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Showing papers on "Gravitational field published in 1982"



01 Dec 1982
TL;DR: In this paper, the authors study the solutions of the gravitational field equations which describe the contraction of a heavy star, and give general and qualitative arguments on the behavior of the metrical tensor as the contraction progresses.
Abstract: When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

1,052 citations


Journal ArticleDOI
TL;DR: In this article, a pedagogical review of recent work in which the Einstein-Hilbert gravitational action is obtained as a symmetry-breaking effect in quantum field theory is given, with particular emphasis on the case of renormalizable field theories with dynamical scale-invariance breaking.
Abstract: This article gives a pedagogical review of recent work in which the Einstein-Hilbert gravitational action is obtained as a symmetry-breaking effect in quantum field theory. Particular emphasis is placed on the case of renormalizable field theories with dynamical scale-invariance breaking, in which the induced gravitational effective action is finite and calculable. A functional integral formulation is used throughout, and a detailed analysis is given of the role of dimensional regularization in extracting finite answers from formally quadratically divergent integrals. Expressions are derived for the induced gravitational constant, for the induced cosmological constant, and for quantized matter theories on a background manifold, and a strategy is outlined for computing the induced constants in the case of an SU(n) gauge theory. By use of the background field method, the formalism is extended to the case in which the metric is also quantized, yielding a derivation of the semiclassical Einstein equations as an approximation to quantum gravity, as well as general formulas for the induced (or renormalized) gravitational and cosmological constants.

590 citations


Journal ArticleDOI
TL;DR: In this article, the behavior of fluids in microgravity conditions is examined, with particular regard to applications in the growth of single crystals, and the effects of gravity on fluid behavior are reviewed, and a Shuttle flight is noted to offer extended time for experimentation and processing in a null-gravity environment, with accelerations resulting solely from maneuvering rockets.
Abstract: The behavior of fluids in micro-gravity conditions is examined, with particular regard to applications in the growth of single crystals. The effects of gravity on fluid behavior are reviewed, and the advent of Shuttle flights are noted to offer extended time for experimentation and processing in a null-gravity environment, with accelerations resulting solely from maneuvering rockets. Buoyancy driven flows are considered for the cases stable-, unstable-, and mixed-mode convection. Further discussion is presented on g-jitter, surface-tension gradient, thermoacoustic, and phase-change convection. All the flows are present in both gravity and null gravity conditions, although the effects of buoyancy and g-jitter convection usually overshadow the other effects while in a gravity field. Further work is recommended on critical-state and sedimentation processes in microgravity conditions.

394 citations


Journal ArticleDOI
TL;DR: In this article, a scalar-tensor theory of gravitation is formulated by imposing global scale invariance to the matter part, which is not a variable-G theory in the usual sense.
Abstract: A viable scalar-tensor theory of gravitation is formulated by imposing global scale invariance to the matter part. Nonvanishing masses m of elementary particles as well as the gravitational constant G emerge through the cosmological background value of the scalar field. The scalar field maintains a dynamical degree of freedom in exchange for conformal invariance enjoyed otherwise by the gravity part. The temporal developments of G, m, and the scale factor of the Universe are determined simultaneously by solving coupled differential equations. In the simplest single-scalar model the result is not a variable-G theory in the usual sense. Departures from the standard theory occur through the time-dependent cosmological term. Of particular interest among the solutions are the asymptotically standard solutions.

264 citations



Journal ArticleDOI
TL;DR: In the 'fourth test of general relativity' the gravitational acceleration of celestial bodies-the Earth and the Moon-were experimentally compared in the gravitational field of the Sun as discussed by the authors, and it was found that the Earth and Moon's acceleration in the Sun's gravitational field are the same to one part in 1011.
Abstract: In the 'fourth test of general relativity' the gravitational acceleration of celestial bodies-the Earth and the Moon-were experimentally compared in the gravitational field of the Sun. Because such bodies obtain an appreciable fraction of their total mass-energy from their internal gravitational self-energy (5*10-10 for the Earth), this comparison of free-fall rates measures, among other things, how gravity pulls on gravitational energy and how gravitational energy contributes to the inertial mass of celestial bodies. Using high-precision laser ranging between Earth and reflectors on the Moon's surface, it was found that the Earth and Moon's acceleration in the Sun's gravitational field are the same to one part in 1011. Hypothesising that the gravitational to inertial mass ratio of a celestial body may differ from one by the order of the gravitational self-energy content of the body divided by the total mass-energy: MG/MI=1+ eta (UG/Mc2) eta being a dimensionless constant determined by gravitational theory, the lunar laser ranging experiment limits mod eta mod to less than 1.4*10-2. This experiment is consistent with general relativity which predicts eta =0, but scalar-metric tensor theories, such as the Brans-Dicke theory, vector-metric tensor theories and two-tensor theories of gravity are inconsistent with this experiment unless sufficient adjustable parameters are used.

