Renormalized Stress Tensor in One-Bubble Spacetimes

We compute the two-point function and therenormalized expectation value of the stress tensor ofa quantum field interacting with a nucleating bubble.Two simple models are considered. One is the massless field in the Vilenkin-IpserSikivie spacetimedescribing the gravitational field of a reflectionsymmetric domain wall. The other is vacuum decay in flatspacetime where the quantum field only interacts with the tunneling field on the bubble wall. Inboth cases the stress tensor is of the perfect fluidform. The asymptotic form of the equation of state aregiven for each model. In the VIS case, we find that p = –(1/3), where the energydensity is dominated by the gradients ofsupercurvature modes.     

The validity of the principle of equivalence in the WKB limit of quantum mechanics

In the context of the causal interpretation of quantum mechanics one can formulate the equation of motion of a quantal particle in the presence of a gravitational field. It is pointed out that, in the WKB limit of high quantum numbers, states exist for which one component of classical equivalence (that all bodies fall at an equal rate independent of their mass) is not recovered, due to quantum effects mediated by the quantum potential.1. The classical limit of the uncertainty relations is obtained when part of the quantum stress tensor of the field may be neglected - it is not necessary or necessarily consistent to let h 0 here either [3].2. In the relativistic case, one can nevertheless still geometrize quantum mechanics in the presence of gravity by introducing metrics that depend on particle characteristics (e.g. Finsler metric). The equation of motion is then a geodesic in this generalized space [8,9].     

Energy-nonconserving Planck fluctuations and strong forces

On the basis of the recent demonstration that sources of the dual Riemann tensor are violations of local energy-momentum conservation, it is hypothesized that matter is subject to the Heisenberg uncertainty principle because of stochastic Planck-scale fluctuations in the Euclidean geometry of the vacuum. The identification of such singularities with unitons, whose masses are quantized in discrete units of the Planck mass, and also with the sources of strong gravity, is shown to lead to the correct strength, range, and duration of strong interactions. A vacuum-induced cosmological term, due to coupling of spin to space-time torsion, results in massive gravitons, with mass similar to the spin-2 mesons, and a Yukawa, rather than Newtonian, variation of the hadron gravitational potential, thus adding support to strong gravity theories of the strong force.     

Gravitational Potentials of Triaxial Ellipsoids in Weyl Gravity

We present analytic expressions for the gravitational potentials associated with triaxial ellipsoids, spheroids, spheres and disks in Weyl gravity. The gravitational potentials of these configurations in Newtonian gravity, i.e. the potentials derived by integration of the Poisson equation Green's function 1/|r – r| over the volume of the configuration, are well known in the literature. Herein we present the results of the integration of |r – r|, the Green's function associated with the fourth order Laplacian ⁴ of Weyl gravity, over the volume of the configuration to obtain the resulting gravitational potentials within this specific theory. As an application of our calculations, we solve analytically Euler's equations pertaining to incompressible rotating fluids to show that, as in the case of Newtonian gravity, homogeneous prolate configurations are not allowed within Weyl gravity either.     

Massless and massive quanta resulting from a mediumlike metric tensor

We formulate a simple model of the primordial scalar field theory in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less thanc. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the spontaneous splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle.     

Field equations and conservation laws in the nonsymmetric gravitational theory

The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an Einstein plus fields theory. From this, it is deduced that the energy is positive in the radiation zone.     

Lie-symmetry vector fields for linear and nonlinear wave equations

We derive the Lie symmetry vector fields for the linear wave equation u=0 and nonlinear wave equation u=u ³. The conformal vector fields for the underlying metric tensor fieldg are also given. We construct the conservation laws and derive similarity solutions. Furthermore, we perform a Painlevé test for the nonlinear wave equation and discuss whether Lie-Bäcklund vector fields exist.     

The relation between the relativistic 5D Wesson theory and the Newtonian variable mass theory

The existence of Newtonian analogs to spatially homogeneous and isotropic cosmological models of the relativistic 5D Wesson variable mass theory is investigated. By treating the continuous universe matter creation process by the methods of standard hydrodynamics, it is shown that classical analogs are obtained only if the cosmological constant is null and the spatial curvature is positive.     

Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation

Semiclassical versions of the static (diabatic) and adiabatic coupling schemes are applied to a two-level-one-mode system at total energies above the cross-over level. The corresponding rates of nonradiative multiphonon transitions reduce to alternativemonotonous dependences on the usual Landau-Zener parameter. Static coupling gives an increasing transition probability (per oscillation) of the familiar formP ^st() = 4. Adiabatic coupling associated with a sufficiently low mechanism-specific potential barrier of Born's type produces a decreasing transition probability of the formP ^ad() exp (–2). The underlying Beyond-Non-Condon calculation procedure shows that (1) the weak dependence of the pre-exponential factorP ^ad is a consequence of the-independent normalization of the electronic matrix element governing the non-adiabaticity operator and (2) the occurrence of the mechanism-specific tunnelling factor exp(–2) is due to the avoided crossing of adiabatic oscillator potentials. Ranges of applicability of both alternative coupling schemes are limited by comparison with earlier non-perturbational results.     

