Nonlinear gauge theory of Poincaré gravity

A Poincaré affine frame bundle (M) and its associated bundleÊ are established. Using the connection theory of fiber bundles, nonlinear connections on the bundleÊ are introduced as nonlinear gauge fields. An action and two sets of gauge field equations are presented.     

Effective Einsteinian gravity from Poincaré gauge field theory

The Poincaré gauge theory of gravity should apply in the microphysical domain. Here we investigate its implications for macrophysics. Weakly self double dual Riemann-Cartan curvature is assumed throughout. It is shown that the metrical background is then determined by Einstein's field equations with the Belinfante-Rosenfeld symmetrized energy-momentum current amended by spin squared terms. Moreover, the effective cosmological constant can be reconciled with the empirical data by absorbing the corresponding constant curvature part into the dynamical torsion of recently found exact solutions. Macroscopically this extra torsion remains undetectable.     

A magnetic-monopole-type solution in the Poincaré gauge field theory of gravity

In a microscopical theory of gravity the coupling of internal gauge degrees of freedom to those of space-time are studied. A magnetic-monopole-type solution for the coupledSO(3) Yang-Mills-Higgs system in a space-time with curvature and torsion is derived. The coupling constant of the Lorentz gauge bosons can be related directly to the (constant) Higgs field and to the cosmological constant which is induced by the quadratic curvature terms in the Lagrangian. This reveals a new interpretation of the parameters entering the general Lagrangian density of the Poincaré gauge field theory (PG).     

All torsion-free spherical vacuum solutions of the quadratic Poincaré gauge theory of gravity

We find all torsion-free, spherically symmetric, vacuum solutions to the theory of gravity recently proposed by Hehl, Ne'eman, Nitsch, and von der Heyde. There are three classes of solutions: (A) the Schwarzschild metrics with arbitrary mass,M, and arbitrary cosmological constant, ; (B) the Nariai-Bertotti metrics with arbitrary positive cosmological constant, ; and (C) the conformally flat metrics whose conformai factor is ²/ ² where is a function of only the time coordinate , and the radial coordinate, and satisfies the wave equation in these variables. Hence there is no Birkhoff theorem for this theory. In fact, solutions (C) include some asymptotically flat but nonstationary solutions. On the other hand, solutions (A) include a gravitational confinement potential, as was sought by Hehl et al., since when <0, the weak field limit of the Schwarzschild metric becomes a harmonic oscillator potential. We also discuss the relationship of this theory to the Eddington theory, the Lichnerowicz-Kilmister-Newman-Yang theory, the Nordström theory and the Einstein theory with a cosmological constant.     

Geometrical meaning of the Poincaré group gauge theory

We find a condition (6) under which a gauge theory of the Poincaré group is equivalent to the Einstein-Cartan theory of gravitation.     

On Poincaré gauge theory of gravity,its equations of motion,and Gravity Probe B

We discuss the structure of the Poincaré gauge theory of gravity (PG) that can be considered as the standard theory of gravity with torsion. We reconfirm that torsion, in the context of PG, couples only to the elementary particle spin and under no circumstances to the orbital angular momentum of test particles. We conclude that, unfortunately, the investigations of Mao et al. (2007) and March et al. (2011)—who claimed a coupling of torsion to orbital angular momentum, in particular in the context of the Gravity Probe B (GPB) experiment—do not yield any information on torsion.     

Yukawa-type potential besides newtonian potential in Poincaré gauge theory of gravitation

It is shown that the spin gauge fields with non-zero mass mediate the Yukawa-type interactions besides the short-range spin-spin interactions in the Poincaré gauge theory of gravitation. The interaction range of spin gauge fields is determined from the coupling constants. The coupling constant in front of the R(W) term is bounded by the requirement of a non-oscillating solution.     

Gravity as an internal Yang-Mills gauge field theory of the Poincaré group

In the framework of affine bundles we present gravity as an internal gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.     

A remark on the axisymmetric Chen et al. solution of the Poincaré gauge theory

Recently the search for exact solutions of the Poincaré gauge theory of gravity was highlighted by the independent discovery of two Kerr-type solutions with dynamic torsion. Some properties of these axisymmetric solutions, found by Chen et al. and by McCrea et al., are compared and put into proper perspective. In particular we show that the Chen et al., solution, in marked contrast to the more general McCrea et al. solution, belongs to a class of quadratic Poincaé gauge lagrangians of a highly degenerate nature, which admits non-unique solutions already in the limit of spherical symmetry.     

The phase structure of SU(2) × U(1)Y lattice gauge theory

Using analytic and Monte Carlo techniques, we determine the phase structure and nature of spontaneous symmetry breaking of the SU(2) × U(1)_Y electroweak gauge theory with fixed-length Higgs fields on a lattice. We find that it has two completely separated phases: (a) a disordered, symmetric phase and (b) a phase in which SU(2) × U(1)_Y is spontaneously broken to U(1)_em, which is realized in its deconfined Coulomb phase with massless photons. Exact analytic results and approximate series expansions are given for various special cases of the theory.     

Conserved charges of Kerr–Ads spacetime using Poincaré gauge version

The process of covariant conserved charge of gravitational theory, which is covariant under general coordinate and local Lorentz transformations, has been applied to many tetrad fields, which reproduce Kerr-Ads spacetime, to calculate their conserved charges. It is shown that this process gives an infinite value of the conserved charges for Kerr–Ads spacetime. Therefore, the method of “regularization through relocalization”, i.e., modification of the Lagrangian of the gravitational field through a total derivative, is used. This method gaves a finite and a consistent result of total energy and angular momentum for Kerr–Ads spacetime.