Showing papers on "Gravitation published in 1988"

The Rapid Evaluation of Potential Fields in Particle Systems

Abstract: The evaluation of Coulombic or gravitational interactions in large-scale ensembles of particles is an integral part of the numerical simulation of a large number of physical processes. Examples include celestial mechanics, plasma physics, the vortex method in fluid dynamics, molecular dynamics, and the solution of the Laplace equation via potential theory. In a typical application, a numerical model follows the trajectories of a number of particles moving in accordance with Newton's second law of motion in a field generated by the whole ensemble. In many situations, in order to be of physical interest, the simulation has to involve thousands of particles (or more), and the fields have to be evaluated for a large number of configurations. Unfortunately, an amount of work of the order $O(N\sp 2)$ has traditionally been required to evaluate all pairwise interactions in a system of N particles, unless some approximation or truncation method is used. As a result, large-scale simulations have been extremely expensive in some cases, and prohibitive in others. We present an algorithm for the rapid evaluation of the potential and force fields in large-scale systems of particles. In order to evaluate all pairwise Coulombic interactions of N particles to within round-off error, the algorithm requires an amount of work proportional to N, and this estimate does not depend on the statistics of the distribution. Both two and three dimensional versions of the algorithm have been constructed, and we will discuss their applications to several problems in physics, chemistry, biology, and numerical complex analysis.

Models for universal reduction of macroscopic quantum fluctuations

Abstract: This paper adopts the hypothesis that the absence of macroscopic quantum fluctuations is due to a certain universal mechanism. Such a mechanism has recently been proposed by Ghirardi et al. [Phys. Rev. D 34, 470 (1986)], and here we recapitulate a compact version of it. K\'arolyh\'azy [Nuovo Cimento 52, 390 (1966)] showed earlier the possible role of gravity and, along this line, we construct here a new parameter-free unification of micro- and macrodynamics. We apply gravitational measures for reducing macroscopic quantum fluctuations of the mass density. This model leads to classical trajectories in the macroscopic limit of translational motion. For massive objects, unwanted macroscopic superpositions of quantum states become destroyed in very short times. The relation between state-vector and density-operator formalisms has also been discussed. We only anticipate the need for elaborating characteristic predictions of the model in the region separating micro- and macroscopic properties.

Model-independent constraints on possible modifications of Newtonian gravity.

Abstract: New model-independent constraints on possible modifications of Newtonian gravity over solar-system distance scales are presented, and their implications discussed. The constraints arise from the analysis of various planetary astrometric data sets. The results of the model-independent analysis are then applied to set limits on a variation in the l/r-squared behavior of gravity, on possible Yukawa-type interactions with ranges of the order of planetary distance scales, and on a deviation from Newtonian gravity of the type discussed by Milgrom (1983).

Non-perturbative 2 particle scattering amplitudes in 2+1 dimensional quantum gravity

Abstract: A quantum theory for scalar particles interacting only gravitationally in 2+1 dimensions is considered. Since there are no real gravitons the interaction is entirely topological. Nevertheless, there is non-trivial scattering. We show that the two-particle amplitude can be computed exactly. Although the complete “theory” is not well understood we suggest an approach towards formulating theN particle problem.

Scattering from black holes

Abstract: This book investigates the propagation of waves in the presence of black holes Astrophysical black holes may eventually be probed by these techniques The authors emphasise intuitive physical thinking in their treatment of the techniques of analysis of scattering, but alternate this with chapters on the rigourous mathematical development of the subject High and low energy limiting cases are treated extensively and semi-classical results are also obtained The analogy between Newtonian gravitational scattering and Coulomb quantum mechanical scattering is fully exploited The book introduces the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical black hole It then develops the formalism of spin-weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic and gravitational scattering Research workers and graduate and advanced undergraduate students in scattering theory, wave propagation and relativity will find this a comprehensive treatment of the topic

Action principle and partition function for the gravitational field in black-hole topologies.

Abstract: Statistical mechanics of gravitational fields describing the black-hole topological sector, and the correspondence to thermodynamics, are considered. The Euclidean action is evaluated on the constraint hypersurface and a measure is obtained, resulting in a path-integral form of the canonical partition function. We obtain the usual black-hole entropy plus quantum corrections when the temperature and size of the system are appropriate. Under other conditions, we give evidence for the existence of a phase transition (change of topology).

Quantum gravitational effects near cosmic strings

Abstract: The gravitational field associated with cosmic strings can produce a variety of quantum field effects, such as vacuum polarisation and particle production. The authors investigate the behaviour of particle detectors near straight strings in free space, immersed in thermal radiation, and passing through black holes. The expectation values of the stress-energy-momentum tensor for a scalar field near straight strings through black holes and in Robertson-Walker cosmological spacetimes are also calculated.

On Theories of Gravitation With Nonlinear Lagrangians

Abstract: It is shown that any theory of gravitation with a nonlinear Lagrangian depending on the Ricci tensor is equivalent to the Einstein theory of gravitation interacting with additional matter fields.

