Introduction

In this chapter we shall deal with the problem of charged dust (pressureless matter) rotating steadily about an axis of symmetry. The rotation is steady in the sense that the motion is stationary, i.e. independent of time. The dust distribution has axial symmetry. The forces acting on a typical portion of the dust are centrifugal, gravitational, electric and magnetic.

The problem of rotating charged dust might not be astrophysically interesting, but it is nevertheless important because it pertains to a well defined physical situation in which the interplay of several forces can be studied, both in Newton–Maxwell theory and in general relativity, and a fruitful comparison can be made. As mentioned earlier, it is rare to find interior solutions for the Einstein or the Einstein–Maxwell equations. This problem has already yielded a number of exact interior solutions of the Einstein–Maxwell equations for a physically well defined energymomentum tensor. A great deal remains to be understoood about this problem and I believe that when a complete analysis of it is carried out much useful insight into the physical content of general relativity will be gained.

This chapter is based almost entirely on the author's work (Islam, 1977, 1978a, 1979, 1980, 1983a, b, c, 1984; see also Boachie and Islam, (1983), and Islam, Van den Bergh and Wils, 1984). After getting an introduction to this problem here the interested reader can refer to other work.