Spacetime tangent bundle with torsion

It is demonstrated explicitly that the bundle connection of the Finslerspacetime tangent bundle can be made compatible with Cartan's theory of Finsler space by the inclusion of bundle torsion, and without the restriction that the gauge curvature field be vanishing. A component of the contorsion is made to cancel the contribution of the gauge curvature field to the relevant component of the bundle connection. Also, it is shown that the bundle manifold remains almost complex, and that the almost complex structure can be made to have a vanishing covariant derivative if additional conditions on the torsion are satisfied. However, the Finsler-spacetime tangent bundle remains complex only if the gauge curvature field vanishes.     

Theory of gravitation in a space of absolute parallelism

A theory of the gravitational field in a fiber bundle of absolute parallelism is proposed. It is shown that such a theory generalizes the Einstein equations for empty space and eliminates some of the difficulties in Einstein's theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, pp. 142–147, June, 1977.     

On a new metric affine theory of gravitation

We present three hypotheses which underlie a new general relativistic theory of gravitation for microphysical systems. According to this theory the metric and the independent affine connection of spacetime are determined by the momentum current and the newly recognized “hypermomentum” current of matter.     

On spherically symmetric fields with dynamic torsion in gauge theories of gravitation

Within the framework of the Poincaré gauge field theory of gravity, the general gravitational Lagrangian coupled to the electromagnetic field is investigated. We treat the case of a static, spherically symmetric field with space reflection invariance. The exact solutions presented will be generated by a double-duality ansatz for the curvature. The Reissner-Nordström metric is singled out within a class of Lagrangians admitting an asymptotically flat metric.     

A Berger-type theorem for metric connections with skew-symmetric torsion

We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere, then the space must be locally isometric to a Lie group with a bi-invariant metric or its symmetric dual (we assume the space to be locally irreducible). We also prove that a (simple) Lie group with a bi-invariant metric admits only two flat metric connections with skew-symmetric torsion: the two flat canonical connections. In particular, we get a refinement of a well-known theorem of Cartan and Schouten. Finally, we show that the holonomy group of a metric connection with skew-symmetric torsion on these spaces generically coincides with the Riemannian holonomy.     

Spinors in quantum space with torsion

Dirac spinors are considered in quantized fiber-bundled spaces. It is shown that the spin connection has the same internal structure as in the Riemann-Cartan space as well as the quantized one. It is also assumed that the neutrino oscillation mechanism can be linked to the quantized and fibered character of the space at small distances.     

A maximally symmetric space with torsion

A maximally symmetric space, i.e., homogeneous and isotropic at every point, possessing totally antisymmetric torsion is dealt with. It is found that maximum symmetry restricts the dimension of the space to three. The three-curvature tensor for the space is obtained and from its form a three-metric is then constructed. The three-space is then allowed to evolve in time so that a four-metric of the formds ²= –dt ²+ (3)g _ij dx ⁱ dx ^j is possible. From this an equation of motion is obtained which predicts an initial- and final-state singularity.Part of this work was done as a doctoral thesis requirement at Queen Mary College, University of London.     

The Casimir operator of a metric connection with skew-symmetric torsion

For any triple (Mⁿ,g,) consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second-order operator Ω acting on spinor fields. In case of a naturally reductive space and its canonical connection, our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly Kähler, cocalibrated G₂-structures) admit unique connections with skew-symmetric torsion. We study the corresponding Casimir operator and compare its kernel with the space of -parallel spinors.     

Tetrad fields and metric tensor in the gauge theory of gravitation

The most relevant geometrical aspects of the gauge theory of gravitation are considered. A global definition of the tetrad fields is given and emphasis is placed on their role in defining an isomorphism between the tangent bundle of space-time and an appropriate vector bundle B associated to the gauge bundle. It is finally shown how to construct the fundamental geometrical objects on space-time, starting from B.     

Dependence of a common effective action in a multidimensional R2 gravitation on the metric of the configuration space

A common effective action in a multidimensional R² gravitation on a plane R_d or R_k × T_d–k background is analyzed. The dependence of this effective action on the metric of the configuration space is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 74–76, July, 1991.     

Gravitational waves and Papapetrou metric in the six-dimensional treatment of gravitation

Six-dimensional treatment of gravitation based on the principle of simplicity to which there corresponds motion of particles with the speed of light in the Compton neighborhood of the three-dimensional space along the geodesics complying with the Fermat principle is given to the Papapetrou metric and gravitational waves. The envelope of the geodesics has the form of a tubular surface with the Compton transverse sizes in the additional subspace where the radius and speed of light vary along the tube. Gravitational waves, which are perturbations of these radii and speed of light, turn out to attenuate exponentially here. Their amplitudes are considered in the near-field zone of the rotator with n Maltese cross lobes and calculated at n = 4.     

A class of metric theories of gravitation on Minkowski spacetime

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian , from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.     

Fermions in a two-dimensional theory of gravity with dynamical metric and torsion

We propose a new model which reduces a two-dimensional gravitational model with dynamical metric and torsion in a conformal gauge. We also find the instanton-like solutions and discuss their symmetry properties and eigenmodes.This work was partially supported by TBTAK, the Scientific and Technical Research Council of Turkey.     

Spinor and electromagnetic fields in space with torsion

A combined system of Einstein-Cartan, Ivanenko-Heisenberg, and Maxwell equations is reduced to a combined system of Einstein, Dirac, and Maxwell equations in Riemann space. A solution in which metric singularities are absent is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 31–35, November, 1978.     

Quadratic Lagrangians in a space with torsion

A general expression is given for a quadratic (with respect to the curvature tensor) Lagrangian in a space with torsion. The given formalism is discussed in application to generalized Einstein-Cartan gravitation theory and the theory of the spin gauge field introduced in localization of the tetrad Lorentz transformation group.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 7–10, December, 1977.The author is indebted to Prof. D. D. Ivanenko, V. N. Ponomarev, and P. L. Poznanin for a useful and stimulating discussion.     

Homogeneous isotropic cosmological model of space-time with torsion in the Einstein-Cartan theory of gravitation

A systematic treatment is applied to the cosmological problem in the Einstein-Cartan theory of gravitation on the basis of the variational principle formulated previously for an ideal fluid in space with torsion. Exact solutions are obtained for homogeneous isotropic cosmological models with flat three-dimensional space filled with powdery matter and a fluid with an equation of state p=/3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 24–28, March, 1977.The author thanks Professor D. D. Ivanenko and members of the seminar conducted by him for useful discussions.