Static fields in generalized theory of gravitation

Solutions of field equations of the generalized theory of gravitation for neutral and charged point masses are found. The problem is formulated so that the solution may be expressed in harmonic, isotropic, Schwarzschild and, if necessary, any other coordinates. A method for the solution of the static axisymmetric problem (an analogue of a well-known Weyl's solution) is also proposed.     

New approach to solution of axisymmetric stationary equations of general relativity

Erevan State University. Translated from Astrofizika, Vol. 32, No. 3, pp. 453–463, May–June, 1990.     

Stationary axisymmetric fields in Generalized Theory of Gravitation

The problem of stationary axisymmetric gravitational fields is formulated within the framework of Generalized Theory of Gravitation. It is shown that solutions of the problem mentioned above may be found, if analogous solutions in General Relativity are obtained. As an illustration a Kerr-like solution is offered. A generation theorem for finding magnetostatic solution from stationary vacuum solutions is proposed.     

Cosmological Scalar in the Jordan-Brans-Dicke Theory. I

A variant of the Jordan-Brans-Dicke (JBD) theory is examined which contains a cosmological scalar that is written so that on going to the Einstein representation it becomes the ordinary cosmological constant of general relativity theory. This paper is divided into two parts. In Part I we examine the cosmological solutions for the Einstein representation of the JBD theory, i.e., in the presence of a minimally coupled scalar field. In Part II we shall study the cosmological solutions in the proper representation of the JBD theory with a self consistent scalar field. The analysis of these solutions is of interest in connection with modern concepts of the evolution of the universe, in particular, with the observed acceleration of cosmological expansion and estimates of the density of dark matter and dark energy.__________Translated from Astrofizika, Vol. 48, No. 3, pp. 455–462 (August 2005).     

Gravitational field of a concentrated mass in Jordan—Brans—Dicke theory

The problem of determining the gravitational field of a static, spherically symmetric, self-gravitating object is formulated. The small number of physically applicable exact solutions of the equations in Jordan—Brans—Dicke theory is augmented with new exact solutions describing the external gravitational field of the given body. Once a solution has been found, it can be rewritten in modified curvature, homogeneous, and other coordinates by appropriate gauging. In a special case the solution coincides with the well-known Schwarzschild solution.Translated from Astrofizika, Vol. 37, No. 2, pp. 339–350, April–June, 1994.The authors are grateful to members of seminars convened by the Theoretical Physics Department of Erevan State University and the Space, Time, and Gravitation LTF of the Joint Institute for Nuclear Research for discussions.This work has received partial support from a Meyer Foundation Grant awarded by the American Physical Society.     

Status of physical observables of a friedmann universe in the classical and quantum hamiltonian formalisms

The paper is devoted to an investigation of the relationships between the classical Friedmann cosmology and the Dirac Hamiltonian approach to quantization of the universe, based on the simple but important example of a homogeneous universe filled with excitations of a scalar field. The method of gaugeless reduction is used to completely separate the sector of physical variables from the purely gauge sector, making it possible to find the relationship between cosmological observables in the Friedmann — Einstein sense and observables of the Dirac Hamiltonian formalism in the Narlikar conformai reference frame. Gaugeless reduction enabled us to establish that in the process of reduction, one of the variables of the nonphysical sector is converted into an invariant time parameter and cannot be treated as a dynamical variable in either the functional or the operator approach to quantization. It is shown that in this conversion of a variable into a time parameter, the Hartle-Hawking functional integral is the reason why the wave function of the Wheeler—De Witt (WDW) equation cannot be normalized and why an infinite gauge factor arises. The gaugeless reduction provides a certain recipe for mathematical and physical interpretation of the WDW equation and wave functions, the use of which makes their relationship to observational cosmology clear and transparent. It is shown, in particular, how the WDW wave function describes the Friedmann evolution with respect to proper time. Translated from Astrofizika, Vol. 40, No. 2, pp. 303–321, April–June, 1997.     

A Friedmann universe in the quantization scheme of reduced phase space

It is shown how, using action-angle variables in the scheme of quantization of reduced phase space, to construct a wave function for a Friedmann universe filled with harmonic excitations of photons and massive fermions, as well as to find physically observable quantities. Such an approach leads to an equation of the Schrödinger type, admits of a simple interpretation of the wave Junction, and enables one to trace the connection with classical evolution, which is fully reproduced in the proposed model. Within the framework of the reduced theory, massive fermions are described by action of the Nambu-Jona-Lasinio type with spontaneous breaking of chiral symmetry. The proposed scheme leads to consequences that are consistent with the Mach principle and Dirac’s hypothesis of large numbers.