Abstract
A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters Θμν. A deformed real metric is defined and its components are obtained. The noncommutativity correction to the red shift test of general relativity is calculated and it is concluded that the correction is too small to have observable effects. Implications of such a deformed Schwarzschild metric are also mentioned.
Highlights
The noncommutativity of space-time is a compelling option for the description of quantized space-time and its study is significant for answering the ultimate question about the quantum nature of space-time at very high energy scales
The twisting procedure insures the invariance of the algebra [xμ, xν] = i Θμν defining the noncommutativity of the space-time; it turned out that the dynamics of the noncommutative gravity coming from string theory [14] is much richer than the one in this version of deformed gravity [13]
In this paper, proceeding along the approach in Ref. [8], we present a deformed Schwarzschild solution in noncommutative gauge theory of gravitation
Summary
The noncommutativity of space-time is a compelling option for the description of quantized space-time and its study is significant for answering the ultimate question about the quantum nature of space-time at very high energy scales. [8] for example, a deformation of Einstein’s gravity was studied by gauging the noncommutative SO(4, 1) de Sitter group and using the Seiberg-Witten map [2, 10, 11] with subsequent contraction to the Poincare (inhomogeneous Lorentz) group ISO(3, 1) Another construction of noncommutative gravitational theory, based on the twisted Poincare algebra [12] was proposed in Ref. The deformed gauge potentials (tetrad fields) are obtained up to the second order of the expansion in Θ Based on these results, we define a deformed real metric and calculate its components in the case of a Schwarzschild solution.
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