Gauge Theory Of Gravity Research Articles

Gauge theory of gravitational interaction of macroscopic matter

Within the framework of the gauge theory of gravitation as a gauge theory of the local group P4 × D (Poincare and dilatation), the gravitational interaction of a continuous medium in Weil space, in which the Weil nonmetricity is due to localization of the dilatation group, and its source is the mass flux density of matter, i.e., its dilatational current, is considered. Using the variational principle, with the curvature scalar in Weil space as the geometric Lagrangian, dynamic equations of the theory are obtained, and the corresponding accurate solutions are found.

Prolongation structure and Backlund transformations of gravitational double duality equations

The authors derive two different Cartan differential ideals for the generalized double duality equations of gravitational gauge theories and Einstein's field equations with a cosmological constant. Using the spinor formalism for Riemann-Cartan spacetimes two different prolongations of these ideals are given. The prolongation structure will be used to construct a Backlund transformation for the coupled equations and using this general scheme the Kerr solution with dynamic torsion presented by McCrea (1988) and co-workers will be derived. Using this Kerr-de Sitter solution with dynamic torsion as a seed solution a new solution of the Poincare gauge field equations with an axial torsion part can be constructed. It turns out that this new solution leads to a vanishing Riemann-Cartan curvature and hence it is a solution of the teleparallelism theory of gravitation.

Topological pregauge-pregeometry

The pregauge-pregeometric action, i.e. the fundamental matter action whose quantum fluctuations give rise to the Einstein-Hilbert and the Yang-Mills actions, is investigated from the point of view of the topological field theory. We show that the scalar pregauge-pregeometric action is a topological invariant for appropriate choices of the internal gauge group. This model realizes the picture that the gravitational and internal gauge theory at the low energy scale is induced as the quantum effects of the topological field theory at the Planck scale.

An Extended New General Relativity as a Reduction of $\overline{\mbox{Poincar\'{e}}}$ Gauge Theory of Gravity

An extended new general relativity (E. N. G. R.) is formulated as a reduction of Poincaré gauge theory (P, G. T.) of gravity whose gauge group is the covering group of the Poincaré group. Fundamental fields in the theory are a Higgs-type field ψ k , and the translational gauge potential Akµ and a matter field φ a . The components ekµ of the duals of the vierbein fields are given by ekµ = ∇ *µ ψ k = ψ k,µ + Akµ . Internal translation and the field ψ k , which the conventional new general relativity lacks, play fundamental roles in E. N. G. R. as well as in P, G. T. The restrictions on the Lagrangian density, identities and differential conservation laws following from the ( local internal translation ⊗ global SL (2, C ) ) ⊗ general coordinate transformations are given. For the specific gravitational Lagrangian LT = -(1/3κ) tklmtklm + (1/3κ) vkvk + a3akak , the generators of internal \overlinePoincaré and general affine coordinate transformations for an isolated system are examined. The results are quite parallel to those in P, G. T., but the former is not trivial reductions of the latter. The following is worth noticing also in E. N. G. R.: For the case in which {ψ k , Akµ , φ a } with ψ k ≃ e (0) kµyµ + ψ (0) k is employed as the set of independent variables, (a) the generators of ( internal translation ⊗SL (2, C )) give the energy-momentum and the total angular momentum for an isolated system, and (b) the generators of general affine coordinate transformations vanish and are trivial.

Gravitation theory in the spacetimeR�S 3

A geometric formulation of the gravitation theory in the spacetime R × S 3 is given. A linear connection is introduced on the tangent bundle T(R × S 3 ) and then the connection coefficients and the Riemann curvature tensor are calculated. It is shown that their expressions differ from those of Carmeli and Malin [Found. Phys.17, 407 (1987)] by supplementary terms due to the noncommutativity of derivatives used on the spacetime R × S 3 . The Einstein field equations are written as usually and a comparison with other results is given. Finally, some observations about a possible gauge theory of gravitation in the spacetime R × S 3 are made.

