Two component plasma in a Flamm's paraboloid
The two component plasma (TCP) living in a Flamm's paraboloid is studied at a value of the coupling constant Γ = 2 for which an analytic expression for the grand canonical partition function is available. Two cases are considered: the plasma in the half surface with an insulating horizon and the plasma in the whole surface. The Green's function equation necessary to determine the n-particle truncated correlation functions is explicitly found. In both cases this proves too complicated to be solved analytically. Therefore we present a method of solution reducing the problem to finding the two linearly independent solutions of a linear homogeneous second order ordinary differential equation with polynomial coefficients of high degrees. In the flat limit one recovers the solution for the structure of the TCP in a plane in the first case but the collapse of opposite charges at the horizon means that the structure of the plasma is physically not well defined in the second case. © 2012 IOP Publishing Ltd and SISSA Medialab srl.