane the Riemann tensor has a δ-like singularity and is exactly of Petrov typeN.
595 citations
TL;DR: Werner10 has presented a plausible case for believing that his detectors may indeed have monitored frequent and sharply pulsed gravitational waves, which seem to be emanating from the centre of the authors' galaxy.
Abstract: IT has long been recognized that Einstein's gravitational equations admit wave-like solutions. But because of the smallness of the gravitational constant it would require an exceedingly violent astronomical process to generate gravitational waves of sufficient intensity to be detectable with available apparatus. Weber10 has, however, presented a plausible case for believing that his detectors may indeed have monitored frequent and sharply pulsed gravitational waves, which seem to be emanating from the centre of our galaxy. Because such waves could give some very significant information about extraordinary processes which may be taking place in certain regions of the universe, the detection of gravitational waves may be important in the observational astronomy of the future.
294 citations
TL;DR: New boundary conditions on the Einstein-Rosen-Bondi gravitational-wave metrics yield closed inhomogeneous universes which solve Einstein's vacuum field equations exactly as discussed by the authors, and these universes have either the three-sphere topology S3 or the wormhole (hypertorus) topologyS1⊗S2.
Abstract: New boundary conditions on the Einstein-Rosen-Bondi gravitational-wave metrics yield closed inhomogeneous universes which solve Einstein's vacuum field equations exactly. Space sections of these universes have either the three-sphere topology S3 or the wormhole (hypertorus) topology S1⊗S2.
181 citations
01 Jan 1971
165 citations
TL;DR: In this article, matched asymptotic expansions were used for radiating systems in the near zone and wave zone. But their results do not depend upon any definition of gravitational field energy.
Abstract: This paper treats the slow‐motion approximation for radiating systems as a problem in singular perturbations. By using the method of matched asymptotic expansions, we can construct approximations valid both in the near zone and the wave zone. The outgoing‐wave boundary condition applied to the wave‐zone expansion leads, by matching, to a unique and easily calculable radiation resistance in the near zone. The method is developed and illustrated with model problems from mechanics and electromagnetism; these should form a useful and accessible introduction to the method of matched asymptotic expansions. The method is then applied to the general relativistic problem of gravitational radiation from gravitationally bound systems, where a significant part of the radiation can be attributed to nonlinear terms in the expansion of the metric. This analysis shows that the formulas derived from the standard linear approximation remain valid for gravitationally bound systems. In particular, it shows that, according to general relativity, bodies in free‐fall motion do indeed radiate. These results do not depend upon any definition of gravitational field energy.
153 citations
TL;DR: In this paper, the Earth gravity field and satellite tracking stations positions geodetic parameters in geocentric reference frame and positions geodesic parameters in the reference frame of the Earth's gravity field.
Abstract: Earth gravity field and satellite tracking stations positions geodetic parameters in geocentric reference frame
142 citations
TL;DR: In this paper, it was shown that given a curved space-time with a metric tensorgij, Maxwell's equations may be written as if they were valid in a flat space time in which there is an optical medium with a constitutive equation.
Abstract: Given a curved space-time with a metric tensorgij, Maxwell's equations may be written as if they were valid in a flat space-time in which there is an optical medium with a constitutive equation.
132 citations
Book•
01 Jan 1971
TL;DR: A general review of the gravity and magnetic techniques applied in the search for petroleum can be found in this article, where the authors show that the seismic method and its associated data processing account for approximately 95 percent of the total expenditures in petroleum exploration.
Abstract: The purpose of this work is a general review of the gravity and magnetic nlethodsods of geophysicael xplorationa s applied in the search for petroleum. This material is not designed for the gravity and magnetic specialistb ut rather lo)r the geologistsa nd seismologistwsh o may not have a thorough appreciation of the applications of these metht)ds in the overall expl()ration picture. A subtitlc for this monograph might well be "-l'hc Other Five Percerot." This is because the seismic method and its associated data processing account for sornc 95 percent of the total expenditures Ik)r petroleum exploration geophysicss o that whatever application is made of the gravity and magnetic noethods comes out of the other 5 percent. This does not mean that these methods make a proportionately small contribution to the overall exploration effort. Because of the relatively rapid rate of progress in the field, particularly by airborne magnetics. the total area covered by gravity and magnetic surveys may bc greater than that covered by the much greater seismic expendituresA. s a very rough rule-ofthumb, the relative cost per unit area of magneticg, ravity and seismicf ield work with data processings tand in the ratio of I to 10 to 100. It is the hope and purposeo f this monographth at a better appreciatioonf the valueo f the potential methods and understanding of their applicationsm ay be broughta bouts t) that they can be applied with proper perspective in the overall exploration picture. From the beginning of geophysical exploration in the petroleum industry in the 192()'s, three basic physical principles were used: i.e., the measurement of small variations in the magnetic field, the measurement of small variations in the gravitational field, and the propagation of elastic waves through the earth. These three and only these three physical principles are the basis for practically all of the geophysical work up to the present time. Many other methods have been conceived and tried in the field in a limited way, but none has persisted to the extent that field operations are carried out n a scale at all comparable with that of the three primary methods listed above. The seismic method, of course, usually is much more direct in its relation to the geologyt han the potentialm ethodsR. etlection zones or horizons frequently are directly correlative with geologic strata and give relativelya ccuratem easureosf their depth and form.
