The role of torsion and a scalar field $ϕ$ in gravitation, especially, in the presence of a Dirac field in the background of a particular class of the Riemann-Cartan geometry is considered here. Recently, a Lagrangian density with Lagrange multipliers has been proposed by the author which has been obtained by picking some particular terms from the SO(4,1) Pontryagin density, where the scalar field $ϕ$ causes the de Sitter connection to have the proper dimension of a gauge field. In this formalism, conserved axial vector matter current can be constructed, irrespective of any gauge choice, in any manifold having arbitrary background geometry. This current is not a Noether current.
In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus the responsible for the Lense-Thirring effect.
In the framework of spacetime with torsion and without curvature, the Dirac particle spin precession in the rotational system is studied. We write out the equivalent tetrad of rotating frame, in the polar coordinate system, through considering the relativistic factor, and the resultant equivalent metric is a flat Minkowski one. The obtained rotation-spin coupling formula can be applied to the high speed rotating case, which is consistent with the expectation.
We consider generalised pp-waves with purely axial torsion, which we previously showed to be new vacuum solutions of quadratic metric-affine gravity. Our analysis shows that classical pp-waves of parallel Ricci curvature should not be viewed on their own. They are a particular representation of a wider class of solutions, namely generalised pp-waves of parallel Ricci curvature. We compare our pp-waves with purely axial torsion to solutions of Einstein-Weyl theory, the classical model describing the interaction of gravitational and massless neutrino fields.
Some times ago, a Lagrangian density has been proposed by the author where only the local symmetries of the Lorentz subgroup of (A)ds group is retained. This formalism has been found to produce some results encompassing that of standard Einstein-Hilbert formalism. In the present article, the conserved axial vector matter currents, constructed in some earlier paper, have been found to be a result of Noether's theorem.
We construct new explicit vacuum solutions of quadratic metric-affine gravity. The approach of metric-affine gravity in using an independent affine connection produces a theory with 10+64 unknowns, which implies admitting torsion and possible nonmetricity. Our spacetimes are generalisations of classical pp-waves, four-dimensional Lorentzian spacetimes which admit a nonvanishing parallel spinor field. We generalize this definition to metric compatible spacetimes with pp-metric and purely axial torsion. It has been suggested that one can interpret that the axial component of torsion as the Hodge…
The teleparallel version of Lewis-Papapetrou space-time is investigated. For this space-time the true discussion of the geometric and physical properties is given. We show that the value of space-like torsion-axial vector does not depend on the choice of tetrad field. Consequently, the spin procession of the Dirac particle and the corresponding Hamiltonian do. The energy and momentum densities for such space-time are calculated. We show that when choosing two sets of tetrad fields the dependence and independence of the aforementioned quantities on the tetrad field depend on the Lorentz factor,…
We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto …
Dynamo action is shown to be induced from homogeneous non-minimal photon-torsion axial coupling in the quantum electrodynamics (QED) framework in Riemann flat spacetime contortion decays. The geometrical optics in Riemann-Cartan spacetime is considering and a plane wave expansion of the electromagnetic vector potential is considered leading to a set of the equations for the ray congruence. Since we are interested mainly on the torsion effects in this first report we just consider the Riemann-flat case composed of the Minkowskian spacetime with torsion. It is also shown that in torsionic de Sit…
In the framework of parallelism general relativity (PGR), the Dirac particle spin precession in the rotational gravitational field is studied. In terms of the equivalent tetrad of Kerr frame, we investigate the torsion axial-vector spin coupling in PGR. In the case of the weak field and slow rotation approximation, we obtain that the torsion axial-vector has the dipole-like structure, but different from the gravitomagnetic field, which indicates that the choice of the Kerr tetrad will influence on the physics interpretation of the axial-vector spin coupling.
The local Lorentz group is introduced in flat space-time, where the resulting Dirac and Yang-Mills equations are found, and then generalized to curved space-time: if matter is neglected, the Lorentz connection is identified with the contortion field, while, if matter is taken into account, both the Lorentz connection and the spinor axial current are illustrated to contribute to the torsion of space-time.
We attempt to build systematically the low-energy effective Lagrangian for the Einstein--Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order the fermion action with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a point-…
In this paper we consider torsion gravity in the case of the Dirac field, and by going into the rest frame we study what happens when a uniform precession as well as a phase are taken into account for the spinor field; we discuss how partially conserved axial-vector currents and torsion-spin attractive potentials justify negative Takabayashi angle and energy smaller than mass: because in this instance the module goes to zero exponentially fast then we obtain stable and localized matter distributions suitable to be regarded as a description of particles.
Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler-Bell-Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin 1/2 particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to expl…
We present a simple and natural way to derive the observed small, positive cosmological constant from the gravitational interaction of condensing fermions. In the Riemann-Cartan spacetime, torsion gives rise to the axial-axial four-fermion interaction term in the Dirac Lagrangian for spinor fields. We show that this nonlinear term acts like a cosmological constant if these fields have a nonzero vacuum expectation value. For quark fields in QCD, such a torsion-induced cosmological constant is positive and its energy scale is only about 8 times larger than the observed value. Adding leptons to t…
The interaction of the light with propagating axial torsion fields in the presence of an external magnetic field has been investigated. Axial torsion fields appearing in higher derivative quantum gravity possess two states, with spin one and zero, with different masses. The torsion field with spin-0 state is a ghost that can be removed if its mass is infinite. We investigate the possibility when the light mixes with the torsion fields resulting in the effect of vacuum birefringence and dichroism. The expressions for ellipticity and the rotation of light polarization axis depending on the coupl…
In the Einstein-Cartan space $U_4$, an axial vector torsion together with a scalar field connected to a local scale factor have been considered. By combining two particular terms from the SO(4,1) Pontryagin density and then modifying it in a SO(3,1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then under FRW-cosmological background, where the scalar field is connected to the source of gravitation, the Euler-Lagrange equations ultimately give the constancy of the gravitational constant together with only three kinds of energy densities representing mass, radiation and c…
This work contains the teleparallel version of the stationary axisymmetric solutions. We obtain the tetrad and the torsion fields representing these solutions. The tensor, vector and axial-vector parts of the torsion tensor are evaluated. It is found that the axial-vector has component only along $ρ$ and $z$ directions. The three possibilities of the axial vector depending on the metric function $B$ are discussed. The vector related with spin has also been evaluated and the corresponding extra Hamiltonian is furnished. Further, we use the teleparallel version of M$\ddot{o}$ller prescription to…
Starting from the multiplicative torsion approach of gravity and assuming a Killing vector to be proportional to the axial-vector matter current, here we derive Newton's law of gravity where the logarithm of the proportionality factor has been found to be the potential function.
We present a gauge theory of the conformal group in four spacetime dimensions with a non-vanishing torsion. In particular, we allow for a completely antisymmetric torsion, equivalent by Hodge duality to an axial vector whose presence does not spoil the conformal invariance of the theory, in contrast with claims of antecedent literature. The requirement of conformal invariance implies a differential condition (in particular, a Killing equation) on the aforementioned axial vector which leads to a Maxwell-like equation in a four-dimensional curved background. We also give some preliminary results…
Axial vector torsion in the Einstein-Cartan space $U_{4}$ is considered here. By picking a particular term from the SO(4,1) Pontryagin density and then modifying it in a SO(3,1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then considering torsion and torsion-less connection as independent fields, it has been found that $κ$ and $λ$ of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that $κ$ has been found to be linked with the topological Nieh-Yan density of $U_{4}$ space.
The possibility to distinguish Dirac from Majorana fermion by gravitational interaction and torsion coupling is discussed. The scattering of both Dirac and Majorana particles are the same in the spherically symmetric gravitational field up to the first order perturbation of the fermion-gravity interaction. The scattering behaviors of Dirac and Majorana fermion are also the same by axial vector torsion but different by vector torsion. We get the conclusion that the scattering by vector torsion field can distinguish the Dirac from Majorana neutrino.
A decade ago, a Lagrangian density has been proposed by the author where only the local symmetries of the Lorentz subgroup of (A)ds group is retained. This formalism has been found to produce some results encompassing that of standard Einstein-Hilbert formalism. In the present article, the conserved axial vector matter currents, constructed in some earlier paper, have been found to be a result of Noether's theorem. PACS: 04.20.Fy, 04.20.Cv, 11.40.-q Keywords: Torsion, Axial Current, Noether's Theorem
Inspired by the duality between gravity and defects in crystals, we study lattice field theory with torsion. The torsion is realized by a line defect of a lattice, namely a dislocation. As the first application, we perform the numerical computation for vector and axial currents induced by a screw dislocation. This current generation is called the chiral torsional effect. We also derive the analytical formula for the chiral torsional effect in the continuum limit.
