Black hole Nuetron star paradox

[Ben Ray]

Assume there is a neutron star, it has a mass that is just short of what is required for it to collapse into a black hole. Now suppose there is an observer orbiting the neutron star. Assume that the neutron star and the observer are traveling at a very high velocity with respect to a second observer. To the second observer, the velocity of the neutron star is enough that its mass is increased beyond the critical limit at which it collapses into a black hole. Now, there is 2 observers looking at the same object, however the first observer sees a neutron star and the second sees a black hole. If the second observer throws an object into the black hole, it is irrecoverable once it crosses the event horizon, however the first observer seeing the neutron star could theoretically recover the object(not with current technology but it would be theoretically possible). I find this an interesting paradox assuming I'm not missing something that makes it impossible. Please give your thoughts on the subject.

 

[mathman]

Your original premise is incorrect. To become a black hole the neutron star would have to exceed its mass limit in its own coordinate system. Outside observers don't matter.

 

[cosmik debris]

The idea that mass increases with velocity is an old one. It is the kinetic energy that increases in the second observer's frame, and that form of kinetic energy does not increase the mass.

 

[K^2]

There is relativistic mass and rest mass. Former increases, later does not.

True, gravitational mass is equivalent to relativistic mass, and gravitational mass of a moving neutron star is higher, so I can see why you'd think it would collapse, but moving masses appear to repel, not unlike moving charges. The repulsion won't be strong enough to overcome the gravity, of course, but it's going to be just strong enough to prevent the collapse.

The main point is that General Relativity is postulated in such a way as to make sure that measurements in different coordinate systems are in agreement. (Not equivalent, just agree to within a transformation.) So when you notice that something appears to behave different in different coordinate systems, there is probably a relativistic effect that you forgot to take into a consideration.

 

[Ben Ray]

There is relativistic mass and rest mass. Former increases, later does not.

True, gravitational mass is equivalent to relativistic mass, and gravitational mass of a moving neutron star is higher, so I can see why you'd think it would collapse, but moving masses appear to repel, not unlike moving charges. The repulsion won't be strong enough to overcome the gravity, of course, but it's going to be just strong enough to prevent the collapse.

The main point is that General Relativity is postulated in such a way as to make sure that measurements in different coordinate systems are in agreement. (Not equivalent, just agree to within a transformation.) So when you notice that something appears to behave different in different coordinate systems, there is probably a relativistic effect that you forgot to take into a consideration.

Thank you for your explanation. I have not had any formal physics education so I tend to miss the technical aspects of these scenarios. But I think I understand what you are saying, basically the properties of an object with regards to its mass are an