90 citations
68 citations
TL;DR: Relativistic gravity in solar system, predicting Newtonian gravitational constant anisotropy measurements by Cavendish experiments as mentioned in this paper, has been shown to be a good fit for the Cavendish experiment.
Abstract: Relativistic gravity in solar system, predicting Newtonian gravitational constant anisotropy measurements by Cavendish experiments
61 citations
TL;DR: In this article, Papapetrou's covariant equations of motion for a spinning particle at rest outside a rotating mass were derived using the Kerr metric, and it was shown that Schiff's formula for the mass current effect follows from these equations in the lowest approximation.
Abstract: Papapetrou's covariant equations of motion for a spinning particle in a gravitational field are discussed. The equations of motion for the spin of a particle at rest outside a rotating mass are derived using the Kerr metric. It is shown that Schiff's formula for the mass‐current effect follows from these equations in the lowest approximation.
TL;DR: In this article, a toroidal and poloidal representation of symmetric, traceless, divergenceless, 3-dimensional tensor fields is developed and the properties of the field in the near and far field zones are discussed.
TL;DR: In this article, a dynamic derivation of surface layer representation of the lunar gravitational field from Doppler observations on polar and equatorial lunar orbiters is presented, based on a combination of surface layers.
Abstract: Dynamic derivation of surface layer representation of lunar gravitational field from Doppler observations on polar and equatorial lunar orbiters
TL;DR: The global lunar gravity field was determined from a weighted least squares analysis of the averaged classical element of the five Lunar Orbiters to find the values of the second-degree zonal and sectorial harmonics are compatible with those derived from libration data.
Abstract: The global lunar gravity field was determined from a weighted least squares analysis of the averaged classical element of the five Lunar Orbiters.The observed-minus-computed residuals have been reduced by a factor of 10 from a previously derived gravity field.The values of the second-degree zonal and sectorial harmonics are compatible with those derived from libration data.
TL;DR: In this article, the exact solution for the cosmological equations of Brans and Dicke's scalar-tensor theory when a power law exists between the gravitational constant and the radius of curvature of the universe is sought.
Abstract: The exact solution is sought for the cosmological equations of Brans and Dicke's scalar-tensor theory when a power law exists between the gravitational constant and the radius of curvature of the universe. For the space of negative curvature no solution is possible. On the contrary for a closed space the gravitational constant and the radius of curvature increase linearly with respect to the age of the universe. The parameter ω of the scalar-tensor theory is necessarily negative and can be determined by the present values of the mass-density of the universe, the Hubble-constant and the gravitational constant. The solution has no analogy in Einstein's theory with vanishing cosmological constant, even when the deviations from Einstein's values of the solar relativistic effects are small.
TL;DR: In this paper, a globally static space-time with asymptotically Euclidean behavior representing a finite body of a perfect fluid and a vacuum region is shown to be diffeomorphic to Euclidian space and its metric spherically symmetric whenever the magnitude of the gravitational field strength is only a function of the potential.
Abstract: A globally static space-time with asymptotically Euclidean behavior representing a finite body of a perfect fluid and a vacuum region is shown to be diffeomorphic to Euclidean space and its metric spherically symmetric whenever the magnitude of the gravitational field strength is only a function of the gravitational potential. Under some additional physical assumptions it is then proved that this spherically symmetric solution is not deformable, that is, does not admit a nontrivial first order perturbation that is also a static, asymptotically Euclidean perfect fluid with the same equation of state and the same central value of the pressure and the gravitational potential.
TL;DR: In this article, Doppler tracking of the 5 satellites for which data are available at the National Space Science Data Center have been analyzed to determine the coordinates of 27 tracking stations and the gravity field of the earth represented by the potential of a simple layer.
Abstract: Ten weeks of Doppler tracking of the 5 satellites for which data are available at the National Space Science Data Center have been analyzed to determine the coordinates of 27 tracking stations and the gravity field of the earth represented by the potential of a simple layer. Density values of this layer for 104 surface elements have been computed in a least-squares adjustment and transformed into harmonic coefficients up to the eleventh degree and order. Comparisons with other solutions show good agreement. The results for the equatorial radius of the earth, its flattening, and its gravity at the equator are 6,378,156 meters, 1/298.255, and 978,028.8 mgal, respectively.
