Pentagonal two-loop ring interferometer

Results of work on the assembly and adjustment of an original pentagonal, two-loop interferometer are reported; the interferometer is a passive version of a compact laser gravitational wave detector. It is shown that the correlative automatic noise-compensation system developed for the project is capable of lowering the phase noise level in the resultant signal channel of the detector by two orders of magnitude. Zh. Tekh. Fiz. 68, 121–125 (May 1998)     

Stabilization of the different frequency of reference and signal resonators in the Dulkyn gravitational-wave detector

It is shown that stabilization of the different frequency of optical radiations generated in the reference and signal resonators of the Dulkyn laser-interferometric gravitational-wave detector results in an efficient reevaluation of basic parameters describing the line widths of the laser radiation and the passive resonator, as well as the minimal laser power required to separate the valid signal from noises caused by natural fluctuations.     

The possibility of checking the equivalence principle in a null gravitational redshift experiment by a two-resonator laser system

A scheme of an optical detector is proposed for checking Einstein’s equivalence principle (EEP) in a null gravitational redshift experiment and for testing methods for calculating the length of a resonator in a weak variable gravitational field by recording the variations of the difference frequency of resonators caused by lunisolar variations of the geopotential in a double or a two-resonator laser system.     

Generation of static solutions of a self-consistent system of Einstein-Klein-Gordon equations

A theorem is proved according to which a class of static solutions of a self-consistent system of Einstein-Klein-Gordon equations dependent on one arbitrary function is set in correspondence with a static solution of the Einstein equations with any given energy-momentum tensor T_ij. Two particular cases are examined as an illustration of this theorem. Methods of constructing the static solutions of a system of Einstein-Klein-Gordon equations with an ideal fluid energy-momentum tensor and a massive scalar field are indicated therein.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–14, June, 1989.     

Equilibrium distribution of an ideal fluid in space-times permitting groups of concircular motions

A space — time with an ideal fluid as a source that permits groups of concircular motions is investigated. It is assumed that the velocity vector of the fluid is directed along a time-like group vector. A theorem on the properties of such a fluid and its relation with symmetries of the space — time is proven. Kazan’ State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 7–13, June, 1997.     

Test of local position invariance using a double-cavity laser system

The results of testing local position invariance, which is a constituent of the Einstein equivalence principle, in a “null” gravitational redshift experiment are reported. The processing of the experimental data collected during the five-month operation of a double-c avity laser system, where one cavity operates in the free generation mode and the frequency of the second cavity is stabilized with the nonlinear ultranarrow absorption resonance of the methane molecule, has confirmed the universality of the gravitational redshift law at a level of 0.9%. This result almost doubly improves the best existing accuracy (1.7%) of testing local position invariance for clocks of different physical natures.     

Isometric motions of a perfect charged fluid

Space-times with perfect charged fluids as sources, that admit groups G_r of isometric motions, are investigated. It is assumed that the velocity vector of the fluid is collinear to the timelike Killing vector ⁱ of group G_r. It is shown that the macroscopic motion of a perfect charged fluid can occur only in the direction of such a Killing vector ⁱ that defines an operator in an invariant subgroup or, in particular, an operator of the center of the group. Parametric representations of the generalized equations of state for the pressure p, the energy density of the fluid, , and the electric charge density are established. All these quantities are functions of the norm of the Killing vector ⁱ and the projection of the 4-potential of the electromagnetic field onto this vector ⁱ. In the approximation of the weak field in the coordinate system where ⁱ= ₄ ⁱ , these functional dependences imply that p, , and are functions of Newtonian and electrostatic potentials.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 25–29, October, 1987.     

Homogeneous solutions of the Einstein equations with an ideal charged fluid

The space-times V₄ with an ideal charged fluid as source allowing the motion group G_r, r 4, are investigated. It is assumed that the fluid velocity vector is directed along the timelike vector of the Killing group. In the case of groups G₄, acting on V₄, as well as groups of higher mobility, a complete investigation is performed of the space-times by using the system of Einstein-Maxwell equations. Exact solutions are found with fourth- and fifth-order groups.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 74–79, December, 1984.     

Generation of static solutions of the self-consistent system of Einstein-Maxwell equations

A theorem is proved, according to which to each solution of the Einstein equations with an arbitrary momentum-energy tensor in the right hand side there corresponds a static solution of the self-consistent system of Einstein-Maxwell equations. As a consequence of this theorem, a method is established of generating static solutions of the self-consistent system of Einstein-Maxwell equations with a charged grain as a source of vacuum solutions of the Einstein equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 98–102, February, 1988.