A rotating charged black hole. An exact, unique, and complete solution to the Einstein field equations in the exterior of such a black hole was found by Newman et al. (1965), although its connection to black holes was not realized until later (Shapiro and Teukolsky 1983, p. 338). In the coordinates of Boyer and Lindquist (1967), the exterior metric for a black hole with mass M, angular momentum J, and charge Q has the form

where




The corresponding electromagnetic field tensor, written as a two-form, is given by

(Misner et al. 1973, p. 877).