Two component plasma in a Flamm’s paraboloid

Abstract

The two component plasma (TCP) living in a Flamm’s paraboloid is studied at a value of the couplingconstant Γ = 2 for which an analytic expression for the grand canonical partition function is available. Twocases are considered: the plasma in the half surface with an insulating horizon and theplasma in the whole surface. The Green’s function equation necessary to determine then-particle truncated correlation functions is explicitly found. In both cases this proves toocomplicated to be solved analytically. Therefore we present a method of solution reducingthe problem to finding the two linearly independent solutions of a linear homogeneoussecond order ordinary differential equation with polynomial coefficients of highdegrees. In the flat limit one recovers the solution for the structure of the TCPin a plane in the first case but the collapse of opposite charges at the horizonmeans that the structure of the plasma is physically not well defined in the secondcase.