Spinning fluids in the Einstein-Cartan theory: A variational formulation

In this work we propose a lagrangian for spinning fluids in the Einstein-Cartan theory. The basic characteristic of the model is to consider each infinitesimal volume element as replicas of micro-rigid bodies. The theory obtained represents the thermodynamical equilibrium limit of a more general situation where dissipative processes due to spin take place. We outline the extension of such processes to the Einstein-Cartan theory.     

Nonlocal integral conservation laws and tetradic currents in the Einstein-Cartan theory I. Nonlocal conservation laws

Nonlocal integral conservation laws in the Einstein-Cartan theory for the energy-momentum tensor of general-form sources, in essence being an integral equivalent of convoluted Bianchi identities, are obtained.     

Torsion and conservation laws

The interaction of spinor and electromagnetic fields with the torsion of space-time is studied within the framework of the Einstein-Cartan theory. The equivalent nonlinear theory in Riemann space is obtained. The conservation laws for the vector and pseudovector currents are investigated in the nonlinear theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–52, February, 1986.     

A non-singular homogeneous universe with torsion

The Raychaudhuri equation and other relations for a spinning fluid in the framework of the Einstein-Cartan theory are obtained. It is shown that non-singular cosmological models of the Bianchi types I÷VIII are possible. As an example, a class of solutions for the I and the V type is presented.     

Metric-torsion gravitational theories

It is shown that under certain assumptions the Einstein-Cartan field equations are not unique but may reasonably be modified to a degree. These modified Einstein-Cartan equations are proven to be unique under quite general conditions and are likely the most general equations in any metric-torsion gravitational theory whose field equations are derivable from a variational principle and such that their geometric part is independent of constants other than the speed of light and the gravitational constant.     

Torsion Degrees of Freedom in the Regge Calculus as Dislocations on the Simplicial Lattice

Using the notion of a general conical defect, the Regge Calculus is generalized by allowing for dislocations on the simplicial lattice in addition to the usual disclinations. Since disclinations and dislocations correspond to curvature and torsion singularities, respectively, the method we propose provides a natural way of discretizing gravitational theories with torsion degrees of freedom like the Einstein-Cartan theory. A discrete version of the Einstein-Cartan action is given and field equations are derived, demanding stationarity of the action with respect to the discrete variables of the theory.     

Static dust sphere in Einstein-Cartan theory

Physically meaningful solutions of the field equations for static spherical dust distributions in the Einstein-Cartan theory have been obtained. There is one in which the spin is zero at the center and another with zero spin at the boundary of the sphere.     

On ghost neutrinos in the Einstein-Cartan theory of gravitation

Different characterization of ghost neutrinos in the Einstein-Cartan theory of gravitation are proposed and analyzed.     

Spherically symmetric static solutions with a completely polarized Cosserat medium in the Einstein-Cartan theory of gravitation

On the basis of a variational principle introduced earlier, exact self-consistent spherically symmetric static solutions are obtained in the Einstein-Cartan theory of gravitation with a completely polarized Cosserat medium.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 21–24, August, 1979.     

Friedmann-like cosmological models without singularity

The Einstein-Cartan theory of gravitation (general relativity with spin) provides a specific spin-spin contact interaction of matter, in addition to the usual long-range gravity. This new interaction enables us to prevent singularities in Cosmological models. It is shown how this mechanism works in the case when the standard Einstein-Cartan equations are valid at a microphysical level, and some spin-spin terms remain from the averaging procedure for randomly distributed spins. In contrast with the case of aligned spin distributions, it is possible to take over the isotropic and spatially homogeneous (i.e., Friedmannian) models into the Einstein-Cartan theory. These models can be made free from singularity, thanks to the self-interaction of spinning fluid.     

Stochastic Quantization of Einstein-Cartan Gravitational Theory

We apply the stochastic quantization method to Einstein-Cartan gravitational theory. The stochastic propagators are calculated and the cooperation of modes in such a theory is investigated. It was shown that in equilibrium limit our result is equivalent to the propagator for the symmetric part of tetrads.     

Einstein-Cartan引力理论中的广义协变守恒定律

本文从广义Noether定理出发,对Einstein-Cartan引力理论中一般拉氏量所对应的守恒定律作了普遍的讨论,并由广义位移交换x^μ＇=x^μ+e_d^μb^a得到了包含挠率的一般拉氏密度所对应的广义协变能量动量守恒定律,并论述了超势存在的必然性。它是文献[1]和[2]理论的自然推广。 关键词：     

Einstein-Cartan gravity with scalar-fermion interactions

In this paper, we have considered the g-essence and its particular cases, k-essence and f-essence, within the framework of the Einstein-Cartan theory. We have shown that a single fermionic field can give rise to the accelerated expansion within the Einstein-Cartan theory. The exact analytical solution of the Einstein-Cartan-Dirac equations is found. This solution describes the accelerated expansion of the Universe with the equation of state parameter w = −1 as in the case of ΛCDM model.     

The earliest evolutionary stages of the universe and space-time torsion

A model of the early universe is proposed on the basis of Einstein-Cartan theory. The evolution of the universe begins from the primary static stage. The problems of gravitational stability are investigated.     

Some stationary cylindrically symmetric solutions of the equations of the Einstein-Cartan theory

Within the framework of the Einstein-Cartan theory new solutions are found that describe a cylindrically symmetric distribution of Weyssenhoff fluid for various spatial spin polarizations. The physical characteristics of the fluid and possibilities of splicing with the vacuum solutions are investigated in the static case. The stationary solution generalizes the well-known Stokum-Lanczos metric to the case of the Einstein-Cartan theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 95–99, April, 1977.The author expresses his thanks to Professor N. V. Mitskevich for his constant attention to this work and for valuable remarks.     

Geometrical meaning of the Poincaré group gauge theory

We find a condition (6) under which a gauge theory of the Poincaré group is equivalent to the Einstein-Cartan theory of gravitation.     

Can Torsion Play a Role in Angular Momentum Conservation Law?

In Einstein-Cartan theory, by the use of thegeneral Noether theorem, the general covariantangular-momentum conservation law is obtained withrespect to the local Lorentz transformations. Thecorresponding conservative Noether current is interpreted asthe angular momentum tensor of the gravity-matter systemincluding the spin density. It is pointed out that,assuming the tetrad transformation given by eq. (15), then torsion does not play a role in theconservation law of angular momentum.     

Post-Einstein cosmology: Torsion, strings, dual symmetry. I. The necessity of using the Einstein-Cartan theory instead of the Einstein theory

The hypothesis that heavy dichromatic lepton structures corresponding to the dual group SU(2) and called the friedmons are dark matter particles is proposed. Arguments in favor of the Einstein theory generalization to the Einstein-Cartan theory are presented. It is shown that string additions in the Schwarzschild and de Sittermetrics correspond to the cosmological constant.     

Gauge fields with torsion

The Klein-Kaluza theory with a nonvanishing torsion is developed. The torsion is associated with spin and polarization of a gauge field. The electromagnetic polarization is considered as a source of additional components of torsion connected with the fifth dimension. New physical effects obtained due to this torsion are pointed out and some cosmological models are studied. It is proved that new effects are 10³⁶ times bigger than the effects from the Einstein-Cartan theory. The usual Dirac equation is generalized to the Klein-Kaluza theory with and without torsion. The dipole electric moment of a fermion of order 10^–32 cm is obtained. A new generalization of minimal coupling is proposed.Partially supported by Polish Ministry of Science, Higher Education and Technology project No. MR17.