Noncommutativity and Quantum Structure of Spacetime
Noncommutative geometry is a candidate for describing physics at the Planck scale. Although there are various proposals to formulate gravity theories in the noncommutative framework, not many exact solutions of noncommutative gravity theories are known. In this talk we describe a possible noncommutative analogue of the BTZ black hole, which is consistent with the geometric structure of the problem. The spacetime Poisson brackets that we obtain indicate the possibility of the quantization of time. We briefly discuss the issues of symmetries and particle statistics in such a spacetime.