Torsion Field Research Articles

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or non-metricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or non-metricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (which indicates torsion and non-metricity). All this is compared to the recent results of Vandyck.

Mach’s principle and hidden matter

According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor\(\hat \Theta _{ik}\) satisfying the relation\(\hat \Theta _{i;k}^k = 0\). The tensor\(\hat \Theta _{ik}\) is formed from the Einstein-Cartan torsion field given by the anholonomy objects, FAik=2hA[i,k], and appears together with Hilbert’s energy-momentum tensor T* ik and Poincare’s pressure λgik on the right-hand side of Einstein’s equations so that one has $$R_{ik} - (1/2)g_{ik} R = - \kappa T*_{ik} - \lambda g_{ik} - \hat \Theta _{ik}$$ According to this theory, in the universe and in cosmic systems one must excep “invisible masses” described by the Poincare and Einstein-Cartan terms to exist. The torsion field FAik makes the space-time a Machian universe; it is of the same nature as the “weak interacting matter” discussed in astrophysics.

Non-Riemannian gravitational interactions

Recent developments in theories of non-Riemannian gravitational interactions are outlined. The question of the motion of a fluid in the presence of torsion and metric gradient fields is approached in terms of the divergence of the Einstein tensor associated with a general connection. In the absence of matter the variational equations associated with a broad class of actions involving non-Riemannian fields give rise to an Einstein-Proca system associated with the standard Levi-Civita connection.

Torsion Field Equation and Spinor Source

We propose a geometrical theory of gravitation based on a non-orthogonal tetrad field which plays the role of a torsion potential. Starting from the gravitational Lagrangian defined by scalar curvature, we obtain two field equations, the Einstein equation and the torsion field equation. The latter is a second-order differential equation for the torsion potential, and therefore the torsion has acquired a dynamical property. When we consider the torsion coupling to spinor fields, the torsion field equation has a difficulty. We show that this difficulty can be overcome by adding appropriate quadratic terms of the torsion tensor to the Lagrangian. Using the generalized Lagrangian, we study the torsion field equation and its solution in the weak field approximation.

Helicity flip cross section from gravity with torsion

In gravitation with torsion of the string theory type, it is shown that the Dirac equation acquires a coupling of the form where is due to the torsion field. It is shown that this interaction produces a mechanism for spin flipping, and the cross section for this process is calculated. The results are applied to solar neutrinos.

FOUR-DIMENSIONAL N=2 SUPERSTRING BACKGROUNDS AND THE REAL HEAVENS

We study N=2 superstring backgrounds which are four-dimensional, non-Kählerian and contain nontrivial dilaton and torsion fields. In particular we consider the case where the backgrounds possess at least one U(1) isometry and are characterized by the continual Toda equation and the Laplace equation. We obtain a string background associated with a nontrivial solution of the continual Toda equation, which is mapped, under the T duality transformation, to the Taub-NUT instanton background. It is shown that the integrable property of the non-Kählerian spaces has a direct origin in the real heavens: real, self-dual, Euclidean, Einstein spaces. The Laplace equation and the continual Toda equation imposed on quasi-Kähler geometry for consistent string propagation are related to the self-duality conditions of the real heavens with “translational” and “rotational” Killing symmetry respectively.

Black holes with Weyl charge and non-Riemannian waves

A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of electromagnetism. These equations are shown to possess solutions analogous to those found in the Einstein-Maxwell system. In particular one finds gravi-electric and gravi-magnetic charges contributing to a spherically symmetric static Reissner - Nordström metric. Such Weyl `charges' provide a source for the non-Riemannian torsion and metric gradient fields instead of the electromagnetic field. The theory suggests that matter may be endowed with gravitational charges that couple to gravity in a manner analogous to electromagnetic couplings in an electromagnetic field. The nature of gravitational coupling to spinor matter in this theory is also investigated and a solution exhibiting a plane-symmetric gravitational metric wave coupled via non-Riemannian waves to a propagating spinor field is presented.

Duality-invariant superstring actions.

The world sheet supersymmetric string action is written in duality-invariant form for flat as well as curved backgrounds. First the action in flat backgrounds is written by introducing auxiliary fields. We also give the superfield form of these actions and obtain the off-shell supersymmetry algebra. The action has a modified Lorentz invariance and supersymmetry and reduces to the usual form when the auxiliary fields are eliminated using their equations of motion. The superstring action coupled to world sheet supergravity is also written in duality-invariant form. Also the supersymmetric nonlinear \ensuremath{\sigma} model in curved backgrounds is written in manifestly duality-invariant form when the background metric and torsion fields are independent of some of the coordinates.

One-loop divergences of linear gravity with torsion terms

We investigate the role of the torsion field at the quantum level. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field. We have shown that the theory is finite at the one-loop level.

Rodichev condition on torsion, spinors, and conservation laws in Riemann-Cartan space

We examine the consequences of the Rodichev condition of complete antisymmetry of the torsion tensor in an orthonormal reference frame, which is equivalent to the condition of the existence of a pair of mutual spinor connectivities. It is shown that it makes possible a reformulation of general theorems about the relationship between first integrals of the geodesic equations and the Killing vectors, conservation laws for the symmetric energy—momentum tensor, and the Lagrangian formalism for a spinor field in the case of Riemann-Cartan space in the effective Riemann spacetime with an external torsion field.

Phase transition in conformally induced gravity with torsion.

We have considered the quantum behavior of a conformally induced gravity in the minimal Riemann-Cartan space. The regularized one-loop effective potential considering the quantum fluctuations of the dilaton and the torsion fields in the Coleman-Weinberg sector gives a sensible phase transition for an inflationary phase in De Sitter space. For this effective potential, we have analyzed the semi-classical equation of motion of the dilaton field in the slow-rolling regime.

