Poincare Gauge Theory Research Articles

THE TRAUTMAN PROBLEM OF INFORMATION TRANSFER, THE PROBLEM OF ENERGY TRANSFER BY GRAVITATIONAL WAVES AND THE STATUS OF THE POINCARE GAUGE THEORY OF GRAVITY

The transfer of information is one of the problems of the propagation of gravitational waves in connection with the prospect of the possible use of high-frequency gravitational waves for the creation of space communications. The requirements for information transfer are formulated in the form of the Trautman problem, which defines the conditions under which gravitational waves invariantly transfer the information contained in them. The second problem of the propagation of gravitational waves is the problem of energy-momentum transfer, which is not solved in general relativity, but can be solved in the punch of the gauge theory of gravity, for which the “criterion of strong localization of the energy-momentum of the gravitational field” is formulated. The features of two approaches in the Poincare gauge theory of gravity are discussed.

Decrease of the effective cosmological constant in the Poincare gauge theory of gravity with a scalar field

Cosmological consequences of the Poincare gauge theory of gravity are considered. An effective cosmological constant depending from the Dirac scalar field is introduced. It is proved that at the super-early Universe, the effective cosmological constant decreases exponentially from a huge value at the Big Bang to its extremely small value in the modern era, while the scale factor sharply increases and demonstrates inflationary behavior. This fact solves the well-known “cosmological constant problem” also in the Poincare gauge theory of gravity.

A Non-Geometrodynamic Quantum Yang–Mills Theory of Gravity Based on the Homogeneous Lorentz Group

In this paper, we present a non-geometrodynamic quantum Yang-Mills theory of gravity based on the homogeneous Lorentz group within the general framework of the Poincare gauge theories. The obstacles of this treatment are that first, on the one hand, the gauge group that is available for this purpose is non-compact. On the other hand, Yang-Mills theories with non-compact groups are rarely healthy, and only a few instances exist in the literature. Second, it is not clear how the direct observations of space-time waves can be explained when space-time has no dynamics. We show that the theory is unitary and is renormalizable to the one-loop perturbation. Although in our proposal, gravity is not associated with any elementary particle analogous to the graviton, classical helicity-two space-time waves are explained. Five essential exact solutions to the field equations of our proposal are presented as well. We also discuss a few experimental tests that can falsify the presented Yang-Mills theory.

Topological Methods in Geometric Foundations of Teleparallel Fused Quantum Gravity

We have studied the gravitation in the context of the noncommutative manifold M₄×Z₂ where Z₂ is not the two point space but corresponds to a direction-vector attached to a space-time point. A local field theory, noncommutative Yang - Mills fields is limited to obtain the return thatsuch a symmetry group differences are. Noncommutative gauge symmetry of space - time and theinternal symmetry of the mixer is a very natural and clear perception that the gravitational forcegauge a characteristic feature of the theory. The gauge fields of the dimensionally reduced noncommutativeYang-Mills theory map onto a Weitzenbӧck spacetime and a teleparallel theory of gravity arisesas the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartanspace-time characterized by connections with both nonvanishing torsion and curvature. This analysissuggests that noncommutative Yang-Mills theory naturally induces gravitation through a torsioned space-time. Thus as in the case of a noncommutative manifold whereZ₂ is a two-point space there appears to be aconnection between gravity and electroweak theory in this formalism this is achieved through therealization of chiral anomaly and torsion. It is noted to be that that Weitzenbӧck geometry thatEinstein's General Relativity with the teleparallel gravity equivalent, provoked by her some notablefeatures are. This show has been that the geometry torsioned space-time at which the the chiralanomaly inconsistencies in the torch made is. This show is that it naturally Weitzenbӧck geometryof the moves that the gravity of a teleparallel formula birth towards.

Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity

In the noncommutative gauge-theoretical formulation of Langman and Szabo, apparently it appears that the torsion generated there is a generalized one i.e. it may containvector, axial vector and tensor components. However, when we transcribe the noncommutative gauge theory in terms of the Maxwell gauge theory using the Seiberg-Wittencorrespondence, we have noted that upto the first order in the noncommutative parameter, this effectively can be taken to induce a change in chiral anomaly and hence theassociated torsion should be an axial vector one. The noncommutative gauge symmetriesgive a very natural and explicit realizations of the mixing of space-time and internal symmetries which is a characteristic feature of the conventional gauge theory of gravity. Thegauge fields of the dimensionally reduced noncommutative Yang-Mills theory map ontoaWeitzenbӧck space time and a teleparallel theory of gravity arises as the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartan space-timecharacterized by connections with both nonvanishing torsion and curvature. However, theteleparallelism equivalent of general relativity involves all the components of torsion. Thechiral anomaly in the Einstein-Cartan space U₄ is characterized by the topological invariants like Pontryagin density as well as the Nieh-Yan density when the latter term involvesthe length scale governed by the measure of noncommutativity of space points. It is shownthat we have discussed the equivalence of this formalism with noncommutative U(1) Yang Mills theory.

Galilean gauge theory from Poincare gauge theory

We provide an exact mapping between the Galilian gauge theory, recently advocated by us \cite{BMM1, BMM2, BM}, and the Poincare gauge theory. Applying this correspondence we provide a vielbein approach to the geometric formulation of Newton's gravity where no ansatze or additional conditions are required.

Cosmology in Poincaré gauge gravity with a pseudoscalar torsion

A cosmology of Poincare gauge theory is developed, where several properties of universe corresponding to the cosmological equations with the pseudoscalar torsion function are investigated. The cosmological constant is found to be the intrinsic torsion and curvature of the vacuum universe and is derived from the theory naturally rather than added artificially, i.e. the dark energy originates from geometry and includes the cosmological constant but differs from it. The cosmological constant puzzle, the coincidence and fine tuning problem are relieved naturally at the same time. By solving the cosmological equations, the analytic cosmological solution is obtained and can be compared with the LCDM model. In addition, the expressions of density parameters of the matter and the geometric dark energy are derived, and it is shown that the evolution of state equations for the geometric dark energy agrees with the current observational data. At last, the full equations of linear cosmological perturbations and the solutions are obtained.

General Poincare Gauge Theory Cosmology

For the quadratic Poincare gauge theory of gravity (PG) we consider the FLRW cosmolo- gies using an isotropic Bianchi representation. Here the considered cosmologies are for the general case: all the even and odd parity terms of the quadratic PG with their respective scalar and pseudoscalar parameters are allowed with no a priori restrictions on their values. With the aid of a manifestly homogeneous and isotropic representation, an effective La- grangian gives the second order dynamical equations for the gauge potentials. An equivalent set of first order equations for the observables is presented. The generic behavior of physical solutions is discussed and illustrated using numerical simulations.

Connection dynamics of a gauge theory of gravity coupled with matter

We study the coupling of the gravitational action, which is a linear combination of the Hilbert–Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory (PGT) with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing but under certain ansatz on the coupling parameters, which leads to a consistent connection dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a SU(2)-connection dynamical formalism of the theory can be obtained. Hence, the techniques of loop quantum gravity (LQG) can be employed to quantize this PGT with non-zero torsion. Moreover, the Barbero–Immirzi parameter in LQG acquires its physical meaning as the coupling parameter between the Hilbert–Palatini term and the quadratic torsion term in this gauge theory of gravity.

A study of plane torsion waves in the Poincaré gauge theory of gravity

The variational equations of the gravitational field in Riemann-Cartan space are derived in the external forms formalism using the method of Lagrange indefinite multipliers for the Poincare gauge theory of gravity with quadratic Lagrangians in the general form. The structure of the irreducible parts of torsion propagating in the form of plane waves in Riemann-Cartan spacetime is investigated.

Spinor coupling to the weak Poincare gauge theory of gravity in three dimensions

Minimal coupling of a Dirac field to gravity with the most general non-propagating torsion is considered in (1+2)-dimensions. The field equations are obtained from a lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of a quadratic spinor condensate plus coupling coefficients. Firstly we give circularly symmetric rotating exact solutions that collapse to $AdS_3$ geometry in the absence of the Dirac condensate. Secondly we investigate a BTZ-like solution.

