Will our sun become black hole if it were moving fast enough?

[aaryan0077]

Okay, I know that sun won't become BH (Black Hole) , and I know about Chandrasekhar limit and Tolman-Oppenheimer-Volkoff limit, etc.
But my question is different.
We know,
M = m × √(1-v^2/c^2 ) . where m is rest mass. ( Don't know much latex, sorry )
So now we do know the rest mass of sun, so if it were moving fast its mass should increase, in accordance to equation so, at some velocity (definitely less than c, as at that velocity mass will be ∞) its mass will be that much as is required for black hole formation. Also the physical laws that are required for BH formation such as exclusion principle and chemical interaction etc. should hold good in that reference system too.
(As says the Principle of relativity)
Does at that point will our sun become BH.
And if it does; than for whom, for someone in reference system K' or for someone observing it from system K.
_{Please don't say, that sun can't (or won't) be moving at that speed, or ask me how will I get it to that speed
I am not taking about "how and when"
I am talking about "what if" case?}

 

[Fredrik]

See e.g. http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html for a partial answer. You may also want to do a search in this forum, because this question has been asked many times before.

By the way, most of us aren't big fans of the concept "relativistic mass", which we consider a useless concept. So when we say mass, we mean rest mass. There are lots of threads about that too.

 

[HallsofIvy]

Please note that "relativity" means just that. It does not make sense to talk about the sun, or any other body, moving "fast" without saying what frame of reference it is moving relative to. And whether it became a black hole or not must then be "as seen from that frame of reference". Theoretically there exist some frame of reference with respect to which the sun is moving at, say, 99.9999% the speed of light. If the sun were a "black hole" as seen from that frame of reference, since the Earth is moving with the sun, no change would be observed from the earth.

 

[Dale]

Also, mass is not the source of gravity in GR. The http://en.wikipedia.org/wiki/Stress-energy_tensor" is. It includes energy (masss) as one component, but the other components such as momentum ensure that a fast moving object has the same event horizon as a slow moving object of the same rest mass.