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Noncommutative Quantum Gravity

We discuss the BRST and anti-BRST symmetries for perturbative quantum gravity in noncommutative spacetime. In this noncommutative perturbative quantum gravity the sum of the classical Lagrangian density with a gauge fixing term and a ghost term is shown to be invariant the noncommutative BRST and the noncommutative anti-BRST transformations. We analyse the gauge fixing term and the ghost term in both linear as well as non-linear gauges. We also discuss the unitarity evolution of the theory and analyse the violation of unitarity of by introduction of a bare mass term in the noncommutative BRST and the noncommutative anti-BRST transformations.