Showing papers on "Gravitation published in 1971"
TL;DR: In this article, the authors present a theory intermediate in position between operator field theory and S-matrix theory, which rejects the dogmas of each and gains thereby a calculational ease and intuitiveness that make it a worthy contender to displace the earlier formulations.
Abstract: This classic, the first of three volumes, presents techniques that emphasize the unity of high-energy particle physics with electrodynamics, gravitational theory, and many-particle cooperative phenomena. What emerges is a theory intermediate in position between operator field theory and S-matrix theory, which rejects the dogmas of each and gains thereby a calculational ease and intuitiveness that make it a worthy contender to displace the earlier formulations.
644 citations
TL;DR: In this article, a simple steady-state solution for the outermost halo, defined as the region from which stars may escape after a few additional orbits through the central core of the system, is presented.
Abstract: The accumulation of stars in the halo of a spherical stellar system, together with the escape of stars from the system, result from stellar encounters within a dense central core. The resultant halo structure is studied both analytically and numerically for an isolated system. On the assumption that conditions in the central core remain constant with time, a simple steady-state solution is obtained for the outermost halo, or 'fringe', defined as the region from which stars may escape after a few additional orbits through the central core of the system. In this steady-state solution the density in phase space, obtained from a simple integral equation for the fringe region, is found to vary nearly linearly with the total energy of a star per unit mass for energies which are less than the energy of escape.
444 citations
01 Jan 1971
TL;DR: In this paper, it was shown that the scalar field in a collapsing star neither disappears nor halts the collapse, as the star passes inside its gravitational radius, even with nonspherical perturbations.
Abstract: It is known that there can be no gravitational, electromagnetic, or scalar field perturbations (except angular momentum) of a Schwarzschild black hole. A gravitationally collapsing star with nonspherical perturbations must therefore radiate away its perturbations or halt its collapse. The results of computations in comoving coordinates are presented to show that the scalar field in a collapsing star neither disappears nor halts the collapse, as the star passes inside its gravitational radius.
On the star's surface, near the event horizon, the scalar field varies as a_1 + a_2 exp (-t/2M) due to time dilation. The dynamics of the field outside the star can be analyzed with a simple wave equation containing a spacetime-curvature induced potential. This potential is impenetrable to zero-frequency waves and thus a_1, the final value of the field on the stellar surface, is not manifested in the exterior; the field vanishes. The monopole perturbation falls off as t^(-2); higher l-poles fall off as ln t/t^(2l+3).
The analysis of scalar-field perturbations works as well for electromagnetic and gravitational perturbations and also for zero-restmass perturbation fields of arbitrary integer spin. All these perturbation fields obey wave equations with curvature potentials that differ little from one field to another. For all fields, radiatable multipoles (l ≥ spin of the field) fall off as lnt/t^(2l+3).
299 citations
TL;DR: In this article, the generalized Dirac equation is of a Heisenberg-Pauli type, and nonlinear terms induced by torsion express a universal spin-spin interaction of range zero.
Abstract: In order to take full account of spin in general relativity, it is necessary to consider space‐time as a metric space with torsion, as was shown elsewhere. We treat a Dirac particle in such a space. The generalized Dirac equation turns out to be of a Heisenberg‐Pauli type. The nonlinear terms induced by torsion express a universal spin‐spin interaction of range zero.
263 citations
215 citations
139 citations
TL;DR: In this paper, a model is proposed which allows a dilaton to show up in a possible non-Newtonian part of the gravitational force, and it can be shown that the force-range of the additional force, if it exists, will be either between 10 m and 1 km or smaller than ∼ 1 cm.
Abstract: A model is proposed which allows a dilaton to show up in a possible non-Newtonian part of the gravitational force. By examining the available observational facts it can be shown that the force-range of the additional force, if it exists, will be either between 10 m and 1 km or smaller than ∼1 cm.