A thermal interpretation of the cosmological constant

Abstract: A metric-affine geometrical structure is used to formulate a generalised theory of gravity, in which the motion of a test particle is characterised by a finite proper acceleration in the local tangent space. According to the local equivalence, valid for quantum systems, between acceleration and temperature, the theory is thermally interpreted as an effective classical description of the finite temperature geometry experienced by quantum fields at a microscopic level. In the macroscopic limit, the averaged contribution of the temperature to the effective geometry is represented by a cosmological constant, which can be interpreted then as a measure of the intrinsic temperature of the vacuum. With this interpretation it seems possible to understand why, on a cosmic scale, the current value of the cosmological constant must be so small, as implied by present observations.

Is there really a problem with the teleparallel theory

Abstract: The problem of non-predictable behaviour of the torsion in the experimentally viable one-parameter teleparallel theory of gravity, first pointed out by Kopczynski (1982), is found to be non-generic, occurring only for very special solutions.

Relativistic Theory of Gravity

Abstract: This paper presents a brief critical analysis of General Relativity Theory (GRT). It is shown that the theory, if accepted, leads to repudiation of a number of fundamental principles underlying physics. The article also presents the construction of Relativistic Theory of Gravitation (RTG) in which the gravitational field possesses all the attributes of physical fields and which concurs completely with the fundamental physical principles as well as with the available experimental and observational facts. It also considers the consequences of RTG, dealing, in particular, with the development of collapse and Universe evolution.

Theory of adhesion for the large-scale structure of the Universe

Abstract: At present we see the large-scale distribution of matter in the Universe primarily as clusters and superclusters of galaxies, with giant voids between them1,2. Understanding the origin and evolution of the large-scale structure (LSS) is one of the central problems in cosmology; it is of direct concern in understanding both the nature of the dominant dark matter in the Universe and physical processes in the very early Universe when primordial inhomogeneities were generated3–5. Here we use a new theoretical approach6–8 to the formation of LSS by applying the Burgers' equation9 that mimics the gravitational sticking of matter at the non-linear stage of gravitational instability. In this theory the non-linear evolution, including both the formation and clustering of clumps of matter separated from the Hubble expansion, is directly determined by the geometrical structure of the initial random field of linear newtonian gravitational potential fluctuations o which may be gaussian or non-gaussian, depending on the model.

Existence of the Gravitomagnetic Interaction

Abstract: The point of view expressed in the literature that gravitomagnetism has not yet been observed or measured is not entirely correct. Observations of gravitational phenomena are reviewed in which the gravitomagnetic interaction—a post-Newtonian gravitational force between moving matter—has participated and which has been measured to 1 part in 1000. Gravitomagnetism is shown to be ubiquitous in gravitational phenomena and is a necessary ingredient in the equations of motion, without which the most basic gravitational dynamical effects (including Newtonian gravity) could not be consistently calculated by different inertial observers.

Gravitational measurements, fundamental metrology and constants

Abstract: Can we Calculate the Fundamental Dimensionless Constants of Physics?.- Observables in General Relativity.- The Quantum Hall Effect Part I: Basic Experiments.- Quantum Hall Effect Part II: Metrological Applications.- Fundamental Physical Constants.- Variability of the Physical Constants.- The Measurement Problem of the General Matter Field Theory as Required by the Copenhagen School.- On the Relations between Fundamental Constants.- Quantum Electrodynamics and Fundamental Constants.- Searching for the Source of the Fifth Force.- Lorentz noninvariance and the Universality of free fall in Quasi-Riemannian Gravity.- Status of the Newtonian Gravitational Constant.- Time Variation of the Gravitational Constant.- The Supernova SN 1987A and the Neutrino Mass.- The Fifth Force Experiment at the TIFR.- Analysis of Ground States of General Relativity Theory and Relativistic Theory of Gravitation.- Gravitational-Relativistic Metrology.- Gravitational Waves.- The Gravitational Wave Experiment of the Rome Group. Data Recorded during SN1987A.- Solar-System Tests of General Relativity, the Transition to Second Order.- The Weyl-Dirac Theory and the Variation of the Gravitational Constant.- Selected Problems of Gravitational Wave Experiment.- Introductory Lectures on the Physics of High Energy Densities: Theories, Models, Measurements.- Detectors of Laboratory Gravitation Experiments and a new Method of Measuring G.- to the Theory of Fields in Finsler Spaces.- Neutrinos, Gravitons, Metrology and Gravitational Radiation.- On Quirino Majorana's Papers Regarding Gravitational Absorption.- I: Quelques Recherches sur l'Absorption de la Gravitation par la Matiere.- II: Theoretical and Experimental Researches on Gravitation.

“Superconducting” causal nets

Abstract: The world is described as a relativistic quantum neural net with a quantum condensation akin to superconductivity. The sole dynamical variable is an operator representing immediate causal connection. The net enjoys a quantum principle of equivalence implying local LorentzSL(2,C) invariance and causality. The past-future asymmetry of its cell is similar to that of the neutrino. A net phase transition is expected at temperatures on the order of theW mass rather than the Planck mass, and near gravitational singularities.

Bianchi Identities and the Automatic Conservation of Energy-Momentum and Angular Momentum in General-Relativistic Field Theories

Abstract: Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincare gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.