In Riemann-Cartan spacetimes with torsion only its axial covector piece $A$ couples to massive Dirac fields. Using renormalization group arguments, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^\star A$, as has been claimed in a recent paper [PRD 55, 7580 (1997)].
We present the most general quadratic curvature action with torsion including infinite covariant derivatives and study its implications around the Minkowski background via the Palatini approach. Provided the torsion is solely given by the background axial field, the metric and torsion are shown to decouple, and both of them can be made ghost and singularity free for a fermionic source.
Spin-Polarised cylinders with and without axial magnetic fields are obtained as particular families of solutions of Einstein-Cartan gravity (EC).The first solution represents a spin-polarised cylinder in teleparallel gravity.The second solution is a magnetized solution representing a spin-polarised cylinder where the magnetic fields and spins are distributed along the infinite axis of the cylinder.Altough it seems that the first solution is less realist than the second it could be obtained by shielding the magnetic fields with a superconductor.The second solution is computed by taking into acc…
We study the tetrad formulation of Chern-Simons (CS) modified gravity, which adds a Pontryagin term to the Einstein-Hilbert action with a spacetime-dependent coupling field. We first verify that CS modified gravity leads to a theory with torsion, where this tensor is given by an antisymmetric product of the Riemann tensor and derivatives of the CS coupling. We then calculate the torsion in the far field of a weakly gravitating source within the parameterized post-Newtonian formalism, and specialize the result to Earth. We find that CS torsion vanishes only if the coupling vanishes, thus generi…
In this work we present the general differential geometry of a background in which the space-time has both torsion and curvature with internal symmetries being described by gauge fields, and that is equipped to couple spinorial matter fields having spin and energy as well as gauge currents: torsion will turn out to be equivalent to an axial-vector massive Proca field and because the spinor can be decomposed in its two chiral projections, torsion can be thought as the mediator that keeps spinors in stable configurations; we will justify this claim by studying some limiting situations. We will t…
In the context of the Einstein-Cartan-Dirac model, where the torsion of the space-time couples to the axial currents of the fermions, we study the effects of this quantum-gravitational interaction on a massless neutrino beam crossing through a medium with high number density of fermions at rest. We calculate the reflection amplitude and show that a specific fraction of the incident neutrinos reflects from this potential if the polarization of the medium is different from zero. We also discuss the order of magnitude of the fermionic number density in which this phenomenon is observable, in othe…
The four-fermion gravitational interaction is induced by torsion, and gets dominating on the Planck scale. The regular, axial-axial part of this interaction by itself does not stop the gravitational compression. However, the anomalous, vector-vector interaction results in a natural way both in big bounce and in inflation.
We construct Plebański-Demiański stationary and axisymmetric solutions with two expanding and double principal null directions in the framework of Metric-Affine gauge theory of gravity. Starting from the new improved form of the metric with vanishing cosmological constant recently achieved by Podolský and Vrátný, we extend this form in the presence of a cosmological constant and derive the conditions under which the physical sources of the torsion and nonmetricity tensors provide dynamical contributions preserving it in Weyl-Cartan geometry. The resulting black hole configurations are characte…
Poincaré gauge theories provide an approach to gravity based on the gauging of the Poincaré group, whose homogeneous part generates curvature while the translational sector gives rise to torsion. In this note we revisit the stability of the widely studied quadratic theories within this framework. We analyse the presence of ghosts without fixing any background by obtaining the relevant interactions in an exact post-Riemannian expansion. We find that the axial sector of the theory exhibits ghostly couplings to the graviton sector that render the theory unstable. Remarkably, imposing the absence …
We show that the presence of spacetime torsion, unlike any other non-trivial modifications of the Einstein gravity, does \emph{not} affect black hole entropy. The theory being diffeomorphism invariant leads to a Noether current and hence to a Noether charge, which can be associated to the heat content of the spacetime. Furthermore, the evolution of the spacetime inheriting torsion can be encoded in the difference between suitably defined surface and bulk degrees of freedom. For static spacetimes the surface and bulk degrees of freedom coincides, leading to holographic equipartition. In doing s…
We scrutinize the novel chiral transport phenomenon driven by spacetime torsion, namely the chiral torsional effect (CTE). We calculate the torsion-induced chiral currents with finite temperature, density and curvature in the most general torsional gravity theory. The conclusion complements the previous study on the CTE by including curvature and substantiates the relation between the CTE and the Nieh-Yan anomaly. We also analyze the response of chiral torsional current to an external electromagnetic field. The resulting topological current is analogous to that in the axion electrodynamics.
