A question about the theory of relativity

[IDOGAWACONAN]

Homework Statement

If I fly at the speed which is similar to the speed of light,and I am watching a still star,then because of the theory of relativity,the size of the star will change.If the size of the star turn to the size of a neutron star or a black hole,what will happen?Will I see a neutron star or a black hole?(My English is terrible,so I am sorry if you can't understand it well)

Homework Equations

The Attempt at a Solution

 

[Joe_UK]

Well I am not an expert on relativity in any way really, but the length contraction caused by the lorentz equations would only possibly alter the size of the object that you see, not what it actually "looks" like. A black star "looks" completely different to a star as light cannot escape its gravity, but you moving similar to the speed of light wouldn't make much difference I don't think.

 

[Filip Larsen]

Welcome to PF!

You may want to search your references for "Penrose-Terrell Rotation" and see if that will allow you to draw your own conclusion regarding your questions.

 

[IDOGAWACONAN]

But the mass of the star will grow.When it's beyond the Chandrasekhar'limit,should it become a black hole?

 

[Filip Larsen]

The relativistic mass of the star will grow, but not the rest mass. A star collapsing to a black hole is a very real, local, physical process and not an "observational" effect only, like relativistic mass. You can think of relativistic mass as a kind of a "transformation cheat" used in special relativity to make many other mechanical interactions appear Newtonian.

Others here may be able to offer you a better explanation.

 

[diazona]

The relativistic mass of the star will grow, but not the rest mass. A star collapsing to a black hole is a very real, local, physical process and not an "observational" effect only, like relativistic mass. You can think of relativistic mass as a kind of a "transformation cheat" used in special relativity to make many other mechanical interactions appear Newtonian.

Excellent points.

As far as I know, the conditions under which a star is able to become a black hole (i.e. Chandrasekhar limit) only apply when measured in the rest frame of the star. If you wanted to figure out the conditions required for a star to become a black hole in a reference frame in which the star is moving with some constant velocity, they would presumably be different. In particular, the critical density required to form the black hole would probably be higher. I haven't done the math, so I might be wrong, but it seems like there would be a logical inconsistency if a black hole (i.e. event horizon) existed in one distant inertial reference frame but not another.