Why doesn't length contraction make a star a black hole in some frames?

[luxiaolei]

Hi,all, the problem is:

you and me observe a star, and the star moving with velocity V relative to me, and you are in the rest frame of the star.

Then in my frame of reference, I saw the star length contraction in the direction of its motion relative to me, hence its volume is smaller than its proper volume, and its mass is greater than its rest mass. Then I calculate its gravitational constant, say a.

And you calculate its gravitation constant as well, say you got a'

since i observe smaller volume and larger mass, so a>a'

if a just reach the limit that light can not escape from that star.

Then it will result in, In my frame, that star is a black hole, and in your frame, that star is Not.

however reality is invariant under lorentz transformation, so this can not be true, but where am I wrong??

Thanks in advance!

 

[Vanadium 50]

The answer is on the http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html" .

 

[luxiaolei]

The answer is on the http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html" .

@Vanadium; thanks for replay, however the link you gave only refer to the star become a black hole or not relative to an observer in its rest frame. My question is 2 different observer in two different frame of references, observes same star.
(btw, I don't quite understand under what condition one can form a black hole)
But thanks again.