Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

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.     

Non-existence of stationary,axisymmetric dust solutions of Einstein's equations on spatially compact manifolds

By using a theorem on the classifacation of SO(2)-actions on three-dimensional manifolds, it is shown that axisymmetric, stationary solutions of Einstein's equations do not exist on spacetimes with compact, space-like hypersurfaces, provided that the energy-momentum tensor is trace-free in the two-dimensional space of trajectories.     

Zero-mass scalar and electrostatic fields with the central symmetry in the general relativity

All asymptotically flat space solutions of Einstein equations with energy-momentum tensor of electrostatic and zero-mass scalar static central symmetric fields as a source were found. There are five branches of general solution; only two of them are contained in previous Penney's solution. In a limit of pure electrostatic field and pure scalar field our solutions become identical with corresponding solutions known previously.     

Some Anisotropic Universes in the Presence of Imperfect Fluid Coupling with Spatial Curvature

We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI₀-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinitely expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.     

Classification of Spherically Symmetric Static Spacetimes According to Their Matter Collineations

The spherically symmetric static spacetimes are classified according to their matter collineations. These are investigated when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either four, five, six or ten independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equations are different which on solving can provide physically interesting cosmological solutions.     

Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges

We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions.     

Homogeneous Bianchi type VI0 perfect fluid space-times

An algorithm is presented for generating new exact solutions of the Einstein equations for spatially homogeneous cosmological models of Bianchi type VI₀. The energy-momentum tensor is of perfect fluid type. Starting from Dunn and Tupper's dust-filled universe, new classes of solutions are obtained. The solutions represent anisotropic universes filled with perfect fluid not satisfying the equation of state. Some of their physical properties are studied.     

An Infinite Family of Magnetized Morgan-Morgan Relativistic Thin Disks

Applying the Horsky-Mitskievitch conjecture to the empty space solutions of Morgan and Morgan due to the gravitational field of a finite disk, we have obtained the corresponding solutions of the Einstein-Maxwell equations. The resulting expressions are simply written in terms of oblate spheroidal coordinates and the solutions represent fields due to magnetized static thin disk of finite extension. Now, although the solutions are not asymptotically flat, the masses of the disks are finite and the energy-momentum tensor agrees with the energy conditions. Furthermore, the magnetic field and the circular velocity show an acceptable physical behavior.     

The method of conformal mapping and new solutions of the einstein equations with the energy-momentum tensor of an ideal fluid

Two solutions with the energy-momentum tensor of an ideal fluid are obtained on the basis of theorems proved earlier by the author on the possibility of constructing new solutions of the Einstein equations from solutions already known by means of conformal mapping. The first of these solutions is a conformal correspondent to the De Sitter solution, and the second corresponds to the class of Friedman solutions. The explicit form of the metrics of the new solutions and of the parameters of the energy-momentum tensor is written out, and the properties of the corresponding space-times are also investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 111–115, April, 1977.     

Self-gravitating general-relativistic cosmic strings

We examine the coupled Einstem-Euler-Lagrange equations for nonstationary cosmic strings. Self-consistent solutions to all the equations are found under the assumption that the energy-momentum tensor is of the formT _t ^t =T _z ^z while all other components vanish. It is shown that the strings are necessarily static in this case and that the scalar field potential must be of the usual quartic form with the coupling constants satisfying e²=8.     

Charged Noncommutative Wormhole Solutions via Power-Law f(T) Models

In this paper, we explore static spherically symmetric charged wormhole solutions in extended teleparallel gravity taking power-law f(T) models. We consider noncommutative geometry under Lorentzian distribution. In order to obtain matter components, we develop field equations using effective energy-momentum tensor for non-diagonal tetrad. We explore solutions by considering various viable power-law f(T) models, which also include teleparallel gravity case. The violation of energy conditions obtain by exotic matter to form wormhole solutions in teleparallel case while, physical acceptable wormhole solutions exist for charged noncommutative wormhole solutions for some cases of power-law models. The effective energy-momentum tensor and charge are responsible for the violation of the energy conditions. Also, we check the equilibrium condition for these solutions. The equilibrium condition meets for the teleparallel case and some power-law solutions while remaining solutions are either in less equilibrium or in disequilibrium situation.     

Internal source of the vaidya solution

A nonstatic model of a radiating star is constructed with the energy-momentum tensor of a non-Pascal fluid and nonequilibrium radiation. The gravity equations are reduced to an equation which permits one to immediately generalize known analytic static solutions to nonstatic ones with radiation. The approximation of a homogeneous star is considered in detail, and an evaluation is performed which shows that for a Sun-like star physical parameters which follow from the model, lie between reasonable limits and agree with observations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 36–39, March, 1988.     

