A stationary Michelson interferometer in a Schwarzschild gravitational field

There is shown to be a nonzero effect during the measurement of the time lag in a Michelson interferometer in the earth's gravitational field, for vertical positioning of one of the arms. A formula for calculating the time lag is obtained. The possibility of measuring the interferometer effect with the aid of fiber optics is considered.S. Ordzhonikidze Moscow Aviation Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 95–97, March, 1993.     

Evolution of electromagnetic waves of a point source in the Schwarzschild field

The problem of electromagnetic radiation of a source in the gravity field of a nearby black hole is considered. A complete class of exact axial-symmetric solutions of the eikonal equations is found. The components of the field tensor are obtained in the large frequency approximation. An expression is found for the strength of the observed radiation as a function of the distance between the black hole and the source, and of the angle between the directions black hole-observer and black hole-source. It is shown that the system consisting of a black hole and a normal star in rotation around the common center of gravity must look like an object of variable brightness.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 83–88, October, 1988.     

Spectrum of stationary electromagnetic radiation in a static gravitational field

From the equation of continuity, an equation is derived for the change in the spectrum of radiation stationary in a static gravitational field, as measured by local observers in their proper frame. It is shown that an isotropic solution always exists in which the energy density per unit frequency interval is ³ times an arbitrary function of .     

On the world function of the Schwarzschild field

The representation of the world function of the Schwarzschild field as a power series is investigated. Initially we concern ourselves with a neighborhood of the event horizon. The symmetries of the metric are invoked effectively to reduce the number of independent variables upon which depends from eight to four, and to show that when these are sufficiently small in magnitude is an analytic function of them. A fairly large number of the early terms of the power series for is found explicitly. The condition that one is to remain sufficiently close to the event horizon is then relaxed, it being merely stipulated that the endpoints shall be sufficiently close to each other. Finally, using other variables, the early terms of a series for are obtained for the case in which the endpoints are restricted to lie outside the event horizon and sufficiently close to each other.     

A dispersion relation for gravitational radiation in a Schwarzschild background

A dispersion relation is derived for gravitational radiation emitted from an almost spherical object.     

Calculating the gravitational self-force in Schwarzschild spacetime

We present a practical method for calculating the local gravitational self-force (often called "radiation-reaction force") for a pointlike particle orbiting a Schwarzschild black hole. This is an implementation of the method of mode-sum regularization, in which one first calculates the (finite) contribution to the force due to each individual multipole mode of the perturbation, and then applies a certain regularization procedure to the mode sum. Here we give the values of all the "regularization parameters" required for implementing this regularization procedure, for any geodesic orbit in Schwarzschild spacetime.     

Green function theory of the scattering of electromagnetic waves from a cylindrical boundary of arbitrary shape

It is shown that the use of interior and exterior Green functions satisfying Neumann conditions on the cylindrical boundary reduces the problem of the determination of the scattered field, in all cases of physical interest, to that of the solution of a single integral equation.     

Interaction of a high-temperature plasma with electromagnetic radiation in a gravitational field

The linearized general-relativistic kinetic equation is used to study the interaction of highfrequency electromagnetic radiation with a fully ionized plasma in a gravitational field;, the pseudotensors of the complex conductivity, permittivity, and absorption of energy are constructed.     

Vacuum generation of electromagnetic radiation by a variable gravitational field

Generation of photons in a curved space-time due to polarization of the electron-positron vacuum is considered: R 2. A general expression for the number of photon pairs is obtained, and the limits of its applicability are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 9–12, March, 1987.     

The Dirac equation in Schwarzschild black hole coupled to a stationary electromagnetic field

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzschild solution to an external, stationary electromagnetic field. The set of equations representing the uncharged Dirac particle in the Newman–Penrose formalism is decoupled into a radial and an angular parts. We obtain exact analytical solutions of the angular equations. We manage to obtain the radial wave equations with effective potentials. Finally, we study the potentials by plotting them as a function of radial distance and examine the effect of the twisting parameter and the frequencies on the potentials.     

Polarization effects in electron scattering in the gravitational field of a rotating source

The polarization effects in electron scattering in a gravitational field with the Kerr metric are examined, and a formula is obtained for the deflection angle of a relativistic spin -1/2 particle in such a field by the methods of quantum electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 104–108, May. 1972.The author would like to thank Yu. S. Vladimirov and Professor D. D. Ivanenko for valuable comments and numerous discussions.     

The preferred null symmetries of a null electromagnetic field interacting with a null free gravitational field

The real null vector 1 ^a of the Newman-Penrose formalism is preferred to correspond to a geometrical symmetry as well as a dynamical symmetry. The 16 types of geometrical symmetries expressed through the vanishing of the Lie derivatives of certain tensor fields with respect to 1 ^a are examined separately. Two types of dynamical symmetries are imposed simultaneously on 1 ^a : A null electromagnetic field and a null gravitational field are both chosen to have the same propagation vector 1 ^a . By adopting freedom conditions on 1 ^a , it is shown that the symmetries of the null electromagnetic field are shared neither by the free gravitational field nor by the gravitational potentials. In fact the following five preferred null symmmetries are found to be proper: motion, affine collineation, special curvature collineation, curvature collineation, and Ricci collineation. The scalars characterizing the coupled fields are found to be constant with respect to 1 ^a .     

电磁脉冲模拟器电磁场计算

利用电磁场张量法计算了平行板电磁脉冲模拟器内的电磁场并推导了其时域解析表达式。按照模拟器的平行板段和前后三角板的结构将平板近似为线网格。场的幅值由各线段元的不同滞后时间叠加来确定,其方向由线段元和场点的单位矢量经简单矢量运算来确定。计算结果表明：平行板段内的场具有横电磁分布特性,而靠近三角板处由于各线段元的非对称性贡献将使场出现其它分量。通过对模拟器的电场测量值与理论计算值相比较可知,两者大致相同。