Showing papers on "Gravitational field published in 1980"
TL;DR: In this article, the contribution of photon effective action from one-loop vacuum polarization on a general curved background manifold was calculated, and the corrections to the local propagation of photons were investigated, and it was shown that the quantum corrections introduce tidal gravitational forces on the photons which in general alter the characteristics of propagation, so that in some cases photons travel at speeds greater than unity.
Abstract: We calculate in QED the contribution to the photon effective action from one-loop vacuum polarization on a general curved background manifold, and use it to investigate the corrections to the local propagation of photons. We find that the quantum corrections introduce tidal gravitational forces on the photons which in general alter the characteristics of propagation, so that in some cases photons travel at speeds greater than unity. The effect is nondispersive and gauge invariant. We look at a few examples, including a background Schwarzschild geometry, and we argue that although these results are controversial they do not in fact exhibit any obvious inconsistency.
502 citations
TL;DR: In this article, a simple solution to the vacuum field equations of general relativity in 4 + 1 space-time dimensions leads to a cosmology which at the present epoch has 3 + 1 observable dimensions in which the Einstein-Maxwell equations are obeyed.
Abstract: We show that a simple solution to the vacuum field equations of general relativity in 4 + 1 space-time dimensions leads to a cosmology which at the present epoch has 3 + 1 observable dimensions in which the Einstein-Maxwell equations are obeyed. The large ratio of the electromagnetic to gravitational forces is a consequence of the age of the Universe, in agreement with Dirac's large-number hypothesis.
409 citations
TL;DR: In this article, the authors argue that the quantization of gravity with a cosmological constant, Λ, is both necessary and feasible (in the sense that the evaluation of the functional integral is no more difficult than when Λ= 0).
323 citations
TL;DR: For the spherically symmetric system, this paper proved the existence of a new locally finite flux which can be interpreted to represent the total energy flux of matter and gravitational field, and studied the relation between the behavior of the event horizon and the energy flux across it.
Abstract: For the spherically symmetric system, we prove the existence o{ a new locally cotEen·ecl flux which can be interpreted to represent the total energy flux of matter and gravitational field. ·with the aid of this conservation law, we study the relation between the behavior of the event horizon and the energy flux across it and look for constraints imposed on the total energy radiated to infinity. Some implications of the results of this study to the backreaction problem in the black hole evaporation are discussed.
259 citations
TL;DR: In this article, a line source model is proposed to represent the Kerr metric in the neighborhood of its singular disk, which is shown to lead to a gravitational mass and angular momentum inconsistent with those of the latter metric.
Abstract: A space–time in which in an admissible coordinate system the metric tensor is continuous but has a finite jump in its first and second derivatives across a submanifold will have a curvature tensor containing a Dirac delta function. The support of this distribution may be of three, two, or one dimension or may even consist of a single event. Lichnerowicz’s formalism for dealing with such tensors is modified so as to obtain a formalism in which the Bianchi identities are satisfied in the sense of distributions. The resulting formalism is then applied to the discussion of the Einstein field equations for problems in which the source of the gravitational field is given by a distribution valued stress‐energy tensor. Gravitational shocks are also discussed and their theory is compared with that of high‐frequency gravitational waves given by Y. Choquet‐Bruhat. By considering a class of line sources as obtainable from cylindrical shells by a limiting process, as was proposed by Israel, one may use the distribution formalism developed for hypersurfaces to treat line sources. The line source model proposed by Israel to represent the Kerr metric in the neighborhood of its singular disk is shown to lead to a gravitational mass and angular momentum inconsistent with those of the latter metric. It is proposed to remove this difficulty by changing the assumptions made by Israel concerning the nature of the space–time inside the cylindrical shell which is the support of the distribution in the curvature tensor. The details of the effect of this change are not given in this paper.
186 citations
TL;DR: In this article, the authors discuss the gravity and topography data available for four terrestrial planets (earth, moon, Mars, and Venus), with particular emphasis on drawing inferences regarding the relationship of long-wavelength anomalies to tectonics.
Abstract: The paper discusses the gravity and topography data available for four terrestrial planets (earth, moon, Mars, and Venus), with particular emphasis on drawing inferences regarding the relationship of long-wavelength anomalies to tectonics. The discussion covers statistical analyses of global planetary gravity fields, relationship of gravity anomalies to elastic and viscoelastic models, relationship of gravity anomalies to convection models, finite strength, and isostasy (or the state of isostatic compensation). The cases of the earth and the moon are discussed in some detail. A summary of comparative planetology is presented.