TL;DR: In this article, a fresh look on static gravitational fields in general relativity, eight new theorems have been derived, including invariant necessary integral conditions for the existence of a solution, which corresponds to the equilibrium of matter.
Abstract: In a fresh look on static gravitational fields in general relativity, eight new theorems have resulted. Also in the process of deriving theorems a new solution has emerged. In the first of these theorems an invariant necessary integral condition for the existence of a solution has been derived. Physically this condition corresponds to the equilibrium of matter. In the second theorem a scalar condition has been found which implies the flatness of the static gravitational universe. In the third theorem, it has been proved that there cannot occur any group of motion along ``the lines of forces.'' In Theorems 5 and 6, the questions of whether the spatial part of a static gravitational universe can be Einstein, projectively flat, or Stackel are investigated. In the seventh theorem, the static gravitational field equations have been reduced to the geometrized equations in a spatial universe. In the last theorem, all conformastat gravitational universes have been found. One of these is the universe due to ``an i...
TL;DR: There has been no published support yet for Weber's detection of gravitational waves, so an experiment at its early stages is reported.
Abstract: BECAUSE there has been no published support yet for Weber's detection of gravitational waves1, I venture to report an experiment at its early stages.
TL;DR: In this paper, the undulations of the geoid may be computed from spherical harmonic potential coefficients of the earth's gravitational field using three procedures that reflect various points of view on how this computation should be carried out.
Abstract: The undulations of the geoid may be computed from spherical harmonic potential coefficients of the earth’s gravitational field. This paper examines three procedures that reflect various points of view on how this computation should be carried out. One method requires only the flattening of a reference ellipsoid to be defined while the other two methods require a complete definition of the parameters of the ellipsoid. It was found that the various methods give essentially the same undulations provided that correct parameters are chosen for the reference ellipsoid. A discussion is given on how these parameters are chosen and numerical results are reported using recent potential coefficient determinations.
TL;DR: The general stationary vacuum gravitational field of cylindrical symmetry as recently found by Davies and Caplan is even static as discussed by the authors, and the possible Petrov types of the Riemann tensor are I,D orO.
Abstract: The general stationary vacuum gravitational field of cylindrical symmetry as recently found by Davies and Caplan is even static. The possible Petrov types of the Riemann tensor areI,D orO. In spacelike infinity the spacetime becomes necessarily flat.
TL;DR: In this paper, the motion of a rocket with constant thrust in the gravitational field of a mass point is studied, and it is shown that, for the three dimensional case, the KS-variables produce the separability.
Abstract: The motion of a rocket (with constant thrust) in the gravitational field of a mass point is studied. As is well known, the two dimensional version of this problem is separable in Levi-Civitavariables. It is shown here that, for the three dimensional case, the KS-variables produce the separability. A closed solution is found by using elliptic functions. Equivalent problems are mentioned.
TL;DR: In this article, a simple cosmological model was proposed to explain the missing mass attributed to gravitational waves and dead, dark galaxies, which is described by a simple rate equation containing a characteristic frequency α.
Abstract: The strong bursts of gravitational waves detected by Weber, if confirmed, suggest the presence in the Galaxy of arelativistic cluster of collapsed bodies which «burns» its own gravitational potential energy and slowly decays into a dead, collapsed object. We discuss the possibility of this being a common feature throughout the universe and consider a simple cosmological model in which the «missing mass» is attributed mainly to gravitational waves and dead, dark galaxies. The production of the former is described by a simple rate equation containing a characteristic frequency α. Using the known value of the Hubble constantH and the present visible mass density we find, when the efficiency of the process is, say, 0.5, α≈8H; the corresponding gravitational brightness of an average galaxy turns out to agree with Weber's figure (assuming a wide-band spectrum) to within a factor 2. This model features an isotropic cosmological background of gravitational waves, with energy density about 50 times smaller than the energy arriving from the galactic nucleus.
TL;DR: In this paper, the combined gravitational-neutrino field equations are solved, subject only to the restriction that the energy flow vector of the neutrino fields be timelike or null.
Abstract: The combined gravitational‐neutrino field equations are solved, subject only to the restriction that the energy‐flow vector of the neutrino field be timelike or null. The principal null congruence (pnc) of the neutrino field is necessarily geodesic and shear‐free, and coincides with a repeated pnc of the gravitational field, which is thus algebraically special. The twist of the neutrino pnc plays an important role, and is zero if and only if the neutrino energy‐flow vector is null, in which case the neutrino field represents pure radiation.