Showing papers on "Gravitational field published in 1970"
TL;DR: In this paper, a comparison of massive and mass-less theories with experiment, in particular the perihelion movement of Mercury, leads to the exclusion of the massive theory and it is concluded that the graviton mass must be rigorously zero.
1,201 citations
TL;DR: In this article, an analysis of general scalar-tensor gravitation theory, containing two arbitrary functions of the scalar field, is presented, and the relationship between the properties of the source and its radiation is considered in the weak-source limit.
Abstract: An analysis of general scalar-tensor gravitation theory, containing two arbitrary functions of the scalar field, is presented. The weak-field limit is considered in detail, and predictions for the classical tests of gravitation theory are derived. A definite relationship between the light propagation and perihelion shift effects is found to hold under very general conditions. The theory of the detection of gravitational waves is also investigated, and the observable differences between the scalar and tensor components are indicated. Finally, the relationship between the properties of the source and its radiation is considered in the weak-source limit, and expressions for the rate of energy loss are derived. It is shown that the existing observational data are consistent with the possibility that the scalar field represents a major component of gravitational radiation from astronomical sources.
747 citations
TL;DR: In this article, the authors considered the problem of a small particle falling in a Schwarzschild background ("black hole") and examined its spectrum in the high-frequency limit, in terms of the traceless transverse tensor harmonics called electric and magnetic by Mathews.
Abstract: We are concerned with the pulse of gravitational radiation given off when a star falls into a "black hole" near the center of our galaxy. We look at the problem of a small particle falling in a Schwarzschild background ("black hole") and examine its spectrum in the high-frequency limit. In formulating the problem it is essential to pose the correct boundary condition: gravitational radiation not only escaping to infinity but also disappearing down the hole. We have examined the problem in the approximation of linear perturbations from a Schwarzschild background geometry, utilizing the decomposition into the tensor spherical harmonics given by Regge and Wheeler (1957) and by Mathews (1962). The falling particle contributes a $\ensuremath{\delta}$-function source term (geodesic motion in the background Schwarzschild geometry) which is also decomposed into tensor harmonics, each of which "drives" the corresponding perturbation harmonic. The power spectrum radiated in infinity is given in the high-frequency approximation in terms of the traceless transverse tensor harmonics called "electric" and "magnetic" by Mathews.
708 citations
TL;DR: In this paper, the stability of a horizontal layer of fluid heated from above or below is examined for the case of a time-dependent buoyancy force which is generated by shaking the fluid layer, thus causing a sinusoidal modulation of the gravitational field.
Abstract: The stability of a horizontal layer of fluid heated from above or below is examined for the case of a time-dependent buoyancy force which is generated by shaking the fluid layer, thus causing a sinusoidal modulation of the gravitational field. A linearized stability analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. In this analysis, much emphasis is placed on qualitative results obtained by an approximate solution, which permits a rather complete stability analysis. A useful mechanical analogy is developed by considering the effects of gravity modulation on a simple pendulum. Finally, some effects of finite amplitude flows are considered and discussed.
289 citations
TL;DR: In this article, a means of interpreting the Weyl coordinates for static axially symmetric metrics is presented, which allows a reasonable physical interpretation of any given Weyl metric, if the standard coordinate descriptions are used.
Abstract: One of the major problems in understanding solutions of the gravitational field equations is to determine the physical meaning of the coordinates involved. In particular, for the Weyl solutions if the standard coordinate descriptions are used, then physical interpretation becomes difficult. A means of interpreting the Weyl coordinates for static axially symmetric metrics is presented which allows a reasonable physical interpretation of any given Weyl metric.
218 citations
TL;DR: There is a significant correlation between the Earth's gravitational field and the non-dipole part of the geomagnetic field, provided the latter is displaced in longitude.
Abstract: There is a significant correlation between the Earth's gravitational field and the non-dipole part of the geomagnetic field, provided the latter is displaced in longitude.
