Teichmüller parameters for a multiple BTZ black hole spacetime

We investigate the Teichmuller parameters for a Euclidean multiple BTZ black hole spacetime. To induce a complex structure in the asymptotic boundary of such a spacetime, we consider the limit in which two black holes are at a large distance from each other. In this limit, we can approximately determine the period matrix ij (i.e., the Teichmuller parameters) for the spacetime boundary by using a pinching param- eter. The Teichmuller parameters are essential in describing the partition function for the boundary conformal field theory (CFT). We provide an interpretation of the partition function for the genus two extremal boundary CFT proposed by Gaiotto and Yin that it is relevant to double BTZ black hole spacetime.