163 citations
TL;DR: In this paper, the authors formulate the general problem of perturbing a (non-self-gravitating) perfect fluid potential flow in an arbitrary background gravitational field and derive the following stability results: (i) no unstable normal modes exist which extend outside the sound horizon of the background flow; and (ii) there are no unstalbe modes which represent a standing shock at sound horizon.
Abstract: We formulate the general problem of perturbing a (non--self-gravitating) perfect fluid potential flow in an arbitrary background gravitational field. We then specialize to the case of perturbing stationary, spherical accretion onto a Schwarzschild black hole and derive the following stability results: (i) no unstable normal modes exist which extend outside the sound horizon of the background flow; and (ii) there are no unstalbe modes which represent a standing shock at the sound horizon.
152 citations
142 citations
TL;DR: In this paper, the Dirac constraint is used to compare descriptions of a given quantum state by two different observers and to illustrate how the principle of equivalence works for quantum systems, and they show that quantum states of a particle moving in a homogeneous gravitational field and of the gravitational harmonic oscillator can be reduced to the study of plane waves in an appropriate frame.
Abstract: In Cartan's description, classical particles freely falling in a Newtonian gravitational field follow geodesics of a curved spacetime. We cast this geodesic motion into generalized Hamiltonian form and quantize it by Dirac's constraint method in a coordinate-independent way. The Dirac constraint takes a simplified form in special noninertial frames (nonrotating, rigid, Galilean, and Gaussian). Transformation theory of the state function allows us to compare descriptions of a given quantum state by two different observers and to illustrate how the principle of equivalence works for quantum systems. In particular, we show that quantum states of a particle moving in a homogeneous gravitational field and of the gravitational harmonic oscillator can be reduced to the study of plane waves in an appropriate frame.
141 citations
TL;DR: In this paper, an equation for the vertical gravity field due to a homogeneous body with polygonal cross-section and finite strike-length is derived, which can be separated into the two-dimensional (2-D) terms of Talwani et al. (1959) and exact terms for the contributions of the ends of the prism.
Abstract: An equation is derived for the vertical gravity field due to a homogeneous body with polygonal cross‐section and finite strike‐length. The equation can be separated into the two‐dimensional (2-D) terms of Talwani et al. (1959) and exact terms for the contributions of the ends of the prism. Equations for the magnetic field due to a similar body were derived by Shuey and Pasquale (1973), who coined the term “two‐and‐a‐half dimensional” (212-D) to describe the geometry. Magnetic intensities are expressed as a vector sum, from which the common dot product formulation can be obtained by binomial expansion.
136 citations
TL;DR: In this article, the authors describe the gravitational field of a barred spiral galaxy as a simple model consisting of two variable components: a central or nuclear disk and a homogeneous triaxial spheroid and one fixed component: an extended disk or halo.
Abstract: The gravitational field of a barred spiral galaxy is described by a simple model consisting of two variable components: a central or nuclear disk and a homogeneous triaxial spheroid: and one fixed component: an extended disk or halo. The model is characterized by five free dimensionless parameters: the ratio of bar mass to central disk mass, two axial ratios of the spheroid, the ratio of the central disk length scale to the spheroid semimajor axis, and the corotation radius in units of the spheroid semimajor axis. Two-dimensional, time-dependent gas dynamical calculations are carried out in the gravitational field resulting from this mass model in order to generate a grid of hydrodynamical models on the five-dimensional parameter space. It is found that over a well-defined domain of this parameter space, the steady-state gas density and velocity distributions resemble the observed morphology and kinematics of the gas in actual SBb galaxies.
TL;DR: In this paper, the authors calculate the post-post-Newtonian contribution to the deflection of starlight by the Sun as well as the post Newtonian deflections due to the Sun's gravitational quadrupole moment and angular momentum.
