The double noncommutative spacetime and the double complex symmetric gravitational theory

Abstract

In this paper,the double complex symmetric gravitational theory is established and the concrete expression of the static spherically symmetric double complex metrics is derived by introducing the double complex symmetric metric tensors. In this theory the Moffat's results are extended,the hyperbolic complex symmetric gravitational theory is naturally obtained and the famous Schwarzchild solution is contained as the special case. Moreover,in the linearized weak field approximation the hyperbolic complex symmetric gravitational theory can automatically free from the potential problem of negative energy ghost states. Furthermore，the double complex symmetric gravitational action in the double noncommutative spacetime can be constructed by extending the double complex coordinates to the double noncommutative relation satisfied and doubling the Moyal star product.