Two Component Plasma in a Flamm's Paraboloid

TL;DR

This paper investigates the behavior of a two component plasma on a Flamm's paraboloid at a specific coupling constant, deriving methods to analyze correlation functions and structure, with results connecting to flat space and horizon effects.

Contribution

It introduces a method to analyze the TCP on a curved surface at coupling $b3=2$, including deriving the Green's function equation and addressing the problem's complexity.

Findings

Recovery of flat space plasma structure in the limit

Complexity prevents full analytical solution of correlation functions

Horizon causes charge collapse, affecting plasma structure

Abstract

The two component plasma (TCP) living in a Flamm's paraboloid is studied at a value of the coupling constant $\Gamma=2$ 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. So we present the 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 makes the structure of the plasma physically not well defined in the second case.