Extended class of metric tensors in relativity

An extended metric tensor that is a function of an internal vectory ^a(x) leads to a spin-1 massless field of gravitational origin. It is shown that this new field vanishes in the linear approximation for the extended metric.On leave of absence from the Universidade de Brasilia.     

Mikhailovsky's finite Larmor radius effects and gravitational instability of plasma,treated by method of moments of Boltzmann-Vlasov equation

The effect of the stabilization of the gravitational instability of a hot rarefied plasma by the finite Larmor radius, established by Rosenbluth, Krall and Rostocker with the aid of the collisionless Boltzmann-Vlasov equation, was later derived by several authors from the magnetohydrodynamic equations modified by terms describing the magnetic viscosity of the plasma. It is shown in this paper that even the effect of the disappearance of this stabilization at very low plasma density, as found by Mikhailovsky, may be derived from the two-fluid macroscopic equations (the method of moments of the Boltzmann-Vlasov equation) using a very simple iterative procedure in which directly figures the so-called effective electric field of perturbation employed by some authors for physical interpretation of the effects of the finite Larmor radius.     

On pseudoparticle solutions in Yang's theory of gravity

Within the framework of differential geometry, Yang's parallel-displacement gauge theory is considered with respect to pure gravitational fields. In afour-dimensional Riemannian manifold it is shown that thedouble self-dual solutions obey Einstein's vacuum equations with the cosmological term, whereas the doubleanti-self-dual configurations satisfy the Rainich conditions of Wheeler'sgeometrodynamics. Conformal methods reveal that the gravitational analog of the instanton or pseudoparticle solution of Yang-Mills theory was already known to Riemann.     

Influence of the Flux Density,the Flux,and the Energy of Electrons on the Change in the Optical Properties of ZnO + K2SiO3 Coatings

The change in the diffusion reflection spectra and the total solar radiation absorption coefficient as by a reflecting heat-regulating coating (HRC) fabricated from ZnO pigment and K₂SiO₃ liquid potash glass in the People's Republic of China is investigated as a function of the flux density , the flux , and the energy E of electrons. The established regularities in the changes of a _s and under irradiation provide additional information on the formation of color centers (CC) in these systems and correlate with the results obtained previously for coatings fabricated in Russia.     

Kinetics of small perturbations in an isotropic world

Long-wavelength gravitational perturbations are studied in an isotropic expanding universe filled with an ultrarelativistic gas. A kinetic study in the collisionless approximation shows that scalar and vector perturbations which appear at a time ₀ 1/n, where N is the wave vector and is the time coordinate x⁴, grow if the perturbation of the macroscopic momentum density of the gas at time ₀ is nonvanishing. The growth continues until the time ₁=27₀, at which the perturbation of the macroscopic momentum density of the gas vanishes. A solution is also derived for tensor perturbations in the limit n 1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–45, April, 1978.     

Structural stability properties of friedman cosmology

A dynamical system with Robertson-Walker symmetries and the equation of the statep=, 01, considered both as a conservative and nonconservative system, is studied with respect to its structural stability properties. Different cases are shown and analyzed on the phase space (x=R ^D , y=x).     

A variational principle giving gravitational “superpotentials,” the affine connection,Riemann tensor,and Einstein field equations

A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensorR _k in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational superpotentials closely connected with the Komar conservation laws [7]. Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational superpotentials.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Stability and structure of Newtonian gravitars

The solution r² for a scalar field (gravitational constant), which is asymptotically exact for supercompact configurations and which Saakyan and Mnatsakanyan obtained from the numerical solution of the hydrostatics equations in the Newtonian approximation of the Jordan-Brans-Dicke theory, is used to study the gravitational stability of such configurations. We have found the stability condition 2/3 for polytropic configurations ( is the polytropic exponent) instead of 4/3, which is known for configurations of low compactness. Analytic solutions of the equations of internal structure are found for configurations which are intermediate with respect to stability (=2/3) and for some other important series of configurations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 98–102, July, 1982.In conclusion, the present author expresses his indebtedness and gratitude to V. N. Ponomarev, for assistance in executing the work.     

A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.     

Stochastic and quantum space-time metrics and the weak-field limit

In this review we present a simple method of introducing stochastic and quantum metrics into gravitational theory at short distances in terms of small fluctuations around a classical background space-time. We consider only residual effects due to the stochastic (or quantum) theory of gravity and use a perturbative stochastization (or quantization) method. By using the general covariance and correspondence principles, we reconstruct the theory of gravitational, mechanical, electromagnetic, and quantum mechanical processes and tensor algebra in the space-time with stochastic and quantum metrics. Some consequences of the theory are also considered, in particular, it indicates that the value of the fundamental lengthl lies in the interval 10^–23l10^–22 cm.