Additional conditions for mapping functions in W4, fields

A rigorous basis is given for additional conditions of zero type for mapping functions in conformally planar gravitational fields for an ideal liquid (Wi. fields).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 18–24, December, 1977.     

Fields of a viscous fluiid without shear and rotation

It is shown that in Einstein's theory of gravitation conformally flat gravitational fields of a viscous fluid without shear and rotation are analogous to the fields of an ideal fluid with a conformally flat space-time. Thus, the fluid particles in such fields move along geodesics, and the three-dimensional hypersurfaces determined by the sections x⁰=const are spaces of constant curvature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–40, January, 1981.     

Some properties of the gravitational fields of a hydrodynamical fluid and dust

Conditions are obtained on the four velocity of the particles of a medium in the gravitational fields of a hydrodynamical fluid and dust, and the nature of the motion of the medium in these fields is investigated. It is shown that the gravitational fields of a hydrodynamical fluid and dust do not admit conformal mapping onto Einstein spaces which are not conformally flat spaces (spaces of constant curvature).     

Con formally flat gravitational fields of an ideal fluid

The necessary and sufficient conditions are obtained for gravitational fields of an ideal fluid to be conformally Euclidean. The possible types of field are considered.     

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.     

Conformally flat gravitational fields produced by an ideal fluid

The problem of finding conformally flat gravitational fields produced by a perfect fluid is solved completely.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.12, pp.22–25, December, 1980.     

Centrifugal deformations of the gravitational kink

The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.     

Application of types-N and -O spaces to examples of exact solutions of the gravitational equations

Analysis of the exact solutions of the gravitational equations corresponding to the collision of two gravitational plane waves (typeN) and light-like beams (typeO) and also a Kerr-Schild wave metric with conformally flat background is used to formulate theorems that indicate the resulting type of spacetime if the initial gravitational fields belong to typesN andO. A type-D Weyl matrix always appears, which is due to the nonlinear super-position of gravitational fields, in contrast to the superposition of weak gravitational fields, when the sum of the Weyl matrices for the initial fields corresponds to dropping nonlinear terms in both the curvature tensor and the field equations.Work performed under the auspices of the Russian State Scientific-Technical Program Astronomiya.Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–82, May, 1995.     

Nonstatic gravitational fields of an ideal fluid without shear and rotation

It is shown that in the Einstein gravitational theory there are no nonconformal planar nonstatic gravitational fields of an ideal fluid without shear and rotation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 71–76, August, 1979.     

On the projectivity of conformally flat spaces created by a hydrodynamical energy-momentum tensor

It is shown that under the condition _ju _k = _k u_j imposed on the mapping function the geodesics in conformai gravitational fields are the same. The following fact is also established: all conformally flat spaces satisfying this condition correspond to the gravitational fields of an ideal fluid.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 16–19, 1972.     

A unified conformal model for fundamental interactions without dynamical Higgs field

A Higgsless model for strong, electroweak and gravitational interactions is proposed. This model is based on the local symmetry group SU(3)×SU(2)_L×U(1)×C,where C is the local conformal symmetry group. The natural minimal conformally invariant form of total Lagrangian is postulated. It contains all standard model fields and gravitational interaction. Using the unitary gauge and the conformal scale fixing conditions, we can eliminate all four real components of the Higgs doublet in this model. However, the masses of vector mesons, leptons, and quarks are automatically generated and are given by the same formulas as in the conventional standard model. In this manner one gets the mass generation without the mechanism of spontaneous symmetry breaking and without the remaining real dynamical Higgs field. The gravitational sector is analyzed, and it is shown that the model admits in the classical limit the Einsteinian form of gravitational interactions.     

Conformally flat Stäckel spaces in the Brans–Dicke theory

A problem of classification of the conformally flat St?ckel spaces admitting complete separation of variables in the Hamilton–Jacobi equation is studied within the framework of the Brans–Dicke scalar-tensor gravitational theory. Solutions to the field equations of the theory are found for the conformally flat St?ckel spaces of type (1.1), and explicit forms of the metric and scalar field are presented. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 54–58, February, 2009.     

Variational principle for gravitational equations of the Bianchi identity type

It is shown that a square invariant of the Weyl conformal curvature tensor can lead to a Lagrangian in a variational principle for a gravitational equation in vacuum of the Bianchi identity type which is compatible with the Einstein equation. Moreover we show that such a Lagrangian implicitly includes a conformally invariant theory characterized by two gauge fields and the metric tensor.     

Conformal invariance and spontaneous symmetry breaking

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fieldsand the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of themodel.     

3D collapse of rotating stellar iron cores in general relativity including deleptonization and a nuclear equation of state

We present 2D and 3D simulations of the collapse of rotating stellar iron cores in general relativity employing a nuclear equation of state and an approximate treatment of deleptonization. We compare fully general relativistic and conformally flat evolutions and find that the latter treatment is sufficiently accurate for the core-collapse supernova problem. We focus on gravitational wave (GW) emission from rotating collapse, bounce, and early postbounce phases. Our results indicate that the GW signature of these phases is much more generic than previously estimated. We also track the growth of a nonaxisymmetric instability in one model, leading to strong narrow-band GW emission.     

Invariant solutions and conservation laws of Einstein field equations in non-comoving radiation fields

The exact non-static accelerating solutions of Einstein field equations in non-comoving pure radiation fields, corresponding to an indefinite non-degenerate metric in cartesian coordinates, are obtained. The gravitational field is of Petrov type $D$ and the considered spacetime is not conformally flat. Lie symmetry method is used for symmetry reduction of nonlinear partial differential equations and for finding the exact solutions, comprising both arbitrary functions and known analytic functions. Conservation laws are obtained by using multiplier approach. The graphical representations of solutions are shown by considering different possibilities of the arbitrary functions.     

Conformal off-mass-shell extension and elimination of conformal anomalies in quantum gravity

Radiative corrections in the Einstein quantum gravity are made manifestly conformally invariant without changing the S matrix. The conformally invariant form of the classical gravitational action is restored. It is shown, that conformal anomalies, discovered in gravitating systems, do not affect the S matrix. Off the mass shell these anomalies are eliminated by the appropriate choice of a regularization.     

Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.     

Solutions of Yang's EuclideanR-gauge equations and self-duality

Under some assumptions and transformations of variables, Yang's equations forR-gauge fields on Euclidean space lead to conformally invariant equations permitting one to obtain infinitely many other solutions from any solution of these conformally invariant equations. These conformally invariant equations closely resemble the mathematically interesting generalized Lund-Regge equations. Some exact solutions of these conformally in variant equations are obtained. Except for some singular situations, these solutions are self-dual.