A matrix solution to Maxwell's equations in 2 + 1 dimensional curved space: Two examples

Abstract

In an effort that puts together a paper by Plebanski[1] with a matrix approach to the solution of Maxwell's equations in flat space by Moses[2], Maxwell's equations in 2 + 1 dimensional curved space are solved in two separate cases of the metric given by: a.Banados,Teitelboim and Zanelli[3] and b.Deser,Jackiw and 'tHooft[4] and Clement[5] to obtain the respective time - independent solutions;an extension to time - dependent solutions with the same point of view is also briefly indicated.