Abstract: Using a generalized metric, we calculate the post-post-Newtonian (ppN) contribution to the deflection of starlight by the Sun as well as the post-Newtonian deflections due to the Sun's gravitational quadrupole moment and angular momentum. For light rays grazing the Sun, the magnitudes of these deflections predicted by general relativity are, respectively, about 11, 0.2, and 0.7 ..mu..arcsec. A covariance analysis shows that the ppN contribution could be measured with an uncertainty under 20% with an optical interferometer, in Earth orbit, that can determine the separation of stars with an uncertainty of 1 ..mu..arcsec.
TL;DR: For a certain class of three-manifolds, the angular momentum of an asymptotically flat quantum gravitational field can have half-integral values as discussed by the authors, which is the same as the angular angular momentum for a three-dimensional (3D) sphere.
Abstract: For a certain class of three-manifolds, the angular momentum of an asymptotically flat quantum gravitational field can have half-integral values.
TL;DR: In this paper, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and K1.
Abstract: Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipa‐tionless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and K1. The resulting representations of the global tide are stable over at least a ±5% variation in the mean depth of the model basin, and they conserve mass. The paper presents maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each constituent.
TL;DR: In this paper, the authors explore some of the possibilities for constructing new gravitational instantons and find a new type, a rotating analog of the Taub-"bolt" situation, and also rule out the possibility of various multi-instanton configurations.
Abstract: We explore some of the possibilities for constructing new gravitational instantons. We find a new type, a rotating analog of the Taub-"bolt" situation, and we also rule out the possibility of various multi-instanton configurations.
TL;DR: In this paper, the coupled Einstein-Maxwell system linearized away from an arbitrarily given spherically symmetric background space-time is reduced from its four-dimensional to a two-dimensional form expressed solely in terms of gauge-invariant geometrical perturbation objects.
Abstract: The coupled Einstein-Maxwell system linearized away from an arbitrarily given spherically symmetric background space-time is reduced from its four-dimensional to a two-dimensional form expressed solely in terms of gauge-invariant geometrical perturbation objects. These objects, which besides the gravitational and electromagnetic, also include mass-energy degrees of freedom, are defined on the two-manifold spanned by the radial and time coordinates. For charged or uncharged arbitrary matter background the odd-parity perturbation equations for example, reduce to three second-order linear scalar equations driven by matter and charge inhomogeneities. These three equations describe the intercoupled gravitational, electromagnetic, and acoustic perturbational degrees of freedom. For a charged black hole in an asymptotically de Sitter space-time the gravitational and electromagnetic equations decouple into two inhomogeneous scalar wave equations.
TL;DR: In this article, a generalisation of normal ordering to curved space-time is introduced, based on the construction of adiabatic particle states in Robertson-Walker space time.
Abstract: Renormalisation of lambda phi 4 theory in curved space-time is considered in the interaction picture. A generalisation of normal ordering to curved space-time is introduced, based on the construction of adiabatic particle states in Robertson-Walker space-time. Dimensional regularisation is used to define uniquely the divergent quantities which are removed by normal ordering. It is shown that this normal ordering is sufficient to make finite all physical processes including vacuum polarisation to first order in lambda . An alternative and equivalent procedure is given which requires renormalisation of the mass and of the constant which couples the field to the Ricci scalar. The stress tensor is found to be finite to first order in lambda and it is shown that if the free-field theory in a Robertson-Walker universe predicts that particles are created by the gravitational field with a black-body spectrum then this spectrum is maintained when first-order self-interactions are taken into account. Finally, some aspects of the renormalisation of second-order physical processes are discussed.
TL;DR: An improved model of lunar global gravity has been obtained by fitting a sixteenth-degree harmonic series to a combination of Doppler tracking data from Apollo missions 8, 12, 15, and 16, and Lunar Orbiters 1, 2, 3, 4, and 5, and laser ranging data to the lunar surface as discussed by the authors.
Abstract: An improved model of lunar global gravity has been obtained by fitting a sixteenth-degree harmonic series to a combination of Doppler tracking data from Apollo missions 8, 12, 15, and 16, and Lunar Orbiters 1, 2, 3, 4, and 5, and laser ranging data to the lunar surface. To compensate for the irregular selenographic distribution of these data, the solution algorithm has also incorporated a semi-empirical a priori covariance function. Maps of the free-air gravity disturbance and its formal error are presented, as are free-air anomaly and Bouguer anomaly maps. The lunar gravitational variance spectrum has the form V(G; n) = O(n to the -4th power), as do the corresponding terrestrial and martian spectra. The variance spectra of the Bouguer corrections (topography converted to equivalent gravity) for these bodies have the same basic form as the observed gravity; and, in fact, the spectral ratios are nearly constant throughout the observed spectral range for each body. Despite this spectral compatibility, the correlation between gravity and topography is generally quite poor on a global scale.
