Research Article Field Equations and Radial Solutions in a Noncommutative Spherically Symmetric Geometry Aref Yazdani Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran Correspondence should be addressed to Aref Yazdani; a.yazdani@stu.umz.ac.ir Received 10 June 2014; Revised 6 October 2014; Accepted 19 October 2014; Published 11 November 2014 Academic Editor: Luis A. Anchordoqui Copyright © 2014 Aref Yazdani. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. he publication of this article was funded by SCOAP 3 . We study a noncommutative theory of gravity in the framework of torsional spacetime. his theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded difeomorphism invariant ield theory can be made equivalent to a teleparallel formulation of gravity. Field equations are derived in the framework of teleparallel gravity through Weitzenbock geometry. We solve these ield equations by considering a mass that is distributed spherically symmetrically in a stationary static spacetime in order to obtain a noncommutative line element. his new line element interestingly reairms the coherent state theory for a noncommutative Schwarzschild black hole. For the irst time, we derive the Newtonian gravitational force equation in the commutative relativity framework, and this result could provide the possibility to investigate examples in various topics in quantum and ordinary theories of gravity. 1. Introduction Field equations of gravity and radial solutions have been previously derived in noncommutative geometry [1–5]. he generalization of quantum ield theory by noncommutativity based on coordinate coherent state formalism also cures the short distance behavior of point-like structures [6– 13]. In this method, the particle mass , instead of being completely localized at a point, is dispensed throughout a region of linear size √ , substituting the position Dirac-delta function, describing point-like structures, with a Gaussian function, and describing smeared structures. In other words, we assume that the energy density of a static, spherically symmetric, particle-like gravitational source cannot be a delta function distribution and will be given by a Gaussian distribution of minimal width √  as follows:   () =  (4) 3/2 exp (−  2 4 ). (1) Furthermore, noncommutative gauge theory appears in string theory [14–18]: the boundary theory of an open string is noncommutative when it ends on D-bran with a constant B-ield or an Abelian gauge ield (particularly see [14]). herefore, closed string theories are expected to remain commutative as long as the background is geometric. Recent evidence has found a connection between nongeometry and closed string noncommutativity and even nonassociativity [19–21]; approaches using dual membrane theories [22] and matrix models [23, 24] arrive at the same conclusion. he ordinary quantum ield theory is unable to present an exact description of exotic efects of the inherent nonlocality of interactions, so we need a model to provide an efective description of many of the nonlocal efects in string theory within a simpler setting [25]. he model leads to the gauge theories of gravitation through an ordinary class of dimensional reductions of non- commutative electrodynamics on lat space, which then can be made equivalent to a formulation of teleparallel gravity, macroscopically describing general relativity. Moreover, this model is developed by the parallel theories of gravitation, giving a clear understanding of Einstein’s principle of absolute parallelism. It is deined by a nontrivial vierbein ield and formed by a linear connection. For carrying nonvanishing torsion, this connection is known as Wietzenb¨ ock geometry on spacetime. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2014, Article ID 349659, 9 pages http://dx.doi.org/10.1155/2014/349659