Does relativistic mass affect space time in the same way as rest mass?  

To my understanding, (as I am not an actual physicist, but simply a citizen scientist) relativistic mass is really the measure of an object's energy.  It is not the same as rest mass, which is the definition of mass that a layperson would be familiar with (how much matter an object is composed of).  However, does a change in relativistic mass amount to the same magnitude of gravitational variation as an equivalent change in rest mass?