Scalar Field in Non-commutative Curved Space Time

We study the issue of complex scalar field theories in noncommutative curved space time (NCCST) with a new star-product. In this paper, the equation of motion of scalar field and the canonical energy-momentum tensor of scalar field in static noncommutative curved space time (SNCCST) will be found. The most important point is the assumption of the noncommutative parameter ($\theta$) be $x^{\m}$-independent, the noncommutativity with time attended (TNC) and the metric tensor is time independent.