For a static incompressible perfect fluid cylinder, the physical radius \(R\), and the parameter \(m\) of the exterior Levi–Civita solution, are numerically calculated in terms of the ratio of the central pressure \(p_0\) and the mass density \(\mu _0\).

Evolution of evaporating blank hole in inflationary universe is investigated for a Bardeen–Vaidya–deSitter line element. The Raychaudhuri equation is examined up to second order terms in the luminosity in the vicinity of the black hole event horizon and the equations governing the evolution of a black hole are given. A back reaction programme in a simplified Vaidya–deSitter background is examined and the luminosity formula is found. The effective temperature assigned to the Bardeen—Vaidya—deSitter black hole is proposed.

The Vilkovisky–De Witt effective action for scalar electrodynamics and SU(5) GUT, nonmimmally interacting with torsion, is calculated on de Sitter background with torsion. The same calculation on the same background for quantum gravity with torsion is discussed. A short discussion of Green functions in curved space-time with torsion is also presented.

The embedding of Dirac algebra into a sequence \(N = 1, 2, 3\), … of Clifford algebras is discussed, leading to Dirac equations with N-i additional, electromagnetically “hidden” spins 1/2. It is shown that there are three and only three replicas \(N = 1, 3, 5\) of Dirac particle if the theory of relativity together with the probability interpretation of wave function is applied both to the “visible” spin and “hidden” spins, and a new “hidden exclusion principle” is imposed on the wave function (then “hidden” spins add up to zero). It is appealing to explore this idea in order to explain the puzzle of three generations of leptons and quarks.

The 48-component teosor field which can be used for the geometrized description of fermions with internal degrees of freedom is considered. Its quantum formulation on the basis of Fermi–Dirac statistics is given.

This paper presents a dynamical formulation of electrostatics i.e. a dynamics of static charge distributions. The theory can be quantized and leads to the conclusion that the total electric charge is a multiple of the elementary charge \(e\). Further simple assumptions allow us to derive the inequality 0 less than \(e^2/\hbar c\) less than \(\pi \).

Arguments are presented which allow us to derive the inequality 0 less than \(e^2/\hbar c\) less than \(\pi \) in a purely phenomenological way i.e. without assumptions about the dynamics of sources of the electromagnetic field.

A Hartree–Fock approach with interaction of Skyrme type is used to investigate properties of warm and isospin-asymmetric nuclear matter. The incompressibility turns out to depend sensitively on the neutron excess and temperature. The interaction enhances considerably the proton admixture in beta-stable neutron star matter.

The asymmetry \(T\) of the angular distribution of \(\pi ^0\)-mesons produced in the \(\gamma {\rm d} \to {\rm d} \pi ^0\) reaction, if photons are unpolarized and the deuteron target is vector-polarized, is studied. The calculations take into account the contributions of the impulse approximation and of possibly existing Wide dibaryon resonances with \(J^P = 2^+\) and \(J^P = 3^-\). The energy dependence of the asymmetry \(T\) investigated for fixed 4-momentum transfer squared or at fixed \(\theta \) (\(\theta \) is the angle of \(\pi ^0\) production in the centre-of-mass system of \(\gamma {\rm d} \to {\rm d} \pi ^0\)). The \(\theta \)-dependence of the asymmetry \(T\) at fixed \(E_{\gamma }\) is also considered. The computed asymmetries \(T\) are found to be sensitive to the choice of the Fermi momentum of the nucleon in the deuteron and to the quantum numbers of dibaryon resonances. The asymmetry \(T\) values are as a rule large and can be measured experimentally.