We investigate the Teichm{u}ller 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 e
ach other. In this limit, we can approximately determine the period matrix (i.e., the Teichm{u}ller parameters) for the spacetime boundary by using a pinching parameter. The Teichm{u}ller 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.
We construct quantum field theory in an analogue curved spacetime in Bose-Einstein condensates based on the Bogoliubov-de Gennes equations, by exactly relating quantum particles in curved spacetime with Bogoliubov quasiparticle excitations in Bose-Ei
nstein condensates. Here, we derive a simple formula relating the two, which can be used to calculate the particle creation spectrum by solving the time-dependent Bogoliubov-de Gennes equations. Using our formulation, we numerically investigate particle creation in an analogue expanding Universe which can be expressed as Bogoliubov quasiparticles in an expanding Bose-Einstein condensate. We obtain its spectrum, which follows the thermal Maxwell-Boltzmann distribution, the temperature of which is experimentally attainable. Our derivation of the analogy is useful for general Bose-Einstein condensates and not limited to homogeneous ones, and our simulation is the first example of particle creations by solving the Bogoliubov-de Gennes equation in an inhomogeneous condensate.