A minimal relativistic model of gravitation within standard restrictions of the Classical Theory of Fields

The minimal relativistic model of gravitation on the basis of the gauge-invariant theory of the linear scalar massless field is suggested. The principle of the multiplicative inclusion of gravitational interaction, the requirements being that the simplicity and invariance of the theory under the allowed (gauge) transformation of potential Ф → Ф′ = Ф + const as the basis of the approach, is used. A system of gauge-invariant gravitational field and matter equations is obtained and an energy-momentum tensor with a positively defined density of the field energy is constructed. The exact solutions to equations for the central static field and for fields of spherically symmetric and plane gravitational waves in the free space and in the material media are obtained.     

Positivity of General Superenergy Tensors

Several of the most important results in general relativity require or assume positivity properties of certain tensors. The positive energy theorem and the singularity theorems make assumptions about the energy-momentum tensor and Ricci tensor respectively. Positivity of the Bel–Robinson tensor is needed in the proof of the global stability of Minkowski spacetime. Senovilla has recently presented a procedure of how to construct a superenergy tensor from any tensor. For a Maxwell field or a scalar field the procedure yields the usual energy-momentum tensor, for the Weyl tensor and the Riemann tensor one obtains the Bel–Robinson tensor and Bel tensor respectively. In general, by considering any tensor as an r-fold n ₁,…,n _r )-form, one constructs a rank 2r superenergy tensor from it. By using spinor methods, we prove that the contraction of any such superenergy tensor with 2r future-pointing vectors is non-negative. We refer to this as the dominant superenergy property and it generalizes several previous positivity results obtained for certain tensors as well as it provides a unified way of treating them. Some more examples are given and applications discussed. Received: 21 December 1998 / Accepted: 5 May 1999     

Gravitational waves in the general theory of relativity

The problem of gravitational radiation is discussed with the help of the Rodichev energy-momentum tensor. An invariant criterion is formulated for finding radiation in a space without sources. In general, the question of the presence of radiation in a system is resolved by a local study of the behavior of the energy-momentum tensor in the comoving tetrad. The results are applied to the study of certain exact solutions of the Einstein equations.     

Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes

The matter collineation classifications of Kantowski-Sachs, Bianchi types I and III space times are studied according to their degenerate and non-degenerate energy-momentum tensor. When the energy-momentum tensor is degenerate, it is shown that the matter collineations are similar to the Ricci collineations with different constraint equations. Solving the constraint equations we obtain some cosmological models in this case. Interestingly, we have also found the case where the energy-momentum tensor is degenerate but the group of matter collineations is finite dimensional. When the energy-momentum tensor is non-degenerate, the group of matter collineations is finite-dimensional and they admit either four which coincides with isometry group or ten matter collineations in which four ones are isometries and the remaining ones are proper.     

A generalization of the relativistic equilibrium equations for a non-rotating star

The problem of elastomechanical equilibrium for a static, spherically symmetric star composed of an elastic material is analyzed. A suitable formulation of relativistic elasticity theory is used, and the second order equilibrium equations are found. It is shown that the equilibrium conditions with anisotropic pressure introducedad hoc by some authors are in fact the dynamical conditions for a relativistic elastic material. The corresponding first order equations for the components of the metric and of the energy-momentum tensor reduce to the Tolman-Oppenheimer-Volkhoff equations if the material exhibits no shape-rigidity. Two interesting classes of solutions are discussed.     

Higher dimensional cosmologies

Einstein equations are derived for D-dimensional space-time that spontaneously compactify to the product M⁴ × Π_{i = 1}^α M^d_i in which the metric is taken to be of the generalized Robertson-Walker form. Cosmological solutions for these equations are studied with power law, oscillatory and exponential behaviour for the D-dimensional Einstein-Maxwell, N = 2, D = 10 and N = 1, D = 11 supergravity models. In the Einstein-Maxwell case the presence of a cosmological constant forces the extra dimensions to be static. Nevertheless, it is possible to find solutions with vanishing effective 4 dimensional cosmological constant with an expanding 4-dimensional space-time. In the supergravity models the requirement of having compact extra dimensions restricts the solutions to have expansion only in the 4-dimensional space-time. Matter contribution is added to the energy-momentum tensor in an attempt to find new solutions.     

电磁场存在时宇宙因子不为零的高维类Vaidya时空

本文求出了在宇宙因子不为零时,由高维球对称电磁场和球对称辐射产生的高维类Vaidya时空,并探讨了在高维时空中电磁场能量动量张量的可能表示式。