Approximation scheme for constructing a clumpy universe in general relativity.

Abstract: We shall develop an approximation scheme to construct the metric representing a realistic clumpy universe in general relativity. Spatial averaging is used to express the fact that the expansion of the universe is generated collectively by the clumps of matter. The dynamics of the clumps is treated by the post-Newtonian-type approximation. The scheme allows one to calculate the back reaction due to the growth of clumps on the expansion and vice versa. An expression for the deviation from homogeneous and isotropic expansion is derived in terms of inhomogeneities of the gravitational field generated by clumps. It should also be used as the correct interpretation of the observation of gravitational lenses.

A new formalism for the effect of lateral heterogeneity on normal modes and surface waves—I: isotropic perturbations, perturbations of interfaces and gravitational perturbations

Abstract: SUMMARY Lateral heterogeneities in the Earth produce a coupling of the normal modes of a laterally homogeneous Earth model, and lead to mode interactions for surface waves. Traditionally, this problem was treated by expanding the heterogeneity in spherical harmonics, and was thereby reduced to a complicated algebraic problem requiring the use of Wigner 3j-symbols and generalized spherical harmonics. However, due to the global character of this theory, the resulting equations are not convenient for obtaining physical insight into the problem, and are cumbersome to manipulate. In this paper, the effects of lateral heterogeneity in density, bulk modulus, shear modulus, interface displacements and gravitation are treated without a global expansion in spherical harmonics. Using a simple-operator formalism, the coupling coefficients between the Earth's normal modes can be expressed by an integral over the horizontal extent of the inhomogeneity. The integrand can be expressed by a set of 17 local frequencies of interaction, and some simple geometrical variables. The mode coupling depends in a simple way on the scattering angle, even for modes with such a long period that the concept of scattering is meaningless. Apart from the restrictions of first-order perturbation theory, there are no other restrictions; specifically, it is not necessary to assume a far-field limit. From the expression for normal-mode coupling, a theory for surface-wave scattering and conversion is derived. This leads to a complete set of local surface-wave interaction coefficients, where the effects of sphericity are fully taken into account. The surface-wave polarization vectors and excitation tensor are derived from the source and receiver operators. The resulting theory for normal-mode interactions and surface-wave scattering leads to an efficient method for generating synthetic seismograms in laterally inhomogeneous media, and is simple enough to allow extensive mathematical manipulation of the resulting equations. The effects of anisotropy are treated in the sequel of this paper.

On spherically symmetric shear‐free perfect fluid configurations (neutral and charged). II. Equation of state and singularities

Abstract: Geometrical and physical properties of the solutions derived and classified in Part I [J. Math. Phys. 28, 1118 (1987)] are examined in detail. It is shown how the imposition of zero shear restricts the possible choices of equations of state. Two types of singular boundaries arising in these solutions are examined by verifying the local behavior of causal curves approaching these boundaries. For this purpose, a criterion due to C. J. S. Clarke (private communication) is given, allowing one to test the completeness of arbitrary accelerated timelike curves in terms of their acceleration and proper time. One of these boundaries is a spacelike singularity at which causal curves terminate as pressure diverges but matter‐energy and charge densities remain finite. At the other boundary, which is timelike if the expansion Θ is finite, proper volume of local fluid elements vanishes as all state variables diverge but causal curves are complete. If Θ diverges at this boundary, a null singularity arises as the end pro...

Theories of Gravitation in Two-Dimensions

Abstract: A variety of two-dimensional theories of gravitation with and without torsion are considered. We discuss the invariance properties and geometrical structure of each. One such theory considered predicts nontrivial dynamics for the evolution of the two-dimensional spacetime. We obtain some exact solutions for this theory.

Effect of a uniform sea-level change on the Earth's rotation and gravitational field

Abstract: Global water redistriburtion between the oceans, atmosphere and continents causes changes in the earth's rotation and gravitational field. To conserve water mass, the effect of the small uniform change in sea-level must be considered. Explicit formulas are provided for these sea-level corrections to the gravitational Stokes coefficients, polar motion and length of day. In two recent publications, this sea-level correction term for polar motion was given incorrectly. These errors which arose from normalization conventions with the ocean function are corrected.

Canonical Analysis of the One Parameter Teleparallel Theory

Abstract: Dirac's constraint algorithm is adapted to find the canonical Hamiltonian formulation of the one-parameter teleparallel theory of gravity which is supposed to have some problematical gauge properties. The analysis verifies that the theory has the strange property that generic initial values have deterministic evolution while certain special initial configurations allow some undetermined evolution possibly only within a limited spatial region.

The de Sitter spacetime as attractor solution in eighth-order gravity

Abstract: From the Lagrangian R Square Operator Square Operator R one gets an eighth-order theory of gravitation. It has more promising properties than the previously discussed sixth-order ones. The de Sitter solution has the attractor property; we explicitly show how the modes decay. Further, exactly one power law and one pole-like solution exist. Adding the Einstein-Hilbert and other lower order terms with suitably chosen coefficients, we get a theory without tachyons, with the correct Newtonian limit and with cosmological solutions possessing more than one inflationary phase. (Whether double inflation is typical still remains open).