TL;DR: In this paper, the relativistic theory of isolated systems is described and the derivation of their overall laws of motion along with the asymptotics of gravitational fields near various parts of infinity.
Abstract: Some problems regarding the relativistic theory of isolated systems are described. The description of bodies as a whole and the derivation of their overall laws of motion are considered along with the asymptotics of gravitational fields near various parts of infinity. Attention is given to the connection between near-zone and asymptotic energy-momentum balances, and to the meanings of the following terms: asymptotically flat, physically reasonable T(ab), and condition for absence of incident radiation. In addition, an improved version of a weak-field, slow-motion approximation method for constructing relativistic models of isolated systems containing more than one body is outlined.
TL;DR: In this paper, the accuracy of the geoid maps and sets of harmonic coefficients of order 14, 15 and 30 in the Goddard Earth Model 10B were compared with values obtained independently by analysis of resonant orbits: the results suggest that the values in GEM 10B are realistic for these orders.
Abstract: In recent years the Earth’s gravitational field has been determined with continually improving accuracy, by using hundreds of thousands of observations of Earth satellites, chiefly optical, laser and Doppler, together with surface gravimetry and, most recently, altimeter measurements from the Geos 3 satellite. The geopotential is usually expressed as a double series of tesseral harmonics, and several hundred of the harmonic coefficients are evaluated. Progress in this work during the 1970s is briefly outlined, and some attempt is made to assess the accuracy of current geoid maps and sets of harmonic coefficients, as exemplified in the latest models derived at the Goddard Space Flight Center. The harmonic coefficients of order 14, 15 and 30 in the Goddard Earth Model 10B are compared with values obtained independently by analysis of resonant orbits: the results suggest that the values in GEM 10B are realistic for these orders, and presumably others. It appears that the accuracy of the geoid maps is now approaching 1 m.
TL;DR: In this article, it was shown that any stationary, asymptotically flat solution to Einstein's equation is a solution to the Kerr solution, and a technical lemma on the existence of harmonic coordinates near infinity was proved.
Abstract: Any stationary, asymptotically flat solution to Einstein's equation is shown to asymptotically approach the Kerr solution in a precise sense. As an application of this result we prove a technical lemma on the existence of harmonic coordinates near infinity.
TL;DR: In this paper, a self-contained account of cosmological history and the production of matter in a varying gravitational field is given, which is the origin of the fundamental length scale in field theory, as it is encountered, for example, in present efforts towards grandunification.
TL;DR: In this paper, it was shown that the interaction of the gravitational field with matter leads to a strong modification of the effective gravitational constant in the early universe, and that in certain cases this leads even to the change of sign of the GDC, i.e. to antigravity in the very early universe.
TL;DR: In this article, it is shown that emission of gravitational radiation prevents particles of nonzero rest mass from exceeding the speed of the radiation from the cosmological boundary, and that it is possible for υ g to be less than the speed in the presence of relativistic particles.
TL;DR: In this paper, the authors present algorithms for computing the exact gravitational power radiated and waveforms produced by arbitrary rigid-body freely precessing sources, and present the dominant terms in series expansions of the waveforms for the case of an almost-spherical object with a small wobble angle.
Abstract: A rigid, freely precessing Newtonian body emits gravitational radiation. In this paper I review the classical-mechanics results for free precession which are needed in order to calculate the weak-field slow-motion quadrupole-moment gravitational waves. Within that formalism, I give algorithms for computing the exact gravitational power radiated and waveforms produced by arbitrary rigid-body freely precessing sources. I also present the dominant terms in series expansions of the waveforms for the case of an almost-spherical object precessing with a small wobble angle. These series expansions, which retain the precise frequency dependence of the waves, may be useful for gravitational astronomers when freely precessing sources begin to be observed.
TL;DR: In this paper, the temperature distribution under the Rhinegraben area is constrained by independent geophysical findings: (a) the gravity field and its relation to the crust/mantle boundary, (b) the thinning of the lithosphere, and (c) hot mantle material has been rising during the rifting process.
