Generalized theory of impacts in particulate systems

The theory of collisional systems is generalized for an arbitrary geometry and forces acting in the system, mixtures of different particle types, friction, small deviations from the ideal spherical form, axial rotation, finite size of particles and gravitational interactions. Terms for the formation of new particles and destruction of old ones are also included, and other unspecified parameters can be introduced. Although some approximations are made to simplify the basic equations and to avoid excessive numerical interactions, a comparison with computer simulations shows a good agreement. The tests were continued up to the optical thickness = 5.     

Production of massive spin — 1/2 particles in Robertson-Walker universes with external electromagnetic fields

In this paper we investigate the combined influence of both cosmological and electromagnetic particle creation mechanisms upon massive particles with spin 1/2 on the basis of general covariant Dirac theory.Curved space-time, a radiation-dominated Friedmann universe, is treated as an unquantized gravitational field and the low-frequency part of the 2.7 K background radiation is approximated by homogeneous, constant, and parallel external electric and magnetic fields. We calculate the number density of spin 1/2 particles with massm which are created under the influence of both these external fields.We find that the electric field and the magnetic field both amplify the genuine, purely gravitational particle production. This influence of the magnetic field, which is in contrast to its reducing effect as far as the creation of spin-zero particles is concerned, can clearly be traced back to its coupling to the spin of the particles.Under certain conditions the electromagnetic fields in the early universe can influence the particle creation process even more than the gravitational field.     

Statistical approach to the theory of circumstellar discs

The equations for the viscous motion of a mixture of gas and dust in a gravitational field are derived from the statistics of particle orbits and radiative processes in a general form which gives the Navier-Stokes equation as a special case. Diffusion, partially elastic collisions and — for larger bodies — the gravitational encounters are included. The results are applied to the evolution of circumstellar discs.     

Dust particle in the solar gravitational and electromagnetic fields

The action of the solar electromagnetic radiation (in the form of the Poynting-Robertson effect) on the motion of interplanetary dust particle in the gravitational field of the Sun is discussed from the theoretical point of view. Results are presented to all orders inv/c (c - speed of light,v -orbital velocity of the particle) - general relativistic formula is presented.     

On singularities in electrodynamics and gravitational theory

The singularity and particle problems in electrodynamics and gravitational theory are discussed. Comparing different modifications of MAXWELL 's electrodynamics and general theory of relativity, arguments are given which show possibilities of solving these problems by a modification that replaces EINSTEIN 's equations by those of the EINSTEIN -BACH -WEYL -type.     

Stochastic scattering and other contributions to the Sun's wake in the local hydrogen cloud

Gas streaming through the solar system experiences both destructive and scattering processes, the latter primarily in collisional interactions with the solar wind protons. The scattering interactions can be important in filling the downstream wake. They may effectively increase the velocity dispersion and also cause discrete orbit changes.The downstream intensity moment is here evaluated analytically for particles suffering a single, discrete collision, and compared with the moment from a thermal velocity dispersion (both in the absence of a central force field). The elastic scattering collisions of protons in H-gas lead to a contribution to theL backscatter from the wake equivalent to an initial thermal velocity of about 1 km s^–1, giving an intensity for cool gas of the order of 10R. This exceeds the contribution due to focussing in the solar gravitational field if the radiation pressure is not less than 0.8 of the gravitational attraction.     

Gravitational interaction of bodies immersed in fluids

It is shown that Archimedes' principle can be generalized for external gravitational fields due to stationary macroscopic bodies. For instance, a particle immersed in a homogeneous fluid at the centre of spherical symmetry of the fluid, or anywhere in an unbounded homogenous fluid, experiences — in an external field — a force that it would experience in a vacuum if it had an apparent mass less than the actual one by the mass of displaced fluid. Inversely, if one immerses a particle into a symmetrically arranged homogeneous fluid apart from its centre of symmetry, the particle and the fluid produce, at the centre of symmetry of the fluid, a gravitational field that would be produced in vacuo by a particle of the same size and shape but having apparent mass. Simple laboratory experiments, suitable to verify this inverse theorem, are described. On the other hand, the gravitational force between two particles in an infinite homogeneous fluid is reduced by a factor proportional to the product of their apparent masses which can be positive or negative. Two particles with opposite apparent masses repel each other. The results obtained imply corrections to vacuum of the order of (10^–5–10^–4) G of the gravitational constant,G, measured by the common laboratory methods.     

