Analogs of the double-Reissner-Nordström solution in magnetostatics and dilaton gravity: Mathematical description and basic physical properties

In this paper we consider a magnetic analog of the double-Reissner-Nordström solution and construct the corresponding magnetic potential $A_{\phi }$ in the explicit form. The behavior of the resulting solution under the Harrison transformation then naturally singles out the asymmetric black diholes—configurations composed of two nonextreme black holes possessing unequal masses, and charges equal in magnitude but opposite in sign—as its most general subclass for which equilibrium of the black-hole constituents can be achieved with the aid of the external magnetic (or electric) field. We also generalize the double-Reissner-Nordström solution to dilaton gravity with arbitrary dilaton coupling, yielding the four-dimensional double-Gibbons-Maeda spacetime. The study of some physical properties of the solutions obtained leads, in particular, to very simple formulas for the areas of the horizons and surface gravities.

Figure 1

Location of the black-hole constituents on the symmetry axis.