Showing papers on "Gravitational field published in 1977"

Action Integrals and Partition Functions in Quantum Gravity

Abstract: One can evaluate the action for a gravitational field on a section of the complexified spacetime which avoids the singularities. In this manner we obtain finite, purely imaginary values for the actions of the Kerr-Newman solutions and de Sitter space. One interpretation of these values is that they give the probabilities for finding such metrics in the vacuum state. Another interpretation is that they give the contribution of that metric to the partition function for a grand canonical ensemble at a certain temperature, angular momentum, and charge. We use this approach to evaluate the entropy of these metrics and find that it is always equal to one quarter the area of the event horizon in fundamental units. This agrees with previous derivations by completely different methods. In the case of a stationary system such as a star with no event horizon, the gravitational field has no entropy.

Renormalization of Higher Derivative Quantum Gravity

Abstract: Gravitational actions which include terms quadratic in the curvature tensor are renormalizable. The necessary Slavnov identities are derived from Becchi-Rouet-Stora (BRS) transformations of the gravitational and Faddeev-Popov ghost fields. In general, non-gauge-invariant divergences do arise, but they may be absorbed by nonlinear renormalizations of the gravitational and ghost fields (and of the BRS transformations). Fortunately, these artifactual divergences may be eliminated by letting the coefficient of the harmonic gauge-fixing term tend to infinity, thus considerably simplifying the renormalization procedure. Coupling to other renormalizable fields may then be handled in a straightforward manner.

Large-scale heterogeneities in the lower mantle

Abstract: Coefficients of a spherical harmonic expansion, up to angular order 3, of velocity anomalies in five shells within the earth's mantle were obtained from an analysis of nearly 700,000 P wave travel time residuals. The results for depths less than 1100 km are unreliable; on the basis of tests and numerical experiments we infer that lateral heterogeneities in this depth interval are dominated by velocity perturbations of lateral dimensions less than 5000 km. Relatively large wavelength features were resolved below 1500-km depth; the average perturbation level increases in the lowermost mantle. The region between 1100 and 1500 km may represent a transition zone with respect to the dimensions of anomalies. We present statistical evidence for a negative correlation between the long wavelength gravity anomalies observed at the surface and those computed from velocity anomalies at depths greater than 1100 km under the assumption of proportionality between velocity and density perturbations. The proportionality coefficient Δυ/Δρ has been determined by using two different methods: the values are −4.45 and −6.02 (km/s)/(g/cm3). Only minor changes in the velocity distribution are needed to satisfy the long wavelength gravity field exactly. Possible origins of the correlation are (1) sinking of eclogite-rich material into the lower mantle from regions of lithospheric subduction, (2) chemical plumes of light high-velocity material originating near the core-mantle boundary, (3) temperature differences and perturbations of the core-mantle boundary and the earth's surface associated with mantle-wide convection, or (4) static chemical heterogeneities in a nonconvecting mantle. The first three alternatives, all involving flow in the lower mantle, may be complementary but act on a different time scale. There appears to be a westward or northwestward translation of some anomalies with respect to the pattern obtained for the innermost shell. In particular, the direction of translation of a large negative anomaly under the Pacific is in agreement with the sense of motion of the Pacific plate. We must caution the reader, however, that this is a highly speculative interpretation. If correct, it would favor the convective hypotheses.

The back reaction effect in particle creation in curved spacetime

Abstract: The problem of determining the changes in the gravitational field caused by particle creation is investigated in the context of the semiclassical approximation, where the gravitational field (i.e., spacetime geometry) is treated classically and an effective stress energy is assigned to the created particles which acts as a source of the gravitational field. An axiomatic approach is taken. We list five conditions which the renormalized stress-energy operatorTμv should satisfy in order to give a reasonable semiclassical theory. It is proven that these conditions uniquely determineTμv, i.e. there is at most one renormalized stress-energy operator which satisfies all the conditions. We investigate existence by examining an explicit “point-splitting” type prescription for renormalizingTμv. Modulo some standard assumptions which are made in defining the prescription forTμv, it is shown that this prescription satisfies at least four of the five axioms.

