Double Noncommutative Jackiw--Teitelboim Gravity Model in 1+1 Dimensions

We establish a double noncommutative Jackiw-Teitelboim (JT) gravity model in 1+1 dimensions, which extends the results of Cacciatori et al. (Class. Quant. Grav. 19(2002)4029) by means of the double complex function theory. Not only can the two cases of the cosmological constant λ>0 and λ<0 be discussed in a unified way, but also the double solutions of this model, i.e. the de Sitter (dS₂) and anti-de Sitter (AdS₂) fuzzy spheres, can be derived simultaneously. Hence the results of Cacciatori et al. are included as a special case.