  In this work, we consider a noncommutative (NC) massless scalar field coupled
to the classical nonrotational BTZ geometry. In a manner of the theories where
the gravity emerges from the underlying scalar field theory, we study the
effective action and the entropy derived from this noncommutative model. In
particular, the entropy is calculated by making use of the two different
approaches, the brick wall method and the heat kernel method designed for
spaces with conical singularity. We show that the UV divergent structures of
the entropy, obtained through these two different methods, agree with each
other. It is also shown that the same renormalization condition that removes
the infinities from the effective action can also be used to renormalize the
entanglement entropy for the same system. Besides, the interesting feature of
the NC model considered here is that it allows an interpretation in terms of an
equivalent system comprising of a commutative massive scalar field, but in a
modified geometry; that of the rotational BTZ black hole, the result that hints
at a duality between the commutative and noncommutative systems in the
background of a BTZ black hole.
