Showing papers on "Gravitational field published in 1974"

Perturbations of a Rotating Black Hole

Abstract: Decoupled, separable equations describing perturbations of a Kerr black hole are derived. These equations can be used to study black-hole processes involving scalar, electromagnetic, neutrino or gravitational fields. A number of astrophysical applications are made: Misner's idea that gravitational synchrotron radiation might explain Weber's observations is shown to be untenable; rotating black holes are shown to be stable against small perturbations; energy amplification by "superradiant scattering" of waves off a rotating black hole is computed; the "spin down" (loss of angular momentum) of a rotating black hole caused by a stationary non-axisymmetric perturbation is calculated.

On the gravitational field of a massless particle

Abstract: 1. The problem of gravitational fields of massless particles has been discussed by several authors Ll-3 ]. Aichelburg and Sexl[l] and Andreev[2] have considered the field of point particles created at infinity. According to relativistic quantum mechanics a zero-mass particle (in the sequel we shall call it a photon, for the sake of brevity) cannot be localized with an accuracy exceeding i\\.l4] (x is the wavelength divided by 211), therefore the concept of point-photon is an approximate way of describing a wave packet of finite dimensions c... Bonnor[3] has found an exact solution for the gravitational field of a wave packet of arbitrary shape, also produced at infinity. However, the very concept of photon existing at t = 0() is an idealization; in reality one should consider a photon produced at a finite instant of time, -T. In the present paper we determine in the linear approximation the gravitational field of a light packet of finite size c.. produced at the time -T. The solution of the linearized Einstein equation was taken in the form of retarded potentials. As T 0() the equations obtained here, after a gauge transformation, go over into the corresponding expressions of Bonnor's paperL3]. Letting c.. go to zero we then obtain a formula which coincides with the results of[l,2j.

Covariant quantization of the gravitational field

Abstract: A review dedicated to the contemporary methods of quantization of the gravitational field. In view of possible applications to elementary particle theory, the authors consider only asymptotically flat gravitational fields. The basis of the exposed method of quantization is the method of quantization of gauge fields in the functional integration formalism. The main result is the formulation of covariant rules for a diagrammatic perturbation theory. Its elements are the lines representing gravitons and the vertices of graviton-graviton interaction, as well as the lines and interaction vertices of fictitious vector particles ("Faddeev-Popov ghosts") characteristic for the theory of gauge fields. The expressions for the propagators and vertex functions are given explicitly. It is shown that the presence of fictitious particles in the covariant diagram technique guarantees the unitarity of the theory and the agreement between the covariant quantization with the canonical quantization. The bibliography contains 44 entries (54 names).

Earth's gravity field to the eighteenth degree and geocentric coordinates for 104 stations from satellite and terrestrial data

Abstract: Geodetic parameters describing the earth's gravity field and the positions of satellite-tracking stations in a geocentric reference frame have been computed. These parameters were estimated by means of a combination of five different types of data: routine and simultaneous satellite observations, observations of deep space probes, measurements of terrestrial gravity, and surface triangulation data. The combination gives better parameters than does any subset of data types. The dynamic solution used precision-reduced Baker-Nunn observations and laser range data of 25 satellites. Data from the 49-station National Oceanic and Atmospheric Administration BC-4 network, the 19-station Smithsonian Astrophysical Observatory Baker-Nunn network, and independent camera stations were employed in the geometrical solution.

On the Focusing of Gravitational Radiation

Abstract: We investigate the gain in intensity that can be achieved by using a massive object as a ‘lens’ to focus gravitational radiation incident on the object from a point-like source. An object of massM produces a gain in intensity of the order ofαGM/λc2 whereα is a numerical factor which depends on the mass distribution andλ is the wavelength of the radiation. For large mass, the gain is large, but occurs only in a beam of small angular width.

