I believe that a black hole with only relativistic mass can exist, in other words, it only get's its mass from relativistic effects. If all matter in the black hole is photones, it has no heavy mass. Instead it gets the heavy mass: mass m(photones in black hole)/sqrt(1-v^2/c^2) - m(photones in black hole) I feel like to inform you that pluto, the non-planet, might be a such. A very big such. Most people would consider that nonsence, but if you would just put in the calcule it's speed, and you'll know what I'm saying. Pluto would have, in that case, around 40 solar masses. But then again, maybe that's impossible.
Whose speed? Pluto? Photons? You can't use the gamma factor if you're working with massless particles. They do not have the dynamics of massive particles. Which it isn't, else we'd all be orbiting Pluto and not the Sun. Isn't that obvious? Light things orbit big things and if Pluto were 40 solar masses it'd be much more massive than the Sun, obviously! Incoherent ignorant nonsense? Yes, it is similar to your random guesses. Your work isn't a 'theory', you haven't managed to provide one quantitative testable prediction.
So a relativistik black hole the size of whatever the neutronstar that our sun exploded into quite a long time ago. How big would it's black hole radius be, if there was only the gravitational mass m/sqrt(1-v^2/c^2) - m ? That's the question. The radius should be that of a humongous relativistic room bend in space. And since there is no great momentum in photons, what would the heavy mass be? Can one of those things be anywhere in the vincinity?
This is not the expression for the 'gravitational mass' of anything. An object moving relativistically will have kinetic energy \(\gamma mc^{2} - mc^{2} = mc^{2} (\gamma - 1)\) but this is nothing to do with its gravitational properties. That expression is a special relativity result and special relativity has no description of gravity within it. The energy contained within a region of space due to gravity (ie space-time curvature) is a non-trivial thing to work out. You have to sum over all the curvature in the space the object is in and this has the issue of frame dependence. If you put a mass into otherwise empty space you need to work out the energy variations due to the resultant space-time curvature. You aren't going to get that from special relativity. Instead you need to calculate some particular quantity (I forget what it is now, something to do with fundamental forms) over a sphere enclosing the object and then enlarge that sphere to be of infinite radius. That's needed in order to avoid any issues about frames. Google for things like Komar mass or Bondi mass. Further more, if you have the mass then you know the radius of the event horizon, as uncharged non-spinning black holes only have one parameter, their mass. No, for the same reason we know 'Planet X' or 'Nibiru' isn't going to turn up in 2012, we'd see the orbits of the known planets change due to gravitational interactions. A planet inside the solar system would affect all of the other planets in an obvious way. A neutron star wouldn't even need to be close to the solar system.
Yeah, allright maybe that was jumping to conclusions. I need to think clearly about this... hm...... Suppose that the black hole had no gravitational mass, just as a photon has none, what would've happened, can anyone answer me that?
A black hole with no mass is known as empty space. And while photons don't have rest mass they still contribute to the stress-energy tensor and thus can curve space-time.