An Extended New General Relativity as a Reduction of \overlinePoincare Gauge Theory of Gravity: Generators of Internal and Coordinate Transformations

An extended new general relativity (E. N. G. R.) is formulated as a reduction of Poincare gauge theory (P. G. T.) of gravity whose gauge group is the covering group of the Poincare group. Fundamental fields in the theory are a Higgs-type field <p', and the translational gauge potential A'p and a matter field ,pa. The components e'p of the duals of the vierbein fields are given by e'p =f7t<p'=<p',p+A'p. Internal translation and the field <p',. which the conventional new general relativity lacks, play fundamental roles in E. N. G. R. as well as in P. G. T. The restrictions on the Lagrangian density, identities and differential conservation laws following from the (local internal translation ® global SL(2, e)) ® general coordinate transformations are given. For the specific gravitational Lagrangian LT = - (1/3K)t klm tklm +(1/3K)v'v. + a3a'a., the generators of internal Poincare and general affine coordinate transformations for an isolated system are examined. The results are quite parallel to those in P. G. T., but the former is not trivial reductions of the latter. The following is worth noticing also in E. N. G. R.: For the case in which {<p',A'p, ,pa} with <p''''''e(O)'pY P + <p(0)' is employed as the set of il).dependent variables, (a) the generators of (internal translation ® SL(2, e)) give the energy-momentum and the total angular momentum for an isolated system, and (b) the generators of ~eneral affine coordinate transformations vanish and are trivial.

On spin and (quantum) gravity in 2 + 1 dimensions

We analyze the interaction of point particles in a gauge theory for gravity in 2 + 1 dimensions with particular emphasis on the effects of spin. It is shown that the known space-time solution for spinning sources in Einstein gravity exhibits torsion at the location of the sources. In the gauge theory of gravity, spin arises naturally as one of the charges of the Poincaré group and is not quantized for minkowskian (as opposed to euclidean) signature. Although the full action still looks topological, this property is spoiled by the identification of the coordinates of the particles with “internal” variables of the Poincaré group. We demonstrate the calculation of gravitational scattering amplitudes as an Aharonov-Bohm effect for a particle minimally coupled to the Poincaré field. The interpretation of the dreibein as a soldering form is abandoned and the results of Einstein's theory are recovered from the gauge theory without constructing a metric.

ISO(3,1�N) andOSp(N�4) supergravities

We advance anISO(3,1¦N) extended Poincare supergravity and anOSp(N¦4) de Sitter supergravity by using the supergauge action mechanisms of supergroups on the superspaces and by treating the gravitational parts of these two supergravities as the gauge theories of gravity, give a new matrix representation ofISO(3,1¦N) generators and a new one ofOSp(N¦4) ones, obtain the commutation and anticommutation relations ofiso(3, 1¦N) andosp(N¦4) superalgebras, construct the actions of these Supergravities and discuss some other problems. A particle multiplets method based on the supersymmetry transformation is used and the probable numbers of particles of different helicities in the two supergravities are given.

Group of Paths, Holonomy Groups and Nonintegrable Phase Factors in $\overline{\mathrm{Poincar \'{e}}}$ Gauge Theory of Gravity

In \overlinePoincar é gauge theory of gravity, which is based on the principal fiber bundle P over the spacetime having the covering group P0 of the proper orthochronous Poincaré group as the structure group, we examine the group of paths, holonomy groups and nonintegrable phase factors: (i) Considering the semi-direct product EP0def =[Path]⊗ P0 , where [Path] stands for the group of paths in a four-dimensional Minkowski space, we construct a linear representation of EP0 by defining the action of this group on the fiber bundle P . The parallel transports in P , the holonomy group and the nonintegrable phase factor are all described by this representation. (ii) Corresponding discussions are given for the affine frame bundle over the spacetime. Remarkable is the fact that the motions of a point and of a vector are both described by the nonintegrable phase factor. Discussions can be easily extended to the case in which \overlinePoincar é gauge and Yang-Mills gauge fields coexist. Nonintegrable phase factors are equally important in \overlinePoincar é gauge theory of gravity as well as in the Yang-Mills gauge theory.

Tachyonic torsion shock waves in Poincaré gauge theory

The requirement that the Poincaré gauge theory of gravitation has a correct Newtonian limit leads to tachyonic torsion shock waves. We show that the problems are due to those parts of the Levi-Civita connection which are vertical to the hypersurface in which the shock waves propagate. We argue that, as a consequence of certain symmetries of a (3 + 1)-decomposition of spacetime, the non-dynamical parts are Lagrange multipliers. We point out that this interpretation is not compatible with the minimal coupling procedure.