On the dispersion of small particles suspended in an isotropic turbulent fluid

Abstract: A solution to the dispersion of small particles suspended in a turbulent fluid is presented, based on the approximation proposed by Phythian for the dispersion of fluid points in an incompressible random fluid. Motion is considered in a frame moving with the mean velocity of the fluid, the forces acting on the particle being taken as gravity and a fluid drag assumed linear in the particle velocity relative to that of the fluid. The probability distribution of the fluid velocity field in this frame is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean. It is shown that, in the absence of gravity, the long-time particle diffusion coefficient is in general greater than that of the fluid, approaching with increasing particle relaxation time a value consistent with the particle being in an Eulerian frame of reference. The effect of gravity is consistent with Yudine's effect of crossing trajectories, reducing unequally the particle diffusion in directions normal to and parallel to the direction of the gravitational field. To characterize the effect of flow and gravity on particle diffusion it has been found useful to use a Froude number defined in terms of the turbulent intensity rather than the mean velocity. Depending upon the value of this number, it is found that the particle integral time scale may initially decrease with increasing particle relaxation time though it eventually rises and approaches the particle relaxation time. It is finally shown how this analysis may be extended to include the extra forces generated by the fluid and particle accelerations.

Infrared divergences in a class of Robertson-Walker universes

Abstract: We investigate infrared divergences of expectation values of products of field operators in a class of curved space-times. The massless minimally coupled scalar field and the linearized gravitational field, quantized on a subset of spatially flat Robertson-Walker background metrics, have such divergences for an apparently natural choice of state vectors. For those states which give a large infrared contribution to the energy-momentum tensor, we show that these metrics cannot be self-consistent solutions of Einstein's equations. Finally, we show that such divergences cannot evolve dynamically in these models from initial conditions which are free of them. These divergences provide one possible criterion for limiting the acceptable choices of state vectors in curved space-time.

The necessity of quantizing the gravitational field

Abstract: The assumption that a classical gravitational field interacts with a quantum system is shown to lead to violations of either momentum conservation or the uncertainty principle, or to result in transmission of signals faster thanc. A similar argument holds for the electromagnetic field.

Laboratory experiments to test relativistic gravity

Abstract: Advancing technology will soon make possible a new class of gravitation experiments: pure laboratory experiments with laboratory sources of non-Newtonian gravity and laboratory detectors. This paper proposes seven such experiments; and for each one it describes, briefly, the dominant sources of noise and the technology required. Three experiments would utilize a high-Q torque balance as the detector. They include (i) an "Ampere-type" experiment to measure the gravitational spin-spin coupling of two rotating bodies, (ii) a search for time changes of the gravitation constant, and (iii) a measurement of the gravity produced by magnetic stresses and energy. Three experiments would utilize a high-Q dielectric crystal as the detector. They include (i) a "Faraday-type" experiment to measure the "electric-type" gravity produced by a time-changing flux of "magnetic-type" gravity, (ii) a search for "preferred-frame" and "preferred-orientation" effects in gravitational coupling, and (iii) a measurement of the gravitational field produced by protons moving in a storage ring at nearly the speed of light. One experiment would use a high-Q toroidal microwave cavity as detector to search for the dragging of inertial frames by a rotating body.

Small-scale structure of spacetime as the origin of the gravitational constant

Abstract: We suggest a means of incorporating the Planck length as a fundamental constant determined by the structure of spacetime. In this scheme the spacetime symmetry group is taken as the de Sitter group with radius of curvature proportional to the Planck length, but we argue that the effects of this curvature are not apparent at elementary-particle length scales. To make the connection with gravity we present a formulation of the gravitational interaction as the gauge theory of the de Sitter group. We obtain an action containing the Einstein-Cartan action, but in which the dimensional gravitational constant $G$ appears naturally as the consequence of the commutation relation of the de Sitter group. We also find a cosmological term, higherderivative couplings of the gravitational field, and a propagating torsion field, which we discuss.

