Relativistic mass was just a teaching tool (i.e. a white lie) for explaining why having mass prevents anything from ever reaching the speed of light. Einstein never liked the idea of relativistic mass, except that it helped to teach students who were used to the old Newtonian mechanics as a way to plug the relativistic mass into the old kinetic energy formulas. By replacing rest mass with relativistic mass in the kinetic energy formulas, you will find that kinetic energy shoots through the roof the closer you get to the speed of light. Otherwise, relativistic mass is fictitious. Rest mass is real, relativistic mass is just kinetic energy. So a black hole is just like any other object with mass, it can't be accelerated to the speed of light, only just near the speed of light.