107 citations
TL;DR: In this article, a new approach based on a gravitational potential energy derived from Gupta's quantum theory of gravitation was proposed to carry out the calculations using only the familiar tools of Newtonian mechanics and the Euler-Lagrange equations.
Abstract: Previous work on the gravitational two-body problem is surveyed Next, we present a new approach, which we consider to be simpler and more transparent than the usual methods because it is based on a gravitational potential energy This enables us to carry out our calculations using only the familiar tools of Newtonian mechanics and the Euler-Lagrange equations Starting from a gravitational potential energy derived from Gupta's quantum theory of gravitation, the classical motion of a spherical gyroscope in the gravitational field of a much larger mass with a quadrupole moment is found The results of the precession of the spin are compared with those of Schiff, and a detailed derivation of the results of O'Connell for the effect of a quadrupole moment (and higher moments) on the precession of the spin is presented In addition, we present some new results First, we show that the quadrupole moment manifests its presence in another way, which also contributes to the precession of the gyroscope a term that is about ten times larger than what could be detected Second, with regard to the precession of the orbit, in addition to the usual contributions, our results include the effects of the spin of both particles (which enables us to calculate the effect of the rotation of Mercury on the precession of its perihelion)
101 citations
TL;DR: In this paper, a method for the construction of the generating functional for fields possessing an invariance group is proposed, and the unitarity and gauge independence of the $S$ matrix on the mass shell are seen explicitly.
Abstract: A method is suggested (and applied to the Yang-Mills and gravitational fields) for the construction of the generating functional ($S$ matrix) for fields possessing an invariance group. The unitarity and gauge independence of the $S$ matrix on the mass shell are seen explicitly.
89 citations
TL;DR: In this article, a solution of Einstein's field equations is derived, representing a thin spherical shell of charged fluid, falling in a spherically symmetric field due to mass and charge at its centre.
Abstract: A solution of Einstein’s field equations is derived, representing a thin spherical shell of charged fluid, falling in a spherically symmetric field due to mass and charge at its centre. No restrictions are placed on the equation of state. By integrating the equations of motion, the law of conservation of total energy is obtained, and used to study the equilibrium states of the system, and their stability against collapse. It is found, under reasonable assumptions, that for a given equation of state and a given entropy, there is a maximum equilibrium mass, and that instability sets in at a critical radius which is always larger (very much larger, for a shell of highly relativistic fluid) than the upper Nordstrom gravitational radius. For uncharged bodies, these results completely parallel, and serve as a simple illustration of, the results of the much more complicated analyses needed for fluid balls.
69 citations
TL;DR: In this paper, a description of the gravitational radiation experiments involving detectors at opposite ends of a 1000 kilometer baseline, at Argonne National Laboratory and the University of Maryland, is given.
Abstract: A description is given of the gravitational radiation experiments involving detectors at opposite ends of a 1000 kilometer baseline, at Argonne National Laboratory and the University of Maryland. Sudden increases in detector output are observed roughly once in several days, coincident within the resolution time of 0.25 seconds. The statistics rule out an accidental origin and experiments rule out seismic and electromagnetic effects. It is reasonable to conclude that gravitational radiation is being observed.
52 citations
TL;DR: In this paper, a generalized SU(2) spinor calculus is established on the ''background space'' V3 of the stationary space • time, and the method of spin coefficients is developed in three dimensions.
Abstract: A generalized SU(2) spinor calculus is established on the ``background space'' V3 of the stationary space‐time. The method of spin coefficients is developed in three dimensions. The stationary field equations can be put to a form which in V3 is analogous to the Newman‐Penrose equations. A V3 filling family of curves is determined by the gravitational field and is called the eigenray congruence. Stationary space‐times may be characterized by the geometric properties of eigenrays. The relation of this classification to the algebraic ones is discussed. The method of solving the equations obtainable for various classes is illustrated on the case of nonshearing geodetic eigenrays. Assuming asymptotic flatness, we obtain the Kerr metric.