114 citations
TL;DR: In this paper, the inverse of the gravitational constant was used as an effective cutoff mass, and it was shown that to order the electron and photon self-energies are finite, the cutoff can be interpreted as if the electron had an intrinsic radius equal to its Schwarzschild radius.
Abstract: Computations of gravity-modified quantum electrodynamics are performed using nonpolynominal Lagrangian field-theory techniques. The inverse of the gravitational constant appears as an effective cutoff mass, and, in particular, it is shown that to order ${e}^{2}$ the electron and photon self-energies are finite. The cutoff can be interpreted as if the electron had an intrinsic radius equal to its Schwarzschild radius. A central feature is the construction of the tensor gravity superpropagator.
112 citations
01 Nov 1971
TL;DR: In this paper, the authors present metric theories of gravity, including the definition of metric theory, evidence for its existence, and response of matter to gravity with test body trajectories, gravitational red shift, and stressed matter responses.
Abstract: Metric theories of gravity are presented, including the definition of metric theory, evidence for its existence, and response of matter to gravity with test body trajectories, gravitational red shift, and stressed matter responses. Parametrized post-Newtonian framework and interpretations are reviewed. Gamma, beta and gamma, and varied other parameters were measured. Deflection of electromagnetic waves, radar time delay, geodetic gyroscope precession, perihelion shifts, and periodic effects in orbits are among various studies carried out for metric theory experimentation.
81 citations
TL;DR: Galactic clusters evolution in universe with zero rest mass particles, showing size dependence on cosmic dust energy density as discussed by the authors, showing that the size of the clusters depends on the amount of dust energy.
Abstract: Galactic clusters evolution in universe with zero rest mass particles, showing size dependence on cosmic dust energy density
TL;DR: Relativistic gravity in solar system, predicting Newtonian gravitational constant anisotropy measurements by Cavendish experiments as mentioned in this paper, has been shown to be a good fit for the Cavendish experiment.
Abstract: Relativistic gravity in solar system, predicting Newtonian gravitational constant anisotropy measurements by Cavendish experiments
TL;DR: In this paper, a classification of motion for Newtonian gravitational systems as time approaches infinity is presented, where the basic assumption is that the motion survives long enough to be studied, i.e., the solution exists in the interval (0, co). From this classification it is possible to obtain a sketch of the evolving Newtonian universe.
Abstract: In this paper we obtain a classification of motion for Newtonian gravitational systems as time approaches infinity. The basic assumption is that the motion survives long enough to be studied, i.e., the solution exists in the interval (0, co). From this classification it is possible to obtain a sketch of the evolving Newtonian universe. The mathematical study of Newtonian gravitational systems has a long history and has inspired a considerable amount of modern mathematics such as, among other topics, ergodic theory, algebraic topology, qualitative theory of differential equations and some functional analysis. Yet very little seems to be known about gravitational systems beyond the two-body problem. In 1922, J. Chazy [1] was able to classify the motion of the three-body problem as time, t, approaches infinity. In 1967, H. Pollard [7] obtained the first general n-body results as t -+ oo. He obtained results concerning the maximum and minimum spacing between particles as t -+ oo. His work suggests that the behavior of systems with nonnegative energy is in some sense a generalization of the twoand three-body problems. It is the purpose of this paper to sharpen these results and to provide the first classification of motion of the n-body problem, as t -+ oo independent of the sign of the energy. With this classification of motion a sketch of the evolution of Newton's universe as t -+ oo is possible. Also several remaining problems on the growth of systems are partially answered. It is interesting to note that previous classifications of motion have been attempted in terms of the sign of the total energy of the system. It turns out that this approach is far too restrictive and that the classification should be made according to the rate of separation of the particles, as is done here. It will be shown that in the absence of motion that we will call oscillatory and pulsating, the n-body problem is quite well behaved. It separates into clusters where the mutual distances between particles are bounded as t -+ oo. The clusters form subsystems characterized by the separation of clusters like t213. The centers of mass of the subsystems separate asymptotically from each other as Ct. Most of the results depend quite heavily on Tauberian theorems of the type of Landau [20, p. 194] (we follow the customary usage of the o-O symbols): Presented to the Society, January 23, 1970 under the title Classification of motion for gravitational systems; received by the editors March 12, 1970 and, in revised form, June 19, 1970. AMS 1969 suibject classifications. Primary 7034; Secondary 3440, 85XX.