Index of refraction for scalar, electromagnetic, and gravitational waves in weak gravitational fields

Abstract: We consider the solutions of the scattering of scalar, electromagnetic, and gravitational waves by the gravitational field of a single particle, for the case of small wave amplitudes and weak gravitational fields. Scatterings are considered for both incident plane waves and incident spherical waves. For plane waves incident on a thin sheet of matter composed of free particles, the superimposed wave solutions give rise to a phase change arising from the coordinate dependence of the speed of light on the gravitational potential, focusing of the incident wave by the sheet, and, in some cases, a phase change due to dispersion of the wave by the matter. For gravitational waves, the index of refraction $n$ is given by $n\ensuremath{-}1=\frac{2\ensuremath{\pi}G\ensuremath{\rho}}{{\ensuremath{\omega}}^{2}}$, assuming $n\ensuremath{-}1$ is small, and for electromagnetic waves $n=1$ to the same order. The index of refraction for scalar waves depends on the form of the scalar-wave equation used. The generation of back-scattered waves is also treated. Calculations are repeated for spherical waves incident on a thin spherical shell of matter. The propagation of $\ensuremath{\delta}$-function wave packets is then treated in order to show that the solutions are consistent with causality, even though, in some cases, the group velocity exceeds the velocity of light.

Higher Order Gravitational Potential for Many-Body System

Abstract: Gravitational potential for many-body system is obtained up to post-post-Newtonian order of approximation from the metric tensor derived previously, which is Minkowskian at spatial infinity. The calculation is based on the Lagrangian of Fokker type. The transverse­ traceless part of the metric tensor contributes to the potential of post-post-Newtonian order, even to the G3-static part. The fact that the G3-static potential includes the contribution from the transverse-traceless part is the manifestation of non-linear nature of the theory of gravity. The gravitational potential obtained here coincides with that calculated in the canonical formalism, but does not coincide with that obtained in the conventional formalism of quantized theory.

Nongeodesic motion in general relativity

Abstract: The equations of motion of a spinning body in the gravitational field of a much larger mass are found using both the Corinaldesi-Papapetrou spin supplementary condition (SSC) and the Pirani SSC. These equations of motion are compared with our previous result derived from Gupta's quantum theory of Gravitation. It is found that the spin-dependent terms differ in each of the above three results due to a different location of the center of mass of the spinning body. As expected, these terms are not affected by the choice of either Schwarzschild or isotropic coordinates. Finally, for the presently planned Stanford gyroscope experiment, we find the maximum secular displacement of the orbit of the gyro with respect to the orbit of its non-rotating housing to be of the order of (10−7 cm/year)t, a result much smaller than Schiff's result which is proportional to time squared.

Gravity results from Pioneer 10 Doppler data

Abstract: Two-way Doppler data received from Pioneer 10 during its encounter with Jupiter have been analyzed, and preliminary results have been obtained on the mass and the gravity field of Jupiter and on the masses of the four Galilean satellites. The ratios of the masses of the satellites to the mass of Jupiter are approximately 0.00004696 for Io, 0.00002565 for Europa, 0.00007845 for Ganymede, and 0.00005603 for Callisto (all error estimates presented in this paper are standard errors; those for Pioneer 10 represent our evaluation of the real errors as distinguished from formal errors). The ratio of the mass of the sun to the mass of the Jupiter system is about 1047.342, which is in good agreement with recent determinations from the motions of asteroids. The second- and fourth-degree zonal harmonic coefficients in the gravity field of Jupiter are 0.014720 and -0.00065, respectively, based on an equatorial planetary radius of 71,400 km, and the derived dynamical oblateness is 0.0647 at the same radius. The Pioneer 10 data are consistent with the assumption that Jupiter is in hydrostatic equilibrium at all levels.

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

Abstract: The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 095 and vanishes as the value approaches unity A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics

Goddard Earth Models 5 and 6

Abstract: A comprehensive earth model has been developed that consists of two complementary gravitational fields and center-of-mass locations for 134 tracking stations on the earth's surface. One gravitational field is derived solely from satellite tracking data. This data on 27 satellite orbits is the most extensive used for such a solution. A second solution uses this data with 13,400 simultaneous events from satellite camera observations and surface gravimetric anomalies. The satellite-only solution as a whole is accurate to about 4.5 milligals as judged by the surface gravity data. The majority of the station coordinates are accurate to better than 10 meters as judged by independent results from geodetic surveys and by Doppler tracking of both distant space probes and near earth orbits.