Regular and chaotic motion in softened gravitational systems

The stability of the dynamical trajectories of softened spherical gravitational systems is examined, both in the case of the full N -body problem and that of trajectories moving in the gravitational field of non-interacting background particles. In the latter case, for   N 10 000  , some trajectories, even if unstable, had exceedingly long diffusion times, which correlated with the characteristic e-folding time-scale of the instability. For trajectories of   N ≈100 000  systems this time-scale could be arbitrarily large – and thus appear to correspond to regular orbits. For centrally concentrated systems, low angular momentum trajectories were found to be systematically more unstable. This phenomenon is analogous to the well-known case of trajectories in generic centrally concentrated non-spherical smooth systems, where eccentric trajectories are found to be chaotic. The exponentiation times also correlate with the conservation of the angular momenta along the trajectories. For N up to a few hundred, the instability time-scales of N -body systems and their variation with particle number are similar to those of the most chaotic trajectories in inhomogeneous non-interacting systems. For larger N (up to a few thousand) the values of the these time-scales were found to saturate, increasing significantly more slowly with N . We attribute this to collective effects in the fully self-gravitating problem, which are apparent in the time variations of the time-dependent Liapunov exponents. The results presented here go some way towards resolving the long-standing apparent paradoxes concerning the local instability of trajectories. This now appears to be a manifestation of mechanisms driving evolution in gravitational systems and their interactions – and may thus be a useful diagnostic of such processes.     

引力波、引力波源和引力波探测实验

引力波是爱因斯坦和其他物理学家提出的关于广义相对论的四大预言之一。除了PSR1 91 3 + 1 6引力辐射阻尼的观测提供了引力波存在的间接证据外 ,科学家至今仍没有在实验室中确证引力波的存在。由于人类目前的技术水平还不可能在实验室中产生强度可供探测的引力波 ,而宇宙中存在大量大质量、高速运动的天体 ,有可能产生较强的引力波 ,天体引力波源自然成为现阶段科学家研究引力波的首选。本文介绍广义相对论框架下预言的引力波性质 ,引力波探测的理论依据 ,共振型棒式天线和激光干涉仪两大类探测器的基本原理 ,引力波探测实验的现状和面临的困难 ,科学家采取的对策 ,以及爆发型和连续型两类天体引力波源。最后介绍了正在计划中的几个引力波探测空间实验     

Theory of gravitational radiation of the (Ω,A µν )-field

Further exploration of the -field theory as first proposed by Yu (1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation. The same theory is shown to contain an exact gravitational radiation equation derived as a logical consequence of field equations without extra postulates. In this general dynamic context the theory is renamed The (,A _µ )-field Theory.     

Formation of stars and planets: the role of magnetic fields

Star formation is thought to be triggered by gravitational collapse of the dense cores of molecular clouds. Angular momentum conservation during the collapse results in the progressive increase of the centrifugal force, which eventually halts the inflow of material and leads to the development of a central mass surrounded by a disc. In the presence of an angular momentum transport mechanism, mass accretion onto the central object proceeds through this disc, and it is believed that this is how stars typically gain most of their mass. However, the mechanisms responsible for this transport of angular momentum are not well understood. Although the gravitational field of a companion star or even gravitational instabilities (particularly in massive discs) may play a role, the most general mechanisms are turbulence viscosity driven by the magnetorotational instability (MRI), and outflows accelerated centrifugally from the surfaces of the disc. Both processes are powered by the action of magnetic fields and are, in turn, likely to strongly affect the structure, dynamics, evolutionary path and planet-forming capabilities of their host discs. The weak ionisation of protostellar discs, however, may prevent the magnetic field from effectively coupling to the gas and shear and driving these processes. Here I examine the viability and properties of these magnetically-driven processes in protostellar discs. The results indicate that, despite the weak ionisation, the magnetic field is able to couple to the gas and shear for fluid conditions thought to be satisfied over a wide range of radii in these discs.     

Viscous cosmological models with particle creation in Brans-Dicke theory

The effect of bulk viscosity on the evolution of the spatially flat Friedmann-Robertson-Walker models in the context of open thermodynamical systems, which allow particle creation, is analyzed within the framework of Brans-Dicke theory. Particle creation and bulk viscosity have been considered as separated irreversible processes. To accommodate the viscous pressure and creation pressure, which is associated with creation of matter out of gravitational field, the energy-momentum tensor is modified. Dynamical behaviour of the models have been discussed.     

Angular momentum and gyroscope in flat space-time theory of gravitation

The study of a previously proposed theory of gravitation in flat space-time (Petry, 1981a) is continued. A conservation law for the angular momentum is derived. Additional to the usual form, there must be added a term coming from the spin of the gravitational field. The equations of motion and of spin angular momentum for a spinning test particle in a gravitational field are given. An approximation of the equations of the spin angular momentum in the rest frame of the test particle is studied. For a gyroscope in an orbit of a rotating massive body (e.g., the Earth) the precession of the spin axis agrees with the result of Einstein's general theory of relativity.     