Free-air gravity anomalies in the world's oceans and their relationship to residual elevation

Abstract: Summary Surface-ship gravity measurements were used to obtain 5 times 5° average free–air gravity anomalies over much of the world's oceans. Comparison of the surface data with the recent GEM 6 ’combination’ field shows the combination solution to be in reasonable agreement with the surface data in most areas in the general location and amplitude of major features of the Earth's gravity field. There is, however, significant disagreement on the location of extrema and on the exact values at specific points. It is thus necessary to use surface data to make detailed studies of the relationship of the gravity field to surface features at wavelengths of less than 4000 km. Mid-ocean ridges are consistently characterized by a gravity maximum. The gravity anomaly across mid-ocean ridges can be described by an empirical 1°× 1° average gravity–age relationship which shows a positive gravity anomaly of about 25 mgal falling off to zero by about 40 my. The observed gravity–age relationship is generally compatible with current thermal models of the lithosphere. The empirical gravity–age curve was removed from the free–air anomalies to produce residual gravity anomalies which can be compared to similarly obtained residual depth anomalies. A correlation between the two is found over some features. The most prominent of these are intermediate wavelength positive features associated with areas of extensive off-ridge volcanism. This applies not only to recently active areas but also to inactive areas such as Bermuda and aseismic ridges. On the other hand, areas of unusual elevation and volcanic activity located at a mid-ocean ridge crest such as Iceland and the Azores do not have a corresponding gravity amomaly at intermediate wavelengths. The long-wavelength component of the Earth's gravity field is characterized by large areas in which significant anomalies of constant sign are found. There is no apparent relationship between the long-wavelength gravity anomalies and oceanic depths. If the gravity anomalies have their origin within the asthenosphere, the lithosphere must in effect be decoupled from the main body of the asthenosphere. This could result from the effects of a strongly depth-dependent viscosity on the convection pattern under the elastic plates.

The moment of inertia and isostasy of Mars

Abstract: The systematic and large deviation of the gravitational equipotential surface (EPS) of Mars from a spheroid of revolution suggests a description of Mars in terms of a spheroid nearly in isostatic equilibrium with an extra mass in the Tharsis region. The displacement from Mars and the shape of the spheroid are calculated by using this description and a Mars gravity model. The EPS is represented as a contour map of its height above the spheroid. This representation provides the first clear demonstration that the Hellas depression coincides with a depression in the EPS. The disequilibrium contribution of Tharsis to the coefficient J2 of the second-degree harmonics of gravitational potential of Mars is estimated to be (126 + or - 5) times 10 to the minus 6th. The optical flattening and dynamic flattening calculated on this basis are in substantially better agreement than are those calculated in the usual way.

Gravitational radiation from point-masses in unbound orbits: Newtonian results.

Abstract: Gravitational radiation from a system of two point-masses in unbound orbits (orbital eccentricity e> or =1) is calculated to Newtonian order in the multipole formalism. Waveforms of the multipole amplitudes are presented for bound and unbound orbits. The energy emitted in gravitational waves from an unbound encounter is given by an enhancement factor, g (e), times a function of the other orbital parameters (similar to the results of Peters and Mathews for bound systems). Energy spectra of the gravitational radiation emitted are also presented.

On the gravitational potential and field anomalies due to thin mass layers.

Abstract: Summary. The gravitational potential and field anomalies for thin mass layers are derived using the technique of matched asymptotic expansions. An inner solution is obtained using an expansion in powers of the thickness and it is shown that the outer solution is given by a surface distribution of mass sources and dipoles. Coefficients are evaluated by matching the inner expansion of the outer solution with the outer expansion of the inner solution. The leading term in the inner expansion for the normal gravitational field gives the Bouguer formula. The leading term in the expansion for the gravitational potential gives an expression for the perturbation to the geoid. The predictions given by this term are compared with measurements by satellite altimetry. The second-order terms in the expansion for the gravitational field are required to predict the gravity anomaly at a continental margin. The results are compared with observations.

