Static and stationary axially symmetric gravitational fields of bounded sources II. solutions obtainable from Weyl's class

Abstract

This paper shows that a new class of axially symmetric static electrovacuum/magnetovacuum solutions is obtainable from Weyl's class of static vacuum solutions. The new class contains an infinite set of asymptotically flat solutions (in closed form) each of which involves an arbitrary set (d, αi) of parameters. These parameters have to be interpreted as functions of massm, chargee, and higher electric/magnetic multipole momentsα i of the particle. The cased = 0,α i =0 leads to the Darmois solution and the cased = 0,α i ≠0 leads to the results of [1]. The case d≠=0, e=αi=0 leads to the Schwarzschild solution, the cased≠ 0,α i =0,e≠ 0 leads to the Reissner-Nordstrom solution. To get more general examples is a lengthy but straightforward exercise.