Showing papers on "Gravitation published in 1968"

Comments on the scalar-tensor theory

Abstract: Scalar-tensor theories are discussed as encompassing three classical long-range fields, including the electromagnetic field. In order to shed additional light on the restrictive assumptions made by Dicke concerning the coupling of the scalar field with matter, the ponderomotive laws of a scalar-tensor theory are constructed free of approximations in the form of integral laws. The integrals are extended over two- and three-dimensional domains that lie entirely in empty space but surround the regions containing matter; as for the latter, the vacuum field equations are not required to hold, but no further assumptions are made. It turns out that the gradient of the incident scalar field will contribute to the rate of change of the mass and linear momentum of a ‘particle’ an amount proportional to that particle's scalar-field source strength, which in turn is an arbitrary function of time, unless Dicke's special restriction is imposed. To this extent the motion of a test particle is indeterminate, contrary to experience.

New Formulation of the Axially Symmetric Gravitational Field Problem. II

Abstract: The field equations governing the gravitational field of a uniformly rotating axially symmetric source are reformulated in terms of a simple variational principle. The new formalism affords a concise unified derivation of the solutions discovered by Weyl and Papapetrou, and permits a simple derivation of the Kerr metric in terms of prolate spheroidal coordinates. More complex solutions are identified by applying perturbation theory.

Relativity and cosmology

Abstract: : Relativity and Cosmology is a presentation of the fundamentals of special relativity, general relativity, and cosmology- with particular emphasis and development of (1) the electromagnetic stress-energy tensor in special relativity, (2) the poynting-Robertson effect, (3) the experimental basis for special-relativistic gravitational theories, (4) the geometric foundation for Reimannian geometry, (5) the derivation of the cosmological metric from group theory, (6) a discussion of cosmological models, (7) rotation of coordinate systems in general relativity, (8) electromagnetism in media in general relativity, (9) rotationally symmetric general-relativistic solutions, (10) Godel's cosmological model, and (11) geodesic precession.

New Conservation Laws for Zero Rest-Mass Fields in Asymptotically Flat Space-Time

Abstract: Some recently discovered exact conservation laws for asymptotically flat gravitational fields are discussed in detail. The analogous conservation laws for zero rest-mass fields of arbitrary spin s(= 0, $\frac{1}{2}$, 1, $\ldots$) in flat or asymptotically flat space-time are also considered and their connexion with a generalization of Kirchoff's integral is pointed out. In flat space-time, an infinite hierarchy of such conservation laws exists for each spin value, but these have a somewhat trivial interpretation, describing the asymptotic incoming field (in fact giving the coefficients of a power series expansion of the incoming field). The Maxwell and linearized Einstein theories are analysed here particularly. In asymptotically flat space-time, only the first set of quantities of the hierarchy remain absolutely conserved. These are 4s + 2 real quantities, for spin s, giving a D(s, 0) representation of the Bondi-Metzner-Sachs group. But even for these quantities the simple interpretation in terms of incoming waves no longer holds good: it emerges from a study of the stationary gravitational fields that a contribution to the quantities involving the gravitational multipole structure of the field must also be present. Only the vacuum Einstein theory is analysed in this connexion here, the corresponding discussions of the Einstein-Maxwell theory (by Exton and the authors) and the Einstein-Maxwell-neutrino theory (by Exton) being given elsewhere. (A discussion of fields of higher spin in curved space-time along these lines would encounter the familiar difficulties first pointed out by Buchdahl.) One consequence of the discussion given here is that a stationary asymptotically flat gravitational field cannot become radiative and then stationary again after a finite time, except possibly if a certain (origin independent) quadratic combination of multipole moments returns to its original value. This indicates the existence of 'tails' to the outgoing waves (or back-scattered field), which destroys the stationary nature of the final field.

Isotropic Solutions of the Einstein‐Liouville Equations

Abstract: The gravitational fieldgenerated by a gas whose one‐particle distribution function obeys the Liouville equation is examined under the following assumptions: First, the distribution is locally isotropic in momentum space with respect to some world‐velocity field; second, if the particles have rest‐mass zero, the gas is irrotational. It is shown that the model is then either stationary or a Robertson‐Walker model. The time dependence of the radius in the Robertson‐Walker models is given in terms of integrals containing the distribution function.

