I know what you’re thinking, “Not another question on Relativistic Mass.” I’ve spent the better part of a day going down the general and special relativity rabbit holes, and I can not find where this concept has been asked, so here goes.
If a very small, massive object was to be traveling close enough to light speed that it’s relativistic mass increased by several orders of magnitude, would it create gravitational effects relative to a stationary observer?
To be more specific, would an object with the resting mass of a paper clip be able to build up enough kinetic energy that it could bend spacetime, and pull something as massive as the Earth? The Earth being the stationary observer.
As a bonus question, would the near light speed object’s increase in relativistic mass cause gravitational lensing, observable from the stationary object?
A couple things I am aware of: I know the paperclip is only effected by its rest mass; I am purely interested in the frame of the stationary observer. The scientific community now uses “energy density” in place of “relativistic mass”, but I did not know how else to phrase the question. Similar questions have been asked, but every question I could find was asking about objects moving at the same relative speed, rather than one stationary and one moving.
Lastly, I am aware that, given the difference in velocity, the gravitational interaction between the two objects would only last fractions of a millisecond.
I am still a newer student of relativity, so there may be concepts I am unaware of or have misunderstood. I am still not 100% grasping how tensors fit in to this problem. Feel free to educate me as I am here to learn.