TL;DR: In this article, Papapetrou's covariant equations of motion for a spinning particle at rest outside a rotating mass were derived using the Kerr metric, and it was shown that Schiff's formula for the mass current effect follows from these equations in the lowest approximation.
Abstract: Papapetrou's covariant equations of motion for a spinning particle in a gravitational field are discussed. The equations of motion for the spin of a particle at rest outside a rotating mass are derived using the Kerr metric. It is shown that Schiff's formula for the mass‐current effect follows from these equations in the lowest approximation.
TL;DR: In this article, some gravitational radiation antenna designs are discussed which are capable of distinguishing between the spin zero scalar radiation predicted by the Brans-Dicke theory of gravitation and the spin two tensor radiation predicted in the Einstein theory of gravity.
Abstract: Some gravitational radiation antenna designs are discussed which are capable of distinguishing between the spin zero scalar radiation predicted by the Brans-Dicke theory of gravitation and the spin two tensor radiation predicted by the Einstein theory of gravitation. The antennas will also give information concerning the direction to the source of radiation, and will measure the polarization of the tensor radiation. The designs consist of symmetric masses with approapriately spaced and oriented transducers. The transducers are combined to give orthogonal outputs. Linear combinations of these orthogonal outputs then are uniquely associated with the various possible combinations of radiation type, propagation, direction and polarization, orientation.
TL;DR: In this article, a locally Lorentz-invariant curved-space theory of gravitation, where the local field is a massless, spin-2 field, φΜgn, of Pauli-Fierz type, is presented.
Abstract: A locally Lorentz-invariant curved-space theory of gravitation, where the local field is a massless, spin-2 field, φΜgn, of Pauli-Fierz type, is presented. In this theory gΜΝ is no longer the gravitational potential itself, but reduces to a functional gΜΝ(φ{α/Β}) of φΜgn. Several rigorous and a general iteration solution of this type are exhibited. The static central-body problem reduces to author’s 1958 theory as a special case φΜgn → φ00 =φ and ∂Μ φΜgn → ∂0φ= 0 exactly, so that as in that theory the three classical tests are satisfied.
TL;DR: In this paper, the Brans-Dicke scalar-tensor theory of gravity has been studied under scale transformations of the second kind, and it has been shown that the requirement of scale invariance of second kind leads to the unique value −32 of the adjustable parameter ω in the brans-dicke theory.
Abstract: Invariance of the Brans-Dicke scalar-tensor theory of gravity under scale transformations of the second kind is discussed. It is shown that the requirement of scale invariance of the second kind leads to the unique value −32 of the adjustable parameter ω in the Brans-Dicke theory. It is further shown that, in order to obtain a consistent set of equations, matter must be coupled to the scalar-tensor field in such a way that the whole theory can be transformed into the usual Einstein tensor theory. This is accomplished by performing a space-time dependent scale change such that the transformed scalar field is everywhere a constant.
TL;DR: In this paper, some properties of static cylindrically symmetric universes consisting of gravitational and electromagnetic fields with a central axial mass, charge, or current density are discussed.
