GRAVITATIONAL FIELD AND ELECTRIC FORCE LINES OF A NEW 2-SOLITON SOLUTION

Abstract

A new exact solution of the coupled Einstein–Maxwell equations is given and studied. It is found using the soliton method, adding one soliton to the Schwarzschild background. The solution is stationary and axial-symmetric, and has five physical parameters. The physical interpretation we give is that it describes a Kerr–Newman (KN) naked singularity linked by a "strut" to a charged black hole. Indeed, on the axis, between the two bodies an unavoidable anomaly region is present (gφφ < 0 and a conic singularity). The solution is stationary also in the case with zero total angular momentum. Finally, we give the force lines of the electrical field in a general case, and in the case in which the KN singularity has a much smaller mass than the nearby black hole; we also considered the behavior at different distances of the charge. In spite of the naive interpretation suggested by the mathematical construction of the solution, what we expected to be a "Schwarzschild" black hole appears to be charged and rotating; we interpret this fact as a parameter-mixing phenomenon.