TL;DR: Changes in the apparent luminosity and position of a source due to gravitational waves have been examined in the geometrical optics limit by Zipoy2 and here I shall concern myself with fluctuations in the redshift.
Abstract: IT is well known that when light travels through a gravitational field, the field acts like a refracting medium. Even though space may be empty in the sense that the components of the Ricci tensor vanish, we still expect an effect on the propagation of light as suggested by Maxwell's equations where Fμv is the electromagnetic field tensor and Rμvαβ is the Riemann–Christoffel curvature tensor1. If the space between a source of photons and an observer is filled with gravitational radiation, we then expect fluctuations in the appearance of the source analogous to the twinkling of starlight as seen through the Earth's atmosphere. Changes in the apparent luminosity and position of a source due to gravitational waves have been examined in the geometrical optics limit by Zipoy2. Here I shall concern myself with fluctuations in the redshift.
TL;DR: Lunar satellite motion semianalytic solution, considering perturbative effects due to gravitational fields, solar radiation pressure and libration was proposed in this paper, where satellite motion was semianally solved.
Abstract: Lunar satellite motion semianalytic solution, considering perturbative effects due to gravitational fields, solar radiation pressure and libration
01 Jan 1970
TL;DR: In this article, the authors describe two different analyses in which systems which radiate gravitational waves are damped, i.e., two different approaches are used to detect the presence of gravitational waves.
Abstract: Descriptions are presented of two different analyses in which systems which radiate gravitational waves are damped.
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TL;DR: In this article, ifviscosity is taken into account, Keplerian motion of a large number of grains in a gravitational field has a tendency to lead to the formation of jet streams.
Abstract: Ifviscosity is taken into account, Keplerian motion of a large number of grains in a gravitational field has a tendency to lead to the formation ofjet streams.
TL;DR: In this paper, it is shown that the formalism of the previous paper, in which mass and proper time are treated as independent dynamical variables in a canonical formalism, is shown to imply certain physical consequences.
Abstract: The formalism of the previous paper, in which mass and proper time are treated as independent dynamical variables in a canonical formalism, is shown to imply certain physical consequences. There will exist a mass vs proper time uncertainty relation; trajectories and proper time will be exactly determinable in an external gravitational field, while mass will be determinable in an external electromagnetic field; and conventional quantum mechanics will imply that equivalence is invalid for low‐lying quantum states. This leads to a second possible way to quantize a system in a gravitational field, which introduces a fundamental length. It is shown that it is possible to test for quantum interference effects of gravitational systems with present technology and conventional techniques, using the earth's gravitational field.
01 Jan 1970
TL;DR: In this paper, the position of the radio source 3C279 was interferometrically monitored to determine the deviation of its 9.602-GHz radiation in the solar gravitational field.
Abstract: : During its occultation by the sun in October 1969, the position of the radio source 3C279 was interferometrically monitored to determine the deviation of its 9.602-GHz radiation in the solar gravitational field. Rapid instrumental calibration and negligible coronal diffraction enabled the measurement of a General Relativity deflection of 1.77 plus or minus 0.20 seconds at the limb of the sun. This is in close agreement with Einstein's prediction. (Author)
TL;DR: In this article, the tensor field with local gravitation was identified as a tensor tensor with local mass and gravitation, identifying tensor fields with local local mass.
Abstract: Elementary particles gravitational interactions, identifying tensor field with local gravitation
TL;DR: A Schwarzschild field moving with superluminal velocity generates a wake of gravitational radiation which includes a Cerenkov shock-wave as discussed by the authors, which can be seen as an example of a nuclear explosion.
TL;DR: In this paper, the effects of the Moon and Mars gravity field on explosion crater formation and projectile penetration have been investigated, and techniques devised for use in these tests are discussed, as well as approaches used in ultra-high vacuum tests on adhesion and compressibility of basalt powders are discussed.