Cosmological constant and the dynamics of the Bianchi type I models with spin and torsion: A qualitative investigation

By including the cosmological term in the minimum quadratic (Poincare) gauge theory of gravity, the basic equation set for the homogeneous anisotropic Bianchi type I spinning-fluid models are obtained. For the linear equation of state, using methods of qualitative theory of dynamical systems, we make the complete qualitative analysis of properties of every possible solution of these equations, In particular, some solutions with regular behaviour of the metric and torsion are found.

Group of Paths, Holonomy Groups and Nonintegrable Phase Factors in \overlinePoincar e Gauge Theory of Gravity

grou~, we examin~ t~e group of pa.!~~i' holonomx groups and nonintegrable phase factors: (i) Conslderng the seml·dlrect product EPo=[Path]®P o, where [Path] stands for the group of paths in a four· dimensional Minkowski space, we construct a linear representation of EPo by defining the action:of this group on the fiber bundle P. The parallel transports in P, the holonomy group and the nonintegrable phase factor are all described by this representation. (ii) Correpsonding discussions are given for the affine frame bundle over the spacetime. Remarkable is the fact that the motions of a point and of a vector are both described by the nonintegrable phase factor. Discussions can be easily extended to the case in which Poincare gauge and Yang· Mills gauge fields coexist. Nonintegrable phase factors are equally important in Poincare gauge theory of gravity as well as in the Yang·Mills gauge theory.

New variables in gravity theories.

Considering Einstein's gravity theory as a gauge theory of the translation group ${T}^{4}$, we introduce new variables which simplify the field equations of general relativity considerably. In a 3+1 decomposition, we discuss positive-semidefinite gravitational energy and establish a relationship of our variables to Ashtekar's. We show that our method applies also to the Poincar\'e gauge theory of gravitation.

T4 gauge theory of gravity and new general relativity

We formulate a space-time translationT4 gauge theory of gravity on the Minkowski space-time with appropriate choice of the Lagrangian. By comparing the energy-momentum law of this theory with that of new general relativity constructed on the Weitzenbock space-time we find that in the classical limit the gauge potentials correspond to the parallel vector fields in the Weitzenbock space-time and the gauge field equation coincides with the field equation of gravity in new general relativity in the linearized version. Thus we conclude that in the classical limit theT4 gauge theory of gravity leads to the new general relativity.

PPN Metric and PPN torsion in the quadratic poincaré gauge theory of gravity

The post-newtonian approximation of the quadratic Poincaré gauge theory of gravity is studied. As a result of this investigation the modified PPN metric and PPN torsion is obtained. Post-newtonian equations of motion for different test bodies are analyzed and some restrictions on the parameters of the quadratic lagrangian are found.

Spaces with flat symmetry in poincar� gauge theory of gravity

A Taub space is considered in the Poincare gauge theory of gravity. It is shown that the torsion tensor has four nonvanishing components, which can be split into two independent pairs S010, S011, and S230, S231. The analysis of the gravitational field equations leads to the conclusion that in this case only a flat space-time with torsion is possible, and that its metric coefficients and the components of the torsion tensor are described by a wave equation.

General equations of motion for test particles in space-time with torsion

The momentum and spin equations of motion for test particles possessing different spins in space-time with torsion are derived from the most general functional form of ℒ M . The same kinds of equations in general relativity and in Kibble's gauge theory of gravitation are special cases of our equations.

Shock waves in the poincaré gauge theory of gravitation

Algebraic relations for shock waves in the Poincaré gauge theory (PGT) are deduced and investigated. Several conditions on the coupling constants are derived of a Lagrangian quadratic in torsion and curvature. One of these conditions is in conflict with the so-called “viable set”, which seems to be necessary in order to get the correct Newtonian limit.

Metric-torsion gauge theory of continuum line defects

Basic points underlying the geometrization of continuum defects are discussed. Following an analogy with gravitational gauge theories, a metric-torsion gauge theory of continuum line defects is developed. Gauge-invariant action integrals are constructed and their equations of motion are obtained. A Lagrangian containing curvature terms up to second power has constant-curvature solutions. In linear approximation these solutions correspond to line defects which form closed loops separately.

A gauge theory of gravitation based on a specific Lagrangian

The paper is devoted to the presentation of a specific Lagrangian for the Poincare gauge theory of gravity. Interesting and useful properties of the gauge theory of gravitation based on this Lagrangian are briefly outlined.