  We study a noncommutative theory of gravity in the framework of torsional
spacetime. This theory is based on a Lagrangian obtained by applying the
technique of dimensional reduction of noncommutative gauge theory and that the
yielded diffeomorphism invariant field 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
field equations by considering a mass that is distributed spherically
symmetrically in a stationary static spacetime in order to obtain a
noncommutative line element.This new line element interestingly reaffirms the
coherent state theory for a noncommutative Schwarzschild black hole. For the
first 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.