Abstract: Designs for structures, vehicles, and equipment to be used on the surfaces of the moon and Mars cannot be optimized without a knowledge of how soils in various gravitational fields and atmospheric conditions behave when subjected to static and dynamic loading. Strengths of the lunar and Martian gravitational fields (0.17 and 0.38 times terrestrial, respectively) can be simulated for approximately 30 sec by flying the KC-135 aircraft through appropriate parabolas. Effects of gravitational field on explosion crater formation and projectile penetration have been investigated. Techniques devised for use in these tests are discussed. Diameters of explosion craters and depths of projectile penetration in sand were found to increase as the gravitational field strength decreased. Atmospheric pressure variations down to ultra-high vacuum are significant in the behavior of rock powders. Approaches used in ultra-high vacuum tests on adhesion and compressibility of basalt powders are discussed. The forces of adhesion between rock powders and metal alloy surfaces were noted to be greater in ultra-high vacuum than in air. The forces required to compress slowly a basalt powder are greater after bakeout and exposure to ultra-high vacuum than when this rock powder is tested at atmospheric pressure.
TL;DR: In this paper, a differential equation representing radiation solutions of the general relativistic Weyl equation is derived and the optical properties and the group of motion of the corresponding energy-momentum tensor are studied.
Abstract: A differential equation representing radiation solutions of the general relativistic Weyl equation is derived. Their optical properties and the group of motion of the corresponding energy-momentum tensor are studied. If there exists neutrino radiation the Riemann space must be algebraically special and the propagation of the neutrinos occurs only along one of the principal null directions. Gravitational- and neutrinopp-waves taken together, represent an exact solution of the Weyl-Einstein system of field equations.
TL;DR: In this paper, the spin coefficients and the Riemann tensor are represented as linear combinations of the infinitesimal generators of the group SL(2, C) in a way similar to the way Yang and Mills write their dynamical variables in terms of the Pauli spin matrices.
Abstract: We represent the spin coefficients and the Riemann tensor in the form of linear combinations of the infinitesimal generators of the group SL(2, C). This representation is similar to the way Yang and Mills write their dynamical variables in terms of the Pauli spin matrices. The spin coefficients take the role of the Yang‐Mills‐like potentials, whereas the Riemann tensor takes the role of the fields.
TL;DR: In this paper, the mass of the electron and that of the muon are the roots of a simple quadratic equation, which is obtained from the Reissner-Weyl metric for a charged particle by assuming that the gravitational constant suffers a sharp discontinuity at the surface of a particle, and imposing the condition that dr/dt=0 along the null line ds=0.
Abstract: A gravitational theory of leptons is proposed in which the mass of the electron and that of the muon are the roots of a simple quadratic equation. This equation is obtained from the Reissner-Weyl metric for a charged particle by assuming that the gravitational constant suffers a sharp discontinuity at the surface of a particle, and by imposing the condition that dr/dt=0 along the null line ds=0.
01 Jan 1970
TL;DR: A review of procedures and a summary of recent results on the mass and gravitational field of the moon is presented in this paper, where the relative and absolute precisions of the solutions in fitting the data are illustrated by residual plots and other considerations.
Abstract: This paper presents a review of procedures and a summary of recent results on the mass and gravitational field of the moon. Gravitational field solutions as represented by spherical harmonic expansions of the potential through various degrees and order are available, and typical solutions obtained by the different procedures are presented. The relative and absolute precisions of the solutions in fitting the data are illustrated by residual plots and other considerations. Lunar surface elevation plots, based on the gravitational coefficients (assuming homogeneity), illustrate the distribution and magnitude of mass anomalies over the lunar sphere. For a l3th-order field, the contour plots show considerable correlation with published mascon results in regions where such results are available. The recently obtained gravitational field results are applied to determination of the moments of inertia of the moon, which correspond closely to overall homogeneous density distribution in the moon, and to determination of other properties related to mass distribution.