127 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that any static metric on a space-time manifold with nonvanishing first Betti number (R}_{1}$ is a family of solutions to the electromagnetic Aharonov-Bohm effect.
Abstract: It is well known that gravitational fields may be locally the same but globally distinct due to differences in the topology of their underlying manifolds. Globally stationary but locally static gravitational fields provide an example of gravitational fields which are locally the same but globally distinct in spite of the homeomorphism of their underlying manifolds. Any static metric on a space-time manifold with nonvanishing first Betti number ${R}_{1}$ is shown to generate an ${R}_{1}$-parameter family of such solutions. These fields are seen to provide a gravitational analog of the electromagnetic Aharonov-Bohm effect. The exterior field of a rotating infinite cylinder of matter is discussed as an exactly soluble example.

120 citations


Journal ArticleDOI
TL;DR: In this paper, a discussion of the definition and properties of energy in Einstein's theory of gravitation is devoted to a discussion about the relationship between energy and the generator of displacement with respect to asymptotic time.
Abstract: The review is devoted to a discussion of the definition and properties of energy in Einstein's theory of gravitation. Asymptotically flat space-time is defined in terms of admissible asymptotically Cartesian coordinates and a corresponding group of coordinate transformations. A Lagrange function is introduced on such a space-time, and a generalized Hamiltonian formulation of the theory of gravitation is constructed in accordance with Dirac's method. The energy is defined as the generator of displacement with respect to the asymptotic time. It is shown that the total energy of the gravitational field and the matter fields with normal energy-momentum tensor is positive and vanishes only in the absence of matter fields and gravitational waves. The proof follows Witten's proof but contains a number of corrections and improvements. Various standard criticisms of the energy concept in general relativity are discussed and shown to be without substance.

115 citations


Journal ArticleDOI
TL;DR: In this paper, the perturbations of the energy levels of a freely falling one-electron atom in an arbitrary external gravitational field are considered and the energy-level shifts are calculated to first order in the Riemann tensor for the relativistic $2{P}_{\frac{3}{2}}$ levels and the nonrelativistic$3S, $3P, and $3D$ levels.
Abstract: The perturbations of the energy levels of a freely falling one-electron atom in an arbitrary external gravitational field are considered. The energy-level shifts are calculated to first order in the Riemann tensor for the relativistic $2{P}_{\frac{3}{2}}$ levels and the nonrelativistic $3S$, $3P$, and $3D$ levels. These and earlier results are evaluated explicitly for atoms in radial orbits of the Schwarzschild and parametrized post-Newtonian metrics and for atoms in circular orbits of the Schwarzschild metric. Highly excited Rydberg atoms are also discussed.

105 citations


Journal ArticleDOI
L. H. Ford1
TL;DR: In this article, the limits of the semiclassical theory in which gravity is unquantized are discussed and a hypothetical experiment to demonstrate the existence of gravitons by means of such effects is discussed.

Journal ArticleDOI
TL;DR: In this article, a new model of Mars gravity field in spherical harmonics up to eighteenth degree and order has been computed from all available Doppler tracking data of Mariner 9 and Viking 1 and 2 orbiters.
Abstract: A new model of Mars gravity field in spherical harmonics up to eighteenth degree and order has been computed from all available Doppler tracking data of Mariner 9 and Viking 1 and 2 orbiters. It represents an achievement in the knowledge of Mars global gravitational potential, since no more data will be available for such a derivation before the next mission to the planet. The model has been extensively tested from the point of view of orbit representation over periods of time ranging from a few hours to 12 days, and it is currently used for geophysical studies of the Martian lithosphere.



Journal ArticleDOI
TL;DR: In this paper, a geometric unification of the electromagnetic and gravitational fields is presented, described by a linear connection Γ on the space-time, and field equations for the unified field Γ are equivalent to the Einstein-Maxwell equations.
Abstract: A geometric unification of the electromagnetic and gravitational fields is presented. The unified field is described by a linear connection Γ on the space-time. Field equations for the unified field Γ are equivalent to Einstein-Maxwell equations. Field equations for matter interacting with the unified field are the usual ones. The interaction of the unified field with a charged scalar field is studied in detail.

Journal ArticleDOI
TL;DR: In this paper, an explicit expression for the amplitude obtained after steps (i) and (ii) are taken, in the limit of zero hamiltonian signature (strong coupling), is found.