Abstract: Some properties of static cylindrically symmetric universes consisting of gravitational and electromagnetic fields with a central axial mass, charge, or current density are discussed Of three permissible distinct configurations, general solutions of the appropriate equations are given for two The properties of the solutions of these two are then examined in greater detail The equations of motion of test particles (both charged and uncharged) are described for some simple trajectories The qualitative effect of the magnetic field on uncharged test particle behavior in some instances is noted as well as the qualitative distinction in the behavior of charged and uncharged test particles The algebraically independent invariants of the Riemann tensor are calculated A stability analysis is carried out for the two solutions when the system is subjected to radial perturbations It turns out that both solutions are stable The stability analysis is carried out by using the equations of the already unified field theory of Rainich, Misner, and Wheeler
TL;DR: In this article, the statistical mechanics of an isolated self-gravitating system consisting of N uniform mass sheets is considered using both canonical and microcanonical ensembles, and the one-particle distribution function is found in closed form.
Abstract: The statistical mechanics of an isolated self-gravitating system consisting of N uniform mass sheets is considered using both canonical and microcanonical ensembles. The one-particle distribution function is found in closed form. The limit for large numbers of sheets with fixed total mass and energy is taken and is shown to yield the isothermal solution of the Vlasov equation. The order of magnitude of the approach to Vlasov theory is found to be 0(1/N). Numerical results for spatial density and velocity distributions are given.
TL;DR: In this paper, the authors discuss the formulation and numerical integration of large systems of differential equations occurring in the gravitational problem of n-bodies, and present a model for solving the problem.
Abstract: This paper discusses the formulation and the numerical integration of large systems of differential equations occurring in the gravitational problem of n-bodies.
TL;DR: In this article, the authors of geophysics textbooks correct for the Bouguer effect by using the gravitational attraction due to an infinite horizontal slab of material (Dobrin, 1960, p. 189; Griffiths and King, 1969, P. 142; Heiland, 1940, p 137; and Howell, 1959, p 221) and show that such a slab of thickness h and density ρ will give rise to an acceleration a = 2πγρh, where ρ is the universal gravitational constant.
Abstract: It is common practice for authors of geophysics textbooks to correct for the Bouguer effect by using the gravitational attraction due to an infinite horizontal slab of material (Dobrin, 1960, p. 189; Griffiths and King, 1969, p. 142; Heiland, 1940, p. 137; and Howell, 1959, p. 221). Such a slab of thickness h and density ρ will give rise to an acceleration a=2πγρh, where γ is the universal gravitational constant.
TL;DR: In this article, modified Debye potentials for an E.M. wave in a simple, angularly homogeneous, material medium in a Schwarzs-child gravitational field were found.
Abstract: From the physical three-vector Maxwell equations for an electromagnetic (E.M.) field in static gravitation, we examine the artifice of replacing the gravitation by an equivalent medium and we find modified Debye potentials for an E.M. wave in a simple, angularly homogeneous, material medium in a Schwarzs-child gravitational field. The fact that these potentials do not obey the generalized scalar wave equation implies that gravitation scatters the vector E.M. wave and a scalar wave differently. Also, we obtain and solve by perturbation the amplitude and eikonal equations for a high-frequency wave in a weak spherical gravitational field. To the order $\frac{M}{r}$, the state of transverse polarization does not change along a ray path whereas the transverse-field amplitudes are modified by the factor ${e}^{\frac{M}{r}}$ which strengthens the field near the mass. The longitudinal-field amplitude, on the other hand, is modified by ${e}^{\frac{\ensuremath{-}M}{r}}$. These effects, in principle, may provide a further test of classical E.M. theory and general relativity.
TL;DR: In this article, a field modification of classical gravitational theory which is analogous to the classical electrodynamics is proposed to account for some types of behavior of matter occurring under certain extreme physical conditions.
Abstract: A field modification of classical gravitational theory which is analogous to the classical electrodynamics is proposed. Within its framework it is possible to account for some types of behaviour of matter occurring under certain extreme physical conditions. Especially, the energy release in quasars and pulsars may be calculated, under some plausible physical assumptions, to obtain values comparable with the observable ones. Several astrophysical effects (e.g. the occurrence of non-thermal radiation in pulsars and quasars, etc.) find reasonable explanations within this field approach to gravitation.
01 Jan 1971