Charged shells in general relativity and their gravitational collapse

Abstract: The boundary conditions for the gravitational and electromagnetic fields on charged shells are formulated. The shells are characterized in geometrical terms and the boundary conditions are manifestly covariant. The formalism is applied to the study of the gravitational collapse of homogeneous charged spherical shells. The law of conservation of energy, obtained by integrating the equations of motion of the shell and interpreted in full analogy with the special theory of relativity, is the starting point in analyzing the equilibrium states and the motion of the shells. It is concluded that no charge, however high it may be, can stop the gravitational collapse of the shell below the upper Nordstrom radius.

Possibility of the Speed of Sound Exceeding the Speed of Light in Ultradense Matter

Abstract: We show that, in the classical physics of very dense matter, Lorentz invariance imposes no restriction on the speed of sound or on the ratio of pressure to energy density. Indeed, the simplest and most reasonable classical many-particle theory can manifest such apparently noncausal behavior whenever the calculated self-energy of a particle exceeds its observed (renormalized) rest energy. This comes about because ordinary mass renormalization subtracts out part of a particle's self-interaction energy without altering the interaction with other particles that contributes to pressure. Two types of models are exhibited which, at low densities, show normal behavior and, at high densities, become superluminal (speed of sound greater than speed of light in vacuum) and ultrabaric (pressure greater than energy density). One is a system of classical particles which, when stationary, repel each other by a short-range repulsive Yukawa interaction. Although the particles interact through ordinary retarded neutral vector fields, after mass renormalization there must always be a domain of sufficiently high densities where this matter becomes superluminal and ultrabaric. The second group of models is a class of classical Lorentz-invariant nonlinear field theories which, in the limit of low densities, reduces to a noninteracting Klein-Gordon field. If matter deep inside superdense stars could be ultrabaric, then the limiting gravitational red shift from the star's surface would be slightly under 2. This is perhaps suggestive of the observed clustering of quasar absorption-line red shifts at 1.95.

Further examples of ''Machian'' effects of rotating bodies in general relativity.

Abstract: The exact field equations for the metric of axially symmetric, stationary rotating bodies in general relativity are exhibited. They are applied to calculate, to first order in the angular velocity of rotation (but without restriction to weak gravitational fields), the rotation of the inertial frame induced by an incompressible fluid sphere, and by concentric mass shells. In addition, the effect of the exterior field of rotating bodies on light rays is discussed. The results of this paper appear qualitatively to agree with some of Mach’s ideas on the origin of inertia.

Experiments to determine the force of gravity on single electrons and positrons.

Abstract: Gravitational force measurement on electrons and positrons in free fall through vertical metal tubes at low temperatures

Equatorial geodesic motion in the gravitational field of a rotating source

Abstract: The purpose of this note is to investigate the geodesic motion in the gravitational field of a rotating source, making use of the exact empty-space solutions of Einstein’s equations given by Kerr. The earlier weak-field approximate solutions of Lense and Thirring for a rotating body are also examined to compare them with the exact case and with the Schwarzschild nonrotating one, whose geodesic properties are also briefly summarized. The behaviour of single orbits, for example the precession of the pericenter, will not be mentioned since they have been extensively analysed in the cited references. The differential equations of the geodesics are analysed from an analytical point of view in order to recognize the shape of the loci of the turning points for the test particles without introducing numerical values of the parameters involved such asa (specific angular momentum of the rotating body) andΓ (test particle’s effective energy). Diagrams are given which show the behaviour of the geodesics for different ranges of these parameters. An attempt to make a physical comparison between these three cases has been done in the last Section.