Journal ArticleDOI
TL;DR: In this article, the radiative Green functions for the massless scalar, electromagnetic and gravitational perturbations of the Kerr space-time are constructed using the Teukolsky (1973) formalism.
Abstract: The radiative Green functions for the massless scalar, electromagnetic and gravitational perturbations of the Kerr space-time are constructed using the Teukolsky (1973) formalism. The reaction force acting upon a test particle, which can emit radiation of any spin s=0, 1, 2, is calculated and shown to account correctly for the energy and the angular momentum carried away by radiation to infinity and to the event horizon. The azimuthal component of the reaction force is found to remain finite for a particle at rest in the Boyer-Lindquist coordinates owing to non-zero angular momentum transfer to the rotating hole. This anomalous static force of radiation reaction emerges as the counteraction to Hawking's tidal friction.

01 Dec 1982
TL;DR: In this article, a translation of the paper Uber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie by Karl Schwarzschild, where he obtained the metric of a space due to the gravitational field of a point-mass.
Abstract: This is a translation of the paper Uber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie by Karl Schwarzschild, where he obtained the metric of a space due to the gravitational field of a point-mass. The paper was originally published in 1916, in Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften, S. 189–196. Translated from the German in 2008 by Larissa Borissova and Dmitri Rabounski. §1. In his study on the motion of the perihelion of Mercury (see his presentation given on November 18, 1915) Einstein set up the following problem: a point moves according to the requirement δ ∫ ds = 0, where ds = √ Σ gμν dxμdxν , μ, ν = 1, 2, 3, 4 

Journal ArticleDOI
TL;DR: In this article, a method for calculating deformation, gravity and potential changes induced by volcanic loads imposed within and on the earth's crust is presented, which involves application of techniques developed for earthquake loading problems in elastic-gravitational earth models.
Abstract: A method for calculating deformation, gravity and potential changes induced by volcanic loads imposed within and on the earth's crust is presented. The method involves application of techniques developed for earthquake loading problems in elastic-gravitational earth models. By considering the elastic-gravitational equilibrium of the layered system, the gravitational and displacement response due to intruding masses and to pressurized magma chambers can be computed. For applications involving seamount loading, variations in the height of sea level can be calculated by requiring that seawater lie along an equipotential. In continental loading problems the change in potential can be used to calculate the orthometric height cahnge as distinct from the geometric height change. For some plausible loading geometries, the difference between these two qunatities can be significant. Results for various loads and earth structures are shown and discussed. In particular, a magmatic mass intruding into an elastic-gravitational lithosphere overlying a compressible, gravitating asthenosphere produces distinct gravity anomalies which depend on the depth of intrusion. Applications of this result can be made to problems of isostatic compensation. The intrusion of a magmatic mass, together with the associated pressurization of the magma chamber, produces distinctive surface gravity and deformation in the near field. Gravity gradients,more » defined as surface gravity divided by uplift, vary with distance from the source. Moreover, orthometric elevations can be significantly (25%) less than geometric elevations. These results have clear application to data from events such as the posteruption deflation of Kilauea volcano.« less

Journal ArticleDOI
TL;DR: In this article, the vacuum polarization by massive scalar particles in the gravitational field of the Schwarzschild black hole is discussed and explicit expression for the vacuum energy-momentum tensor is obtained in the case when the Compton length λ m =ℏ/mc of the massive particle is much less than the gravitational radius of a black hole.

Journal ArticleDOI
TL;DR: In this paper, a mathematical model is constructed to describe timedependent motions which are small deviations from an initial state that is motionless with respect to the rotating frame of reference, where the basic stable density distribution is allowed to be an arbitrary prescribed function of the gravitational potential.
Abstract: Small amplitude oscillations of a uniformly rotating, density stratified, Boussinesq, non-dissipative fluid are examined. A mathematical model is constructed to describe timedependent motions which are small deviations from an initial state that is motionless with respect to the rotating frame of reference. The basic stable density distribution is allowed to be an arbitrary prescribed function of the gravitational potential. The problem is considered for a wide class of gravitational fields. General properties of the eigenvalues and eigenfunctions of square integrable oscillations are demonstrated, and a bound is obtained for the magnitude of the frequencies. The modal solutions are classified as to type. The eigenfunctions for the pressure field are shown to satisfy a second-order partial differential equation of mixed type, and the equation is obtained for the critical surfaces which delineate the elliptic and hyperbolic regions. The nature of the problem is examined in detail for certain speci...

