Desitter Gauge Theory of Gravitation

Abstract

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

Deformed Reissner–Nordstrom solutions in noncommutative gravity

“…We review first the gauge theory of the de Sitter group SO(4,1) on a commutative 4-dimensional Minkowski space-time endowed with the spherically symmetric metric [21]:…”

“…So in this framework the spin connections are not independent fields, they are determined by the tetrads. Now, we consider a particular form of spherically symmetric gauge fields of the SO(4, 1) group given by the following Ansatz [21]: …”

“…We found these solutions using a spherically symmetric ansatz [21] and solving the corressponding Einstein equations. From the NC tetrad fieldsê a µ (x, Θ) we construct the NC Reissner-Nordstrom metricĝ µν (x, Θ).…”

Spinning black holes in a gauge theory of gravitation

“…They are identified with the four tetrad fields (the gauge field of translational generator), ωμ a5 (x)= eμ a (x), and the six antisymmetric spin connections ωμ ab (x)= -ωμ ba (x). The field strength tensor, associated with the gauge fields ωμ AB (x), which takes its values in the Lie algebra of the DS group (Lie algebravalued tensor) is [2]:…”

“…The gauge gravity for spinning black hole comes as an investigation of possible corrections in order to complete the landscape that exist for a static point-like source of the gravitational field [2], [6], [7] and for gauge gravity of Robertson -Walker analogous [3], [8]. Analytical procedures being conceived in GRTensor under Maple it is allowed to deal with different constant noncommutative parameters and to use several possible simplifications.…”