John Michell and Henry Cavendish: Weighing the Stars

Abstract: Newton wrote in the Principia that all bodies are to be regarded as subject to the principle of gravitation. Every body, however great or small, is related to every other body in the universe by a mutual attraction. It was this postulated universality of the force of gravity which contributed so greatly to the order and unity of the Newtonian world. This unity was, for its followers, an untested article of faith for nearly a century after the Principia. During this time the evidence of gravitational attraction continued to be drawn from the motions of the earth, moon, planets, comets, and falling bodies—phenomena which span an intermediate range of masses, sizes, and distances. In three domains of experience, involving the extreme upper and lower limits of masses and dimensions, the action of gravity had not yet been observed: the gravity of the “fixed” stars; the mutual attraction of terrestrial bodies; and the gravitation of light. The task of deducing observable consequences from each of these supposed instances of universal gravitation fell to the Reverend John Michell (1724–1793), a teacher at Cambridge (1749–1763) and afterwards Rector of Thornhill, Yorkshire. His renowned London friend Henry Cavendish (1731–1810) encouraged him in these researches and became involved in the resulting observational and experimental questions. The immersion of Michell and Cavendish in gravitational studies was an essential feature of their commitment to a unified Newtonian world. Their commitment had yet a broader significance: Newton's theory of gravitation inspired their image of physical reality, and it served as their model of an exact science. This paper is an attempt to relate the personal friendship of Michell and Cavendish, their scientific collaboration, and their common Newtonian philosophy. Its chief focus is on Michell's 1784 plan for weighing the stars by the gravitational retardation of their light; his project of weighing the world by means of a torsion balance is treated by way of an epilogue.

Low-Energy-Theorem Approach to Single-Particle Singularities in the Presence of Massless Bosons

Abstract: By the use of low-energy theorems, which follow from gauge invariance and analyticity assumptions, we determine the nature of the single-particle singularity of a meson propagator in the presence of the known massless bosons:Photons and gravitons. In addition to regaining the well-known results for covariant gauges in electrodynamics, we present new results for covariant gauges in gravity theory, and for radiation gauges in both electrodynamics and gravity theory. The gauges in which no infrared singularities are present are found: For covariant electrodynamics it is of course the Yennie gauge; for covariant gravity theory a similar gauge is given. In radiation gauges it is shown that Schwinger's new gauge has this desirable property for photons, and an analogous gauge is constructed for gravitons. It is established that in these gauges the single-particle singularity of the meson propagator becomes a simple pole.

Hydrstatics in weak force fields

Abstract: Equilibrium forms of a liquid surface in weak gravitation fields have been studied in [1], As noted in [1], not all the equilibrium forms may be realized in practice, since they are not always stable. Below we consider the problem of the stability of the equilibrium state of an ideal, incompressible liquid under the influence of surface-tension forces and a potential mass force field. In solving this problem we use the principle of minimal system potential energy. The stability condition is formulated in terms of the eigenvalues of the linear boundary-value problem which arises in considering the question of the potential energy minimum. This general condition is applied to the axisymmetric problem, and, in particular, to the problem of the stability of a liquid suspended in a cylindrical vessel.

Gravitational experiments with a cylindrical galaxy.

Abstract: Collisionless computer model performing gravitational experiments with two dimensional galaxy

A new determination of the constant of gravitation

Abstract: Summary A new determination of the constant of gravitation is being prepared, more than 30 years after the previous one. The reasons for undertaking a new determination are outlined and the methods that have been adopted in the past are reviewed. The design of the new determination, which incorporates a number of refinements of principle and execution, is discussed.

Acceleration Due to Gravity at the National Bureau of Standards

Abstract: Report describing the determination of the absolute value of the acceleration due to gravity at the National Bureau of Standards.

Cauchy Problem in the Scalar‐Tensor Gravitational Theory

Abstract: We show that the scalar‐tensor gravitational field equations can be split up into a set of initial‐value equations and a set of time‐evolution equations and that the initial‐value equations preserve their form as they propagate forward in time. The proper amount of freedom for the stress‐energy tensor is maintained, and the Cauchy problem is thus posed reasonably well.

Simple Derivations of the Schwarzschild Metric

Abstract: Two derivations, one of the Schwarzschild line element, the other of the gravitational bending of light, both using only special relativity, the equivalence principle, and the Newtonian law of gravity, are examined in detail and shown to be incorrect. In both derivations equations of the correct form were derived, but the physical meanings of the symbols are not what they purport to be. The postulates, in addition to the above three that are necessary to derive the bending of light, are discussed briefly.

Schiff's Proposed Gyroscope Experiment as a Test of the Scalar-Tensor Theory of General Relativity

Abstract: Schiff gyroscope experiment as test of Brans- Dicke scalar tensor general relativity theory, deriving expression for gyroscope momentum precession