The generation of gravitational waves. III. Derivation of bremsstrahlung formulae.

Abstract: Formulas are derived describing the gravitational waves produced by a stellar encounter of the following type. The two stars have stationary (i.e., nonpulsating) nearly Newtonian structures with arbitrary relative masses; they fly past each other with an arbitrary relative velocity; and their impact parameter is sufficiently large that they gravitationally deflect each other through an angle that is small as compared with 90 deg.

Geometrodynamics with tensor sources. IV

Abstract: We develop the Hamiltonian hypersurface dynamics of the gravitational field derivatively coupled to general tensor sources. The closing of constraints follows from the independence of the hypersurface action on the path in the space of embeddings. The derivative coupling breaks the DeWitt supermetric in Riem (m).

Are Particle Rest Masses Variable? Theory and Constraints from Solar System Experiments

Abstract: We consider the possibility that particle rest masses may vary in spacetime. According to arguments originated by Dicke, if this is the case various null experiments indicate that all masses vary in the same way. Their variation relative to the Planck-Wheeler mass defines a universal scalar rest-mass field. We construct the relativistic dynamics for this field based on very general assumptions. In addition, we assume Einstein's equations to be valid in Planck-Wheeler units. A special case of the theory coincides with Dicke's reformulation of Brans-Dicke theory as general relativity with variable rest masses. In the general case the rest-mass field is some power $r$ of a scalar field which obeys an ordinary scalar equation with coupling to the curvature of strength $q$. The $r$ and $q$ are the only parameters of the theory. Comparison with experiment is facilitated by recasting the theory into units in which rest masses are constant, the Planck-Wheeler mass varies, and the metric satisfies the equations of a small subset of the scalar-tensor theories of gravitation. The results of solar system experiments, usually used to test general relativity, are here used to delimit the acceptable values of $r$ and $q$. We conclude that if cosmological considerations are not invoked, then the solar-system experiments do not rule out the possibility of rest-mass variability. That is, there are theories which agree with all null and solar-system experiments, and yet contradict the strong equivalence principle by allowing rest masses to vary relative to the Planck-Wheeler mass. We show that the field theory of the rest-mass field can be quantized and interpreted in terms of massless scalar quanta which interact very weakly with matter. This explains why they have not turned up in high-energy experiments. In future reports we shall investigate the implications of various cosmological and astrophysical data for the theory of variable rest masses. The ultimate goal is a firm decision on whether rest masses vary or not.

Lunar gravity: A harmonic analysis

Abstract: A sixteenth-degree and sixteenth-order spherical harmonic lunar gravity field has been derived from the long-term Keplerian variations in the orbits of the Apollo subsatellites and Lunar Orbiter 5. This model resolves the major mascon gravity anomalies of the lunar near side and is in very good agreement with line-of-sight acceleration results. The far-side map shows the major ringed basins to be strong localized negative anomalies located in broad regions of positive gravity which correspond closely to the highlands. The rms pressure levels calculated from equivalent-surface height variations show that the moon and earth support nearly equal pressures, whereas Mars is appreciably stronger. The moon appears to support larger loads than earth owing to its weaker central gravity field and perhaps a colder upper lithosphere. Significant differences between the low-degree gravity and topography spectra indicate that the longer-wavelength topographic features are isostatically compensated.

What is the principle of equivalence

Abstract: The strong principle of equivalence is usually formulated as an assertion that in a sufficiently small, freely falling laboratory the gravitational fields surrounding the laboratory cannot be detected. We show that this is false by presenting several simple examples of phenomena which may be used to detect the gravitational field through its tidal effects; we show that these effects are, in fact, local (observable in an arbitrarily small region). Alternative formulations of the strong principle are discussed and a new formulation of strong equivalence (the ’’Einstein principle’’) as an assertion about the field equations of physics, rather than an assertion about all laws or all experiments, is proposed. We also discuss the weak principle of equivalence and its two complementary aspects: the uniqueness of free fall of test particles in arbitrary gravitational fields (’’Galileo principle’’) and the uniqueness of free fall of arbitrary systems in weak gravitational fields (’’Newton principle’’).