Emden-Chandrasekhar axisymmetric,rigid-body rotating polytropes

In connection with the basic theory reported in a previous paper (Paper I) for EC1 (rigidly rotating) polytropes, we define exact configurations as configurations for which the equilibrium equation has solutions which are infinitely close to some analytical function and the related gravitational potential coincides, in fact, with the gravitational potential due to mass distribution, at any point not outside the system. Then we restrict to the special casen=5 and divide the related polytropes into two components, a massive body where each mass element has a finite (polytropic) distance from the centre, and a massless atmosphere where each mass element has an infinite (polytropic) distance from te centre. It is found a single exact configuration exists, which under some assumptions may be related to Roche systems. In the special casen=0 it is shown a particular configuration, the spheroidal one, is an exact configuration and evidence is given that spheroidal configurations are the stablest among all the allowed (axisymmetric) configurations. It is also pointed out that EC1 polytropes withn=0 and incompressible MacLaurin spheroids belong to different sequences, even if they exhibit some common features. In the special casen=1 it is shown each allowed configuration is expressible by a convenient series development, which reduces to the relatedn=0 configuration by maintaining only the first two or the first one terms of the sum. It is also deduced, by analogy with the casen=0, that pseudospheroidal configurations are exact and the stablest among all the allowed (axisymmetric) configurations.     

引力波理论和实验的新进展

引力波的存在是爱因斯坦在广义相对论理论中提出的一个重要预言．由于目前技术水平的限制,无法在实验室产生足以被探测到的引力波,因此宇宙中大量的大质量剧烈活动的天体成为科学家研究引力波的首选,从而诞生了引力波天文学．引力波探测将开启研究宇宙的新窗口,是继电磁辐射、宇宙线和中微子探测后探索宇宙奥秘的又一重要手段,对天文学研究有着极为重要的意义.新一代应用了高灵敏度的迈克耳逊干涉仪装置的长基线引力波探测仪正在建造中．该综述从引力波理论出发,阐述了目前研究较多的可探测引力波源,给出了目前观测上的最新进展,并展望了今后的发展前景．     

Relativistic gravitational potential and its relation to mass-energy

From the general theory of relativity a relation is deduced between the mass of a particle and the gravitational field at the position of the particle. For this purpose the fall of a particle of negligible mass in the gravitational field of a massive body is used. After establishing the relativistic potential and its relationship to the rest mass of the particle, we show, assuming conservation of mass-energy, that the difference between two potential-levels depends upon the value of the radial metric coefficient at the position of an observer. Further, it is proved that the relativistic potential is compatible with the general concept of the potential also from the standpoint of kinematics. In the third section it is shown that, although the mass-energy of a body is a function of the distance from it, this does not influence the relativistic potential of the body itself. From this conclusion it follows that the mass-energy of a particle in a gravitational field is anisotropic; isotropic is the mass only. Further, the possibility of an incidental feed-back between two masses is ruled out, and the law of the composition of the relativistic gravitational potentials is deduced. Finally, it is shown, by means of a simple model, that local inhomogeneities in the ideal fluid filling the Universe have negligible influence on the total potential in large regions.     

Galactic chaos driven by an oscillating massive particle

The effect of an oscillating massive particle on the motion of stars in a spherical Plummer gravitational system is examined for chaotic behaviour for ratios of satellite to parent galaxy masses ranging from .001 to .15. Thee-folding times for chaos are calculated for non-zero angular momentum orbits and discussed in relation to the time-scales for dynamical friction.     

Effect of neutrino magnetic moment on solar neutrino observations

Neutrino spin precession effects in the magnetic field of the Sun are considered as an explanation of the outcome of Davis' solar neutrino experiments. Theoretically, it is possible to account for a neutrino magnetic moment only as the result of the interaction of the electromagnetic field with charged particles into which the neutrino can transform virtually. The currently accepted theory of weak interactions (the two component neutrino andV-A interactions) forbids a resulting magnetic moment interaction with the electromagnetic field for all such virtual processes. Modifications of this theory are considered to find out whether an appreciable precession effect is permitted within the experimentally established limits. It is found that the value for the neutrino magnetic moment evaluated under these theoretically anomalous circumstances is still so small that only the largest possible estimate for the magnetic field strength in the Sun's interior would cause the required effect.The author has received scholarship support from the Latin American Scholarship Program of American Universities during the preparation of this work.     

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern Gedanken zu einer Theorie der solaren Neutrinos

The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric g_ik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads h_i^A(x^l) as neutrino-current vectors, firstly. Then, the metric g_ik is defined by the equation g_ik = η_AB h_i^Ah_η^B according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential h_i^A with the matter T_ιⁱ is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric g_ik by four WEYL spinors we are able to construct a conformal flat metric ĝ_ik = ϕ²η_ik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric g_ik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝ_ik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 10¹⁸ times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 10¹⁸ times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c²: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ_ik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝ_ik = ϕ²η_ik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.