We present analytic force-free solutions modeling rotating stars and black holes immersed in the magnetic field of a thin disk that terminates at an inner radius. The solutions are exact in flat spacetime and approximate in Kerr spacetime. The compact object produces a conical jet whose properties carry information about its nature. For example, the jet from a star is surrounded by a current sheet, while that of a black hole is smooth. We compute an effective resistance in each case and compare to the canonical values used in circuit models of energy extraction. These solutions illustrate all of the basic features of the Blandford-Znajek process for energy extraction and jet formation in a clean setting.

• Received 1 September 2015

DOI:https://doi.org/10.1103/PhysRevD.93.044038