Inversion of gravity data for two‐dimensional density distributions

Abstract: By means of an idealized density model composed of two-dimensional rectangular prisms, densities of individual prisms can be determined from a gravity profile by generalized linear inversion Because the analytic expressions for gravitational fields are linear with respect to density, solutions are rapidly determined The principal limitation of the method results from the inherent nonuniqueness of solutions to potential field problems As in any gravity interpretation technique, this difficulty can be partially overcome by the addition of geological or other geophysical information The versatility of the inversion procedure is demonstrated by application to gravity profiles of both noisy and noise-free data over near-surface and deep crustal features

Gravitational Slavnov-Ward identities

Abstract: Functional techniques are used to derive the general Slavnov-Ward identities for the quantized gravitational field. These identities are verified to second order in the coupling constant, employing the technique of dimensional regularization.

Theoretical frameworks for testing relativistic gravity. 5: Post-Newtonian limit of Rosen's theory

Abstract: The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the PPN parameter alpha sub 2, which is related to the difference in propagation speeds for gravitational and electromagnetic waves. Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific but presumably special form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity--and standard solar system experiments cannot distinguish between the two theories.

Generalization of Einstein's principle of equivalence so as to embrace the field equations of gravitation.

Abstract: It is shown that the apparent impossibility of deriving Einstein's field equations of gravitation in a way similar to that used by him in deriving the equations of particle motion and electromagnetism–being a direct generalization of his famous imaginary experiment of a box falling freely in a gravitational field–may be overcome by using the quantal vacuum with its fluctuations instead of the vacuum of ordinary physics with its absolute emptiness. Thus, the Dirac equation with gravitation, thereby used, appears, in contrast to the ordinary view, as the prototype of interaction theory based on general principles, one of them being a generalized principle of equivalence.

Yang's Gravitational Field Equations

Abstract: The gravitational field equations proposed by Yang are shown to be identical with those proposed by Kilmister in 1959. The static, spherically symmetric solution of the Kilmister-Yang field equations is found. It is shown that solar experiments cannot yet distinguish between these equations and Einstein's vacuum equations.

On the stationary gravitational fields

Abstract: The stationary gravitational equations in vacuum are expressed in five different forms. A necessary integral condition on the twist potential φ is derived. The Papapetrou‐Ehlers class of stationary solutions is rederived in a different way. In the study of the complex potential theory it is proved from the field equations that a body admitting an arbitrary symmetry must satisfy an integral condition analogous to the equilibrium criterion. It is proved that the vanishing of the scalar curvature of the associated space implies the flatness of the space‐time metric. A proof is given for the fact that the only analytic functions of the complex potential F which preserve the field equations form a four‐parameter Mobius group. It is also shown that any differentiable function of F and F which preserves the field equations must either be an analytic function of F or the conjugate of such a function. Next the conformastationary vacuum metrics are classified. In the study of the axially symmetric stationary field...

Singularities in Weyl gravitational fields

Abstract: The peculiarities of the scalarS ≡RijklRijkl are exhibited for two axially-symmetric static (Weyl) gravitational fields. By examiningS along curved families of trajectories to the Weyl singularities, examples are found which contradict previous claims by Gautreau and Anderson regarding ‘directional singularities’. Proper circumferences about the Bach and Weyl line-mass singularity are also examined. There is no apparent correlation between the source structure and the behaviour ofS from this analysis.

Gravitational deflection of polarised radiation

Abstract: An upper limit is determined for the difference in the deflection of beams of orthogonally polarised radiation passing through the Sun's gravitational field. A null result is anticipated by present theories of gravitation but this prediction has never been tested.