The Production of Elementary Particles by Strong Gravitational Fields

Abstract: The creation of particles by gravitational fields is a natural consequence of quantum field theory in curved space-time. It occurs in particle-antiparticle pairs in the models considered, and does not violate the local conservation laws. This process has important consequences in cosmological and black hole metrics.

Variational method for electromagnetic waves in a magneto-plasma

Abstract: A variational method is presented to derive the electromagnetic response for waves of a model plasma with arbitrary β in a magnetic field whose curvature simulated by a gravitational field. The variational method is particularly well suited for deriving the electromagnetic local dispersion relation and differential equations of long-wavelength modes. In particular, the result is applied to finding the critical β needed for stabilization of low-frequency drift waves with density and temperature gradients.

Rate of particle production in gravitational fields

Abstract: The local rate of production of massless particles is calculated in a weakly anisotropic homogeneous cosmological model, and also in a weak inhomogeneous gravitational field, in which the condition q/sup i/q/sub i/> or =0 is satisfied for the wave vectors of the nonzero Fourier components in second-order perturbation theory The rate turns out to be proportional to the local values of the invariants of the curvature tensor

Constraints on the gravitational constant at large distances

Abstract: D R Long (1976) and others have speculated that the gravitational force between point masses in the Newtonian regime might not be exactly proportional to 1/r squared Distance-dependent deviations from the 1/r squared law can be represented by a distance-dependent gravitational 'constant', G(r) Long has summarized the experimental evidence which constrains G(r) to be very nearly constant for 5 cm less than r less than 1 m This paper presents observational evidence for constancy in the range 1000 km less than r less than 10 to the eighth km, and points out that the value of G(r) identical to Gc in this range has not been experimentally determined Constraints on G(r) in the intermediate distance range 10 m less than r less than 1 km are so poor that one cannot rule out the possibility that Gc differs greatly from the laboratory value Go Models of the earth and sun are used to argue that Gc differs from Go by not more than approximately 40% Methods of improving the determination of Gc are suggested

Third-Order Solution of an Artificial-Satellite Theory

Abstract: A third-order solution is developed for the motions of artificial satellites moving in the gravitational field of the Earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations are derived by Hori’s perturbations method. All quantities are expanded into power series of the eccentricity, but the solution is obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth satellite with a small eccentricity with an accuracy of better than 1 cm over 1 month.

Topics in theoretical and experimental gravitation physics

Abstract: The Generation of Gravitational Waves: A Review of Computational Techniques.- Effects of Gravitational Radiation upon Electromagnetic Waves in a Dispersive Medium.- Gravitational Waves and Their Interaction with Electromagnetic Field.- Shock Waves in General Relativity.- Editorial Comments.- The Detection of Gravitational Waves and Quantum Nondisturbtive Measurements.- Onedimensional Analysis and Computer Simulation of a Weber Antenna.- Comments on the Gravitational Radiation Experiments.- Estimated Sensitivity of the Low Temperature Gravitational Wave Antenna in Rome.- The L.S.U. Low Temperature Gravity Wave Experiment.- Optimal Detection of Signals through Linear Devices with Thermal Noise Sources and Application to the Munich-Frascati Weber-Type Gravitational Wave Detectors.- Synchrotron Radiation and Astrophysics.- Editorial Comments: Development of Singularities.- On the Behavior of Physical Clocks in the Vicinity of Singularities of a Gravitational Field.- Editorial Comments.- Bimetric Theory of Gravitation.- Speculative Remarks on Physics in General and Relativity in Particular.- Gravitation and Tachyons.- General Relativity and Quantum Theory.- Author Index.

Simple Relation Between the Fine Structure and Gravitational Constants

Abstract: A simple relation between the fine-structure constant $\ensuremath{\alpha}$ and the gravitational constant $G$ is derived in a "truly" unified model of the Nambu-Jona-Lasinio type for all elementary-particle forces including gravity.