Trivial symmetries in a 3D topological torsion model of gravity

We study the gauge symmetries in a Mielke-Baekler type model of gravity in 2+1 dimensions. The model is built in a Poincare gauge theory framework where localisation of Poincare symmetries lead to gravity. However, explicit construction of gauge symmetries in the model through a Hamiltonian procedure yields an apparently different set of symmetries, as has been noted by various authors. Here, we show that the two sets of symmetries are actually equivalent in a canonical sense, their difference being just a set of trivial symmetries.

Lagrangian generators of the Poincaré gauge symmetries

We have systematically computed the generators of the symmetries arising in Poincare gauge theory formulation of gravity, both in 2+1 and 3+1 dimensions. This was done using a completely Lagrangian approach. The results are expected to be valid in any dimensions, as seen through lifting the results of the 2+1 dimensional example into the 3+1 dimensional one.

Cartan’s Spiral Staircase in Physics and, in Particular, in the Gauge Theory of Dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.

Propagation equations for deformable test bodies with microstructure in extended theories of gravity

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory.

One-parameter teleparallel limit of Poincaré gravity

Poincare gauge theories that, in the absence of spinning matter, reduce to the one-parameter teleparallel theory are investigated with respect to their mathematical consistency and experimental viability. It is argued that the theories can be consistently coupled to the known standard model particles. Moreover, we establish the result that in the classical limit, such theories share a large class of solutions with general relativity, containing, among others, the four classical black hole solutions (Schwarzschild, Reisner-Nordstrom, Kerr and Kerr-Newman), as well as the complete class of Friedman-Robertson-Walker cosmological solutions, thereby extending older viability results that were restricted to the correct Newtonian limit and to the existence of the Schwarzschild solution.

Teleparallel limit of Poincaré gauge theory

We will address the question of the consistency of teleparallel theories in presence of spinning matter which has been a controversial subject of discussion over the last twenty years. We argue that the origin of the problem is not simply the symmetry or asymmetry of the stress-energy tensor of the matter fields, which has been recently analyzed by several authors, but arises at a more fundamental level, namely from the invariance of the field equatins under a frame change, a problem that has been discussed long time ago by Kopczynski in the framework of the teleparallel equivalent of general relativity. More importantly, we show that the problem is not only confined to the purely teleparallel theory but arises actually in every Poincare gauge theory that admits a teleparallel geometry in the absence of spinning sources, i.e. in its classical limit.

Massless Modes of Lorentz Gauge Fields in Poincare Gauge Theory of Gravity: The Case with + 2a/3= -2a/3= + 3a/2=0

The Lorentz gauge fields in Poincare gauge theory of gravity are considered in a linear approximation. Propagators of Lorentz gauge fields are examined to show the existence of massless modes of these fields. Our consideration is restricted to the case with the condition a + 2a/3 = β- 2a/3 = γ + 3a/2 = 0, where a, β, γ and a are parameters appearing in the gravitational Lagrangian. We find that four ghost-free theories have normal modes and that each of the theories has a mode with helicity-parity 1 + or 1-. We also demonstrate a duality of the approximated Poincare gauge theories in this case.

Conformal gauge theory of (2+1)-dimensional gravity

A conformal gauge theory of (2+1)-dimensional gravity is developed within a fiber-bundle structure. Here gravitational field variables are triads and Lorentz gauge potentials, both introduced under a nonlinear realization, which leads to a spontaneous break of symmetry. The most general gravitational Lagrangian density is given in a quadratic form of the conformal invariant gauge fields. We also obtain the Poincaré gauge theory in vacuum. In a weak-field limit the gravitational field equations for a static and spinless point-like source, are naturally reduced to the Newtonian case.

Double duality and hidden gauge freedom in the poincaré gauge theory of gravitation

We investigate the double duality ansatz of the Poincare gauge theory of gravitation. It is shown that many known exact solutions belong, as special cases, to larger families of solutions. These families of solutions include several arbitrary functions and can be generated by a transformation which is a Lorentzian rotation of the connection with fixed tetrad. Several new spherically symmetric and wavelike exact solution are presented.