01 Jan 1970
TL;DR: In the absence of matter, there is naturally no centrally-symmetric solution as the free gravitational field cannot have such symmetry as discussed by the authors, and the solution obtained for the centrally symmetrical problem is actually a particular case of a more general class of solutions.
Abstract: Publisher Summary This chapter examines the general properties of the cosmological solutions of the gravitational equations near a time singularity. The customarily used (Friedmann) cosmological solution of Einstein's gravitational equations is based on the assumption that matter is distributed in space homogeneously and isotropically. This assumption is very far-fetched mathematically, apart from the fact that its fulfillment in a real world can at best be only approximate. The solution obtained for the centrally symmetrical problem is actually a particular case of a more general class of solutions. In the absence of matter, there is naturally no centrally-symmetrical solution as the free gravitational field cannot have such symmetry.
TL;DR: In this paper, the origin and significance of the Newman-Penrose (N•P) constants of the motion were examined from the point of view that constants of motion generate invariant transformations.
Abstract: The origin and significance of the Newman‐Penrose (N‐P) constants of the motion are examined from the point of view that constants of the motion generate invariant transformations. Here the calculation makes use of a generalization of Green's theorem to a situation applicable to the coupled Einstein‐Maxwell fields in general relativity. One finds strictly electromagnetic constants generated by an incoming electromagnetic shock wave, with dipole symmetry, at future null infinity. The gravitational constants contain an admixture from the electromagnetic field. They are generated by an incident quadrupole gravitational shock wave at future null infinity (J+). Both the electromagnetic dipole field and the gravitational quadrupole field behave like linearized fields at J+. All higher‐multipole fields do not uncouple from the nonlinear corrections induced by the self‐coupling of the gravitational field and its coupling with the electromagnetic field. It is shown that the gravitational constants are related to t...
01 Jan 1970
TL;DR: From precisely reduced Baker-Nunn observations for 12 artificial satellites with inclinations between 28° and 96°, coefficients of zonal spherical harmonics up to the 21st order in the expression of the gravitational potential of the earth are derived.
Abstract: From precisely reduced Baker-Nunn observations for 12 artificial satellites with inclinations between 28° and 96°, coefficients of zonal spherical harmonics up to the 21st order in the expression of the gravitational potential of the earth are derived.
Journal Article•
TL;DR: In this article, a semianalytical solution for the problem of the motion of a satellite in orbit around the moon is presented, where the principal perturbations on such a body are due to the nonspherical gravity field of the moon, the attraction of the earth, and, to a lesser degree, the sun.
Abstract: Presented in this theory is a semianalytical solution for the problem of the motion of a satellite in orbit around the moon. The principal perturbations on such a body are due to the nonspherical gravity field of the moon, the attraction of the earth, and, to a lesser degree, the attraction of the sun. The major part of the problem is solved by means of the celebrated von Zeipel Method, first successfully applied to the motion of an artificial earth satellite by Brouwer in 1959. After eliminating from the Hamiltonian all terms with the period of the satellite and those with the period of the moon, it is suggested to solve the remaining problem with the aid of numerical integration of the modified equations of motion. This theory was written in 1964 and presented as a dissertation to Yale University in 1965. Since then a great deal has been learned about the gravity field of the moon. It seems that quite a number of recently determined gravity coefficients would qualify as small quantities of order two. Hence, according to the truncation criteria employed, they should be considered in the present theory. However, the author has not endeavored to update the work accordingly. The final results, therefore, are incomplete in the lunar gravitational perturbations. Nevertheless, the theory does give the largest such variations and it does present the methods by which perturbations may be derived for any gravity terms not actually developed.
TL;DR: Altered gravitational field effects on frog eggs centrifuged under various conditions after fertilization were studied in this paper, where the time dependence of induced abnormalities was observed. But no time dependence was found on the induced abnormalities.