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We study modifications of the Schwarzschild solution within thenoncommutative gauge theory of gravity. In the present analysis, the deformedsolutions are obtained by solving the field equations perturbatively, up to thesecond order in the noncommutativity parameter $\Theta$, for both exterior andinterior solutions of the equations of motion for $e_\mu ^a \left(x\right)$.Remarkably, we find that this new noncommutive solution is analogous to theReissner-Nordstr\"om solution in the ordinary spacetime, in which the square ofelectric charge is replaced by the square of the noncommutativity parameter,but with opposite sign. This amounts to the noncommutative Schwarzschild radius$r_{NCS}$ becoming larger than the usual radius $r_S =2M$, instead of smalleras it happens to the Reissner-Nordstr\"om radius $r_{RN}$, implying that$r_{NCS}>r_{S} >r_{RN}$. An intuitive interpretation of this result ismentioned.

Analogy between the Schwarzschild solution in a noncommutative gauge theory and the Reissner-Nordstr\"om metric