Abstract: Summary
The temperature distribution beneath the Rhinegraben area is constrained by independent geophysical findings: (a) the gravity field and its relation to the crust/mantle boundary, (b) the thinning of the lithosphere. The interrelationships between these geophysical properties are discussed. An attempt is made to construct the temperature field as a result of a kinematic model. It is postulated that hot mantle material has been rising during the rifting process. The mass displacement is of the order of 1 mm yr−1. In order to determine the transient temperature field the differential equation of heat transport in a moving medium is solved by a two-dimensional numerical method.
The resulting lateral temperature differences reach values of about 350°. This deep-reaching thermal anomaly is compared with other geophysical findings relevant to temperature. It is shown that it matches well with the pronounced elevated asthenosphere. Taking into account the temperature dependence of density it can be demonstrated that the thermally induced gravity effect serves as gravitational compensation for the upwarped upper mantle (see also part II of this paper, Kahle & Werner 1980).
01 Jan 1980
TL;DR: In this paper, the authors review the standard two-surface integral formulation of gravitational energy and momentum and give a detailed discussion of their asymptotic gauge invariances, concluding with an assessment of the current status of this work.
Abstract: In this article I review the standard two-surface integral formulation of gravitational energy and momentum and give a detailed discussion of their asymptotic gauge invariances. I state, summarize, and criticize the important attempts to prove the truth of the positive energy conjecture, ending with an assessment of the current status of this work. I point out some difficulties with the concept of angular momentum in general relativity and propose some partial solutions.
TL;DR: In this paper, it was shown that the Heavisidian field can be written with linear covariant equations in the same way as for the electromagnetic field, and the possibility of reobtaining with this formulation the remaining famous effects of general relativity is discussed.
Abstract: On introducing a new field (called Heavisidian field) which depends on the velocities of gravitational charges in the same way as a magnetic field depends on the velocities of electric charges, it is shown that a gravitational field may be written with linear covariant equations in the same way as for the electromagnetic field. With such equations some important formulae of general relativity, such as those for gravitational radiation and «Coriolis force», are easily reobtained up to a factor 4. Lense-Thirring precession is the equivalent of Larmor precession. The possibility of reobtaining with this formulation the remaining famous effects of general relativity is discussed in the conclusions. This may be important because, if gravitational fields can be written in a tensorial form similar to electromagnetism, conversely, the latter could be reconsidered in terms of space curvature.
TL;DR: In this paper, an estimate of sixth-degree and sixth-order harmonic coefficients of the global gravity field of Venus is obtained by processing the long periodic variations of the mean orbital elements of the Pioneer Venus orbiter.
Abstract: An estimate of sixth-degree and sixth-order harmonic coefficients of the global gravity field of Venus is obtained by processing the long periodic variations of the mean orbital elements of the Pioneer Venus orbiter. Approximately 220 days of data are included in this reduction, which provides almost complete longitudinal coverage. Oblateness is estimated to be -5.97 + or - 3.2 x 10 to the -6. It is noted that the amplitudes of other coefficients are similar to the predicted coefficients using Kaula's rule under equal stress assumption. Atmospheric density values as a function of altitude are obtained to help model drag perturbation. A radial acceleration map at 100 km above the Venus surface is generated, and correlation between gravity anomalies and major topographic features is observed. Spectral analysis of the harmonic model suggests that the interior density anomalies are like those on earth. The orientation angles of the principal axes of the moments of inertia are computed, and deviation of the maximum moment of inertia axis from the spin axis is observed to be small (less than 5 deg). It is found that the minimum moment of inertia axis passes through the Aphrodite and Beta regions.
TL;DR: In this paper, an argument is presented to determine the accuracy with which a solution of Einstein's field equations of gravitation must be approximated in order to describe the dominant effects of gravitational radiation emission from weak-field systems.
Abstract: An argument is presented to determine the accuracy with which a solution of Einstein's field equations of gravitation must be approximated in order to describe the dominant effects of gravitational radiation emission from weak-field systems. Several previous calculations are compared in the light of this argument, and some apparent discrepancies among them are resolved. The majority of these calculations support the 'quadrupole formulae' for gravitational radiation energy loss and radiation reaction.