|MadSci Network: Physics|
Your point is a good one: if a given object was not a black hole in one reference frame, but was a black hole in another reference frame (moving very near the speed of light), there would be a serious discrepancy. The whole point of relativity is that the same phenomena can be explained in any arbitrary reference frame, so this would be a major dilemma.
But the solution is simple: mass doesn't increase with speed in the first place. That's a mis- representation that has been propagated in a lot of general-audience science writing, but it's flatly incorrect. In some cases, the equations *behave* as if the mass is increasing by a factor (gamma) related to the relative velocity, but in other cases they don't. It works for momentum; p=mv becomes p=gamma m v, but it doesn't work for Newton's second law; F=ma does NOT become F=gamma m a. (See this link for more details on all of this.)
And when it comes to gravitational mass, where mass is used to calculate gravitational forces, you don't get a gamma at all. No matter how fast I'm moving past you, I'm never going to look like a black hole.
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