Journal ArticleDOI
TL;DR: In this article, experiments using neutron interference were proposed to test parity and time-reversal violating effects in the interaction of the neutron with the electromagnetic and gravitational fields, including detection of its electric and gravitational dipole moments.
Abstract: Experiments are proposed, using neutron interference, to test possible parity and time-reversal violating effects in the interaction of the neutron with the electromagnetic and gravitational fields, including detection of its electric and gravitational dipole moments These experiments would also test special relativity and general relativity at the quantum mechanical level

Journal ArticleDOI
TL;DR: In this article, the potential of a disk is given, as well as the gravitational field at a point in space, and formulas for a ring can be obtained as the difference between the results presented here for two different values of the disk radius.
Abstract: The gravitational potential of a disk is given, as is the gravitational field at a point in space. It is pointed out that formulas for a ring can be obtained as the difference between the results presented here for two different values of the disk radius. Results are obtained in terms of elliptic integrals and it is shown how these functions can be computed efficiently. Formulas necessary for the computation of partial derivatives are also presented.

Journal ArticleDOI
TL;DR: In this paper, the asymptotic structure of the gravitational field at null infinity is re-examined by allowing certain potentials to develop "wire singularities" keeping the physical fields smooth.
Abstract: The asymptotic structure of the gravitational field at null infinity is re‐examined by allowing certain potentials to develop ‘‘wire singularities’’, keeping the physical fields smooth. This relaxation of the regularity conditions leads to the introduction of the Newman–Unti–Tamburino (NUT) 4‐momentum which is the ‘‘magnetic’’ or the ‘‘dual’’ counterpart of the Bondi–Sachs 4‐momentum. It is shown that, unlike the Bondi–Sachs 4‐momentum, the NUT 4‐vector is absolutely conserved even in the presence of gravitational radiation. Thus, while the gravitational field resembles the nonabelian Yang–Mills fields in its ‘‘electric’’ properties, it is analogous to the abelian Maxwell field in its ‘‘magnetic’’ properties. It is pointed out that gravitational fields with nonvanishing NUT 4‐momenta may have a substantial role in quantum gravity even though they are not physically significant in classical general relativity.

Journal ArticleDOI
01 Aug 1982-Icarus
TL;DR: In this article, radio tracking data acquired over Beta Regio were analyzed to obtain a surface mass distribution from which a detailed vertical gravity field was derived, which was evaluated solely from the topography of the Beta region.


Journal ArticleDOI
TL;DR: An exact vacuum solution of the field equations describing two isolated bodies balanced by their gravitational spin-spin interaction is presented in this paper, which is based on the same model as ours.
Abstract: An exact vacuum solution of Einstein's field equations describing two isolated bodies balanced by their gravitational spin-spin interaction is presented.

Journal ArticleDOI
TL;DR: In this article, the authors present a new, analytic, two parameter family of magnetic fields in equilibrium with isothermal plasma in a gravitational field, and discuss these models from the viewpoint of the insight into the balance of magnetic pressure gradient, and gravitational forces that they provide.
Abstract: Most models of large scale solar magnetic fields assume either that the fields are potential or that they are force free. We present a new, analytic, two parameter family of magnetic fields in equilibrium with isothermal plasma in a gravitational field. We discuss these models from the viewpoint of the insight into the balance of magnetic pressure gradient, and gravitational forces that they provide. We show that substantial deviations from the potential field configuration are obtained for plasma β of order unity, and we emphasize the variety of possible relationships between isobars and magnetic fieldlines.

Journal ArticleDOI
TL;DR: In this paper, the authors extend the theory of van der Waals and of Fisk and Widom for the interfacial density profile below the critical temperature to the one-phase region above critical temperature.
Abstract: The gravitational field induces density gradients in gases near the critical point. These density gradients are usually evaluated with the assumption that the relationship between the local density and local chemical potential is the same as for a macroscopic system in thermodynamic equilibrium. Very close to the critical point the assumption of local equilibrium ceases to be valid. In this paper we obtain the actual density profiles including nonlocal effects. For this purpose we extend the theory of van der Waals and of Fisk and Widom for the interfacial density profile below the critical temperature to the one-phase region above the critical temperature. The nonlocal effects in the density profiles are found to be significant in temperature intervals that are accessible with currently available experimental techniques for temperature control.

Journal ArticleDOI
A. Zee1
TL;DR: Newton's gravitational constant was calculated in a class of scale-invariant gauge theories with an infrared fixed point as mentioned in this paper, where the sign of Newton's constant depends on the coefficients in the renormalization-group $\ensuremath{\beta}$ function.
Abstract: Newton's gravitational constant $G$ is calculated in a class of scale-invariant gauge theories with an infrared fixed point. The sign of $G$ depends on the coefficients in the renormalization-group $\ensuremath{\beta}$ function.