Effective mass of a rotating black hole in a magnetic field

The authors have given a definition of the effective mass of the Kerr black hole that incorporates a contribution due to rotation as well as agreeing with the Komar integral asymptotically. They apply this definition to compute the effective mass of a Kerr-Newman black hole and a Kerr black hole embedded in the magnetic field. It turns out that rotation and charge on the hole decrease the mass, being least at the horizon (going to zero for the extremal case M²=a²+Q²), while the magnetic field has an enhancing contribution. This gives rise to an interesting situation when the two cancel out each other's contributions yielding the effective mass M at finite r. The effective mass of the distorted Schwarzschild black hole continues to be M, up to the first approximation. Effective mass can be evaluated for all stationary spacetimes, whether they are empty or non-empty or asymptotically flat or non-flat, for instance, the Schwarzschild interior solution and the de Sitter universe.