Three Partial Differential Equations in Curved Space and their Respective Solutions

Abstract

The partial differential equation in curved space whose solution is the electrostatic potential A0 is obtained following Whittaker (Proc. Roy. Soc. A 116, 720 (1927)) in: a. 2 + 1 dimensions with the metric gμν respectively given by i) S. Deser, R. Jackiw and G. ‘t Hooft, Ann. Phys. 152, 220 (1984) and G. Clement, Int. J. Theor. Phys. 24, 267 (1985) and ii) by M. Banados, C. Teitelboim and J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992); and in