Space-time of class one

The general expression of the second fundamental form for the instrinsic rigidity caseR ₄ embedded inE ₅ is obtained. Some examples are investigated.     

An imbedding of spacetimes

It is shown that any two-dimensional spacetimes with compact Cauchy surfaces can be causally isomorphically imbedded into the two-dimensional Einstein’s static universe. Also, it is shown that any two-dimensional globally hyperbolic spacetimes are conformally equivalent to a subset of the two-dimensional Einstein’s static universe.     

Quantum Thermal Effect of Nonstatic Charged Black Hole

The difficulty of calculating energy-momentumtensors is avoided by finding directly the solution ofKlein–Gordon and Dirac equations near the horizon.Both the location of the event horizon and the Hawking radiation temperature of a nonstatic chargedblack hole are shown. The results indicate that theHawking radiation temperature can be regarded as acompensating effect under the timescaletransformation.     

Einstein-Maxwell fields of embedding class one

It is shown that a necessary condition for an Einstein-Maxwell field to be of embedding class one is that the electromagnetic field and Weyl tensor areboth null (and non-zero). All Einstein-Maxwell fields of embedding class one are, in principle, obtained.     

Investigation of one class of Bargman-type potentials

For the spectral problem on the half-axis we derive an expression for the potential with N levels of discrete spectrum that are positioned in a previously determined fashion. We obtain wave functions for the discrete spectrum, Yost’s solution, and the continuous-spectrum functions. We show that the Yost function for this potential is a rational fractional function of the wave number k and, consequently, the potential itself is a potential of Bargman type. Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 34–39, May, 1998.     

非静态球形夸克-胶子等离子体的2π干涉学的检测

提出了一种相对论重离子碰撞中强子物质生成时的π膨胀源模型. 得到了该模型中的小相对论动量区域的2π关联函数及表观π源参数R_a与实际π源参数R_e的关系. 这一关系与QGP生成时的关系有所区别. 这一区别可以用来检测相对论重离子碰撞中产生的非静态球形夸克-胶子等离子体的存在性. 两个关系也显示了一种标度行为.     

Perfect fluid distribution in class one space-time

Space-times of class one for which the elementary divisors of the second fundamental tensor are real but not simple, do not admit perfect fluid distributions.     

A new class of plane symmetric solution

A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different energy conditions are studied. The classical stability of this solution is discussed. The junction conditions matching to Minkowski metric and Taub metric are analyzed respectively.     

An invariant imbedding formulation of coupled-wave theory

An alternative formulation of coupled-wave theory adapted to numerical analyses is developed, using the method of invariant imbedding. Solutions of the coupled-wave equations are represented in terms of a reflectance matrix and a transmission matrix (rather than the transition matrix of the more classical approach).     

About one class of representations of the Lie algebra

LetR(G) be the skewsymmetric representation of the algebraG characterized by the following main property: ifGG is some subalgebra ofG (possible noncompact) thenR(G) is integrable and reducible in the direct sum of irreducible representations of subalgebraG.The paper is devoted to the development of the elementary theory of the described representations, culminating in the proof of one version of Schur's lemma.     

Space times of embedding class one in general relativity

The algebraic structures of both the Ricci and Weyl tensors, given that of the second fundamental tensor, are tabulated. In particular, the Weyl tensor is algebraically special if and only if the second fundamental tensor is algebraically special. A class one perfect fluid is found to possess at least one of the following properties: (a) conformai flatness; (b) the flow is geodesic; (c) it admits a three-dimensional group of isometries with two-dimensional space-like trajectories. All solutions with property (b) are obtained explicitly.     

Characteristic functional for one class of non-Gaussian random functions

A generalization of Poissonian random functions is presented. A characteristic functional is derived that includes four arbitrary functions: the generating function of the factorial moments for the number of bursts; the probability density function for the positions of bursts; the characteristic function for the amplitudes of bursts; and the function describing the shape of a burst depending on its position. In the case of the Poisson distribution of the number of bursts, uniform distribution of burst positions, and independence of the burst's shape on its position, this characteristic functional turns out to be known for Poissonian random functions. Many new formulae for the characteristic functional are presented.     

Non-static non-conformally flat fluid plates of embedding class one

In the present article four non-static perfect fluid solutions have been derived by considering a plane symmetric metric of embedding class one. Out of the solutions so obtained two solutions possess an acceleration free velocity vector field while the other two have flow with acceleration. As far as the authors are aware the solutions with non-vanishing acceleration are new.