Schwarzschild-de-Sitter Solution in Quantum Gauge Theory of Gravity

Abstract

We use the theory based on the gravitational gauge group G to obtain a spherical symmetric solution of the field equations for the gravitational potentials on a Minkowski space-time. The gauge group G is defined and then we introduce the gauge-covariant derivative Dµ. The strength tensor of the gravitational gauge field is also obtained and a gauge-invariant Lagrangian including the cosmological constant is constructed. A model whose gravitational gauge potentials A α µ (x) have spherical symmetry, depending only on the radial coordinate r is considered and an analytical solution of these equations, which induces the Schwarzschild-de-Sitter metric on the gauge group space, is then determined. All the calculations have been performed by GR Tensor II computer algebra package, running on the Maple V platform, along with several routines that we have written for our model.

Thermodynamical properties of a noncommutative anti–de Sitter–Einstein-Born-Infeld spacetime from gauge theory of gravity

“…To illustrate the previous formalism of gauge-gravity [29,[38][39][40] for classical spacetimes, we use it now to obtain a commutative anti-de Sitter-Einstein-Born-Infeld black hole solution. The starting point is a gravitational gauge field with spherical symmetry given by the following Ansatz e 0 µ = (A, 0, 0, 0),…”

Gauge Model Based on Group G × SU (2)

“…On the other hand, the gauge group for the gravitational interaction is the Poincaré group, [6,11,13] or the de Sitter group if we introduce the cosmological constant into the model. [22] A more elaborated model of superstring theory also includes the gauge theory and is considered as an adequate framework to describe all the four fundamental interactions (electromagnetic, weak, strong and gravitational).…”

“…where g is the gauge coupling constant of the gravitational interactions. The corresponding strength field tensor F µν (x) = F α µν (x)P α , with values in the Lie algebra of G, has the components [16,22]…”

“…[15], the quantum gauge theory of gravity imposes the relationship g 2 = 4πG between the gauge coupling constant g of the gravitational interactions and the Newton's gravitational constant G. Therefore, the Schwarzschild solution (23) has a dependence of the gauge coupling constant g, a result that is in accord with both quantum gauge theory of gravity and general relativity. Now, if we introduce the solution (22) in Eq. ( 20), then we obtain the following two possible solutions for the SU (2) gauge potential V (r):…”

“…corresponding to the sign '+' and respectively '−' from the solution (22). The solution V 1 (r) has a singularity in the origin r = 0, while the second one V 2 (r) is finite in the origin r = 0, but it has a singularity for r = −a.…”