Chaotic non-planar vibrations of the thin elastica: Part II: Derivation and analysis of a low-dimensional model

Here, we develop a simple model for the bending-torsion vibrations of the thin elastica; the experimental observations were described in Part I. A geometrically exact rod theory is developed: dimensional analysis demonstrates that a curvature constraint not used in previous analyses is appropriate in our case, and this is used to develop a coupled set of non-linear integro-differential equations for the problem. Using an additional simplifying assumption on the spatial derivative of the torsional field variable, a simplified set of partial differential equations is derived. It is shown that a two-mode projection of these model partial differential equations can be related to an intuitively appealing two-degree-of-freedom mechanical system. Numerical experiments on the two-mode model show that it captures much of the behavior observed in the physical experiments on the thin elastica. In particular, the model possesses a family of bending-torsion non-linear modes with a frequency-amplitude characteristic much like that found experimentally, and the driven problem loses planar stability in a fashion analogous to that observed with the elastica.

Electron gyroscopes to test torsion gravity?

Macroscopic effects of torsion gravity in astrophysics and microscopic gyroscopes to test deviation to Einstein’s theory are shown to lead to the same value for the torsion field of the Earth. Massive electrodynamics with torsion is used to produce an extra precession on the spin vector of an elementary particle placed on electric field. Despite experimental difficulties, calculations show that this precession would be appreciable for a hydrogen-like electron spin.

THE INTERACTION OF QUANTIZED MATTER FIELDS WITH TORSION AND METRIC: NJL MODEL

We consider the interaction of matter fields with classical gravitational background in the framework of Nambu-Jona-Lasinio (NJL) model. Gravity includes not only metric but also independent torsion field. The renormalization group analysis shows that the matter-torsion interaction increases in a strong gravitational field and disappears at low energies.

Quantization of closed orbits in Dirac theory by Maslov's complex germ method

On the basis of Maslov's complex germ method for the Dirac operator in external electromagnetic and torsion fields the quasi-classical spectral series corresponding within the limit h(cross) to 0 to the electron motion along closed stable orbits has been constructed. The quasi-classical energy spectrum is found from the condition of quantization of these orbits, and the quasi-classical asymptotics corresponding to the latter form a complete set of localized quantum state. The method is illustrated in all details by the electron motion in the axial fields as an example.

Reciprocity theorem to compute the static deformation due to a point dislocation buried in a spherically symmetric earth

SUMMARY Intriguing reciprocity relations exist between the static deformation excited by a point dislocation in a SNREI earth and those generated by external forces, such as tidal force, surface loading and surface shear forces. Coseismic deformations can be rewritten as follows: (1) potential change in terms of the tide deformation field, (2) radial displacement in terms of the load and tidal deformation fields, and (3) tangential displacement in terms of shear and torsional deformation fields. The relations greatly reduce the effort to compute the coseismic crustal deformation in a spherically symmetric earth.

Detecting torsion from massive electrodynamics

A new method of detecting torsion in the case of massive electrodynamics is proposed. The method is based on the study of spectral lines of hydrogen-like atoms placed in a torsion field, where the interaction energy between the torsion vector field Q and an electric dipole is given bye ∼ P · Q. All the methods designed so far have been based on spinning test particles interacting with magnetic fields in which the energy splitting is given bye ∼ S · B on a Stern-Gerlach type experiment. We arrive at an energy splitting of order ofe ∼ 10−21erg ∼ 10−9eV, which is within the frequency band of radio waves.

Critical Strings from Noncritical Dimensions: A Framework for Mirrors of Rigid Vacuaa

The role in string theory of manifolds of complex dimension $D_{crit} + 2(Q-1)$ and positive first Chern class is described. In order to be useful for string theory, the first Chern class of these spaces has to satisfy a certain relation. Because of this condition the cohomology groups of such manifolds show a specific structure. A group that is particularly important is described by $(D_{crit} + Q-1, Q-1)$--forms because it is this group which contains the higher dimensional counterpart of the holomorphic $(D_{crit}, 0)$--form that figures so prominently in Calabi--Yau manifolds. It is shown that the higher dimensional manifolds do not, in general, have a unique counterpart of this holomorphic form of rank $D_{crit}$. It is also shown that these manifolds lead, in general, to a number of additional modes beyond the standard Calabi--Yau spectrum. This suggests that not only the dilaton but also the other massless string modes, such as the antisymmetric torsion field, might be relevant for a possible stringy interpretation.

Kalusa-Klein approach in higher-dimensional theories of gravity with torsion

The Kaluza-Klein approach is investigated in the Einstein-Cartan-Sciama-Kibble (ECSK) theory and in a Brans-Dicke-type model with torsion. In particular, the authors focus their attention on the possible coupling of gauge fields and torsion, the principle of minimal coupling and the possible physical meaning of the fields which originate from the higher-dimensional torsion fields. Also, it is known that Brans-Dicke-type models with torsion have an extended conformal symmetry. They investigate the fate of this symmetry when going (via dimensional reduction) to four dimensions. They find that the vectorial part of the torsion acquires a nonvanishing value, thus breaking the symmetry of the original five-dimensional theory.

Torsion, compactification, and inflation.

We study possible implications of a ten-dimensional Einstein-Kalb-Ramond theory. It is speculated that the compactification process and inflationary process are closely related. It is also found that the torsion field tends to vanish after the inflation era is completed. This is in fact a general fea ture for the torsion Lagrangian. Hence the contribution from the Kalb-Ramond action is negligible effectively after the inflationary era. Some solutions to the field equations are also presented