putongren said:
UltrafastPED, thanks for your response. Can you explain the fact that they are invariant geometric objects in spacetime would make it unable for particles to turn into black holes?
I'm really weak in the concept of frames of reference.
The so-called relativistic mass, which is "acquired" by a body moving faster and faster actually depends upon how fast you are moving, and in which direction. It is not a real increase in mass, it is simply an old fashioned way to write the kinetic energy of the object.
Thus it has nothing to do with the mass of the object if you were standing on it; it does not increase the local gravitational field.
"Frames of reference" are simply a way to describe a laboratory - it might be down the hall, or in orbit, or on a fast moving space ship. As long as it is not accelerating it makes a perfectly good inertial reference system, and if you describe some coordinates for it, a reference frame. There are an unlimited number of possible reference frames, some co-moving, some moving wrt each other, in all possible orientations and directions.
According to Special Relativity these are all equivalent for framing the laws of physics, and all physical experiments should yield equivalent results. But looking from one to another you might see things a bit differently ... this is where things often become confusing, and I refer you to the textbooks - I like Taylor & Wheeler's "Spacetime Physics", perfectly adequate for beginners, and requires nothing beyond algebra.
It is this "equivalent result" that dashes the possibility of a black hole from simply going faster - in some frames (co-moving frames - your spaceship is keeping up with the object) the object is standing still, and hence it is what it was all along. If you analyze its relativistic invariants - see Taylor & Wheeler - the physical attributes that are seen as identical between all reference frames - it will always appear as it does to the co-moving frame.
To get the invariants from observations in a moving frame there are some calculations, fairly simple, but you must only use observations from a single moving frame, and combine them using the correct relativistic formulas ... and that gives the particular invariant. In this case, the invariant, or rest mass.
putongren said:
If creating an artificial black hole the way I suggested is impossible, can you think of a way? Or is the only way is just to have an extremely massive star run of fuel and implode?
The Brookhaven hypothesis was not that they were moving fast, but that you could smash together two fast moving, heavy particles - gold nuclei, IIRC - then you obtain a quite high energy density in the center-of-mass frame. This density will be a relativistic invariant (because the rest frame invariants are easy to calculate!) ... so now the question becomes:
"What are the conditions for forming a micro black hole?"
And "Do micro black holes exist?"
Hawking, who came up with the black hole evaporation concept, calculated the life times for black holes of various sizes. It turns out that any that were created during the Big Bang - which had extreme conditions of the most extreme sort - would all have evaporated long ago; thus there can be no observation of them today, and there doesn't seem to be any astronomical evidence that they ever existed.
The usual way to form a black hole is for a massive star to die - when it's internal heat engine no longer produces enough pressure to prevent gravitational collapse. This only produces large black holes, and their coalescence in regions of high stellar density produces the super-massive black holes located at the centers of most galaxies ... and these super massive black holes are the only ones for which we have evidence.
Finally, if one could create mini black holes, nature should have done so long ago (Big Bang), and the extreme cosmic rays should be creating them today: they have much more energy than in any possible accelerator collision that can be managed today. And these extreme cosmic rays hit the Earth on a regular basis ... but so far, no micro black holes the natural way, so it seems likely that they are not possible to create this way.
