I’ve never been clear on what effect the kinetic energy of an object has in general relativity. Since energy and mass are interchangeable, an object’s KE should have some effect on its gravitational attraction. Yet, since velocity is relative, so is KE. Obviously, accelerating a proton to relativistic speeds cannot turn it into a miniature black hole no matter how much “mass” its kinetic energy has, so how does this work in GR?
This is exactly why current treatments of relativity do not rely on relativistic mass. Some popular treatments state incorrectly (or perhaps misleadingly) that as the velocity of an object increases, so does its mass; close to the speed of light the object gets so heavy it cannot be sped up beyond light speed. Students naturally tie this apparent increase in mass to the famous E=mc^2 equation, and the student ends up getting confused by connundrums like above.
The short answer is that an object’s KE has no effect on its gravitation. The long answer will have to come from a real physicist, since I’m as much an amateur as anyone on this board, and there’s a lot of misconception that needs to be untangled here. One place to start is Wikipedia.