A geodesic study of the Erez-Rosen space-time

We present the nature of stable trajectories of neutral particles around an object with a quadrupole moment in both the equatorial (=/2) and the polar (=constant) plane.     

On the geodesics in the Erez-Rosen spacetime

We discuss the problem of motion of test particles in a monopolequadrupole gravitational field and compare the results presented in different publications.     

A Charged Erez-Rosen Spacetime and Gravitational Repulsion

An Erez–Rosen spacetime having a highly-charged source (e> m) is presented. Motions of a neutral particle along the symmetry axis and in the median plane are shown to exhibit repulsion near the source. The absence of frame-dragging effects in this static spacetime permits radial motions and allows for a comparison of motions along these special geodesics.     

Determinism in space-time

Generalizing a definition given by Budic and Sachs we define the set (M) of deterministic points of a space-timeM, and show that (M) Ø implies thatM admits compact achronal slices. Further we give a new characterization of space-times with (M)=M. The relation between determinism, existence of particle horizons, and visible Cauchy surfaces is investigated.     

Polar orbits in the Kerr space-time

The motion of test particles in polar orbit about the source of the Kerr field of gravity is studied, using Carter's first integrals for timelike geodesies in the Kerr space-time. Expressions giving the angular coordinates of such particles as functions of the radial one are derived, both for the case of a rotating black hole as well as for that of a naked singularity.     

Matter fields in the Plebanski-Demianski space-time

We consider the boson (electromagnetic and gravitational) fields and the fermion (electron and neutrino) fields in the Plebanski-Demianski space-time. In the case of the boson field, we observe that the superradiance phenomena occurs, but in the case of the fermion field we find no super-radiance phenomena     

Homothety groups in space-time

This paper investigates space-times which admit anr-dimensional Lie algebra of homothetic vector fields at least one of which is proer homothetic. The situation is resolved completely ifr 6 and some general results are given whenr 5. Some applications to the study of affine vector fields in space-times are also given and the maximum dimension of this latter algebra is computed and corrects an earlier error.     

Gravitation in flat space-time

A previously studied Lorentz-covariant theory of gravitation is given in generally covariant form, i.e., the theory holds for arbitrary reference frames. Flat space-time is a natural condition for the conservation of energy and momentum. The energy-momentum tensor of matter and gravitation is the source of the gravitational field.     

Supersymmetry in complex space-time

An interconnection between superluminal transformation and supersymmetric transformations has been investigated in complex C³-space and the evolution of bosonic and fermionic subspaces in such space has been undertaken. Introducing the suitable anticommuting operators to induce grading in Poincare group in C³-space in terms of components of complex angular momentum operator, the supersymmetric algebra connecting bradyonic and tachyonic bosons and fermions has been constructed and it has been demonstrated that the difference between scales of bosonic and fermionic subspaces in C³-space increases quickly in spite of their closeness initially.     

Clocks in Weyl space-time

This paper deals with the usual methods for the construction of clocks as a first step in the direction of measurements in Weyl space-time. The atomic clocks constructed via atomic transitions, and the gravitational clocks constructed by the method of Marzke and Wheeler measure quantities with Weyl weights zero, whereas the Kundt and Hoffmann method for the construction of a clock was not found to be suitable. The atomic clocks are suitable for the chronometry and as a result of the chronometry it is shown that the Weyl space-time should be integrable.     

f-symbols in Robertson-Walker space-time

In a Robertson-Walker space-time, a spinning particle model is investigated. It is shown that in a stationary case a class of new structures called f-symbols exists ￠ Central European Science Journals. All rights reserved.     

Imaginary Weyl coordinates in the Kerr space-time

By introducing imaginary Weyl coordinates the Kerr geometry can be described by the Weyl coordinate system as good as the Boyer-Lindquist system.     

Definition of the vacuum in curved space-time

It is proposed that the vacuum state of quantized fields in curved space-time be defined as the state which minimizes the average value of the field Hamiltonian. Starting from this definition, equations are obtained for finding positive- and negative-frequency functions for spinor and scalar fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 16–21, July, 1979.     

An electromagnetic field in the Plebanski space-time

The electromagnetic wave equation in the Plebanski space-time has been reduced to a one-dimensional wave equation with real short-range potential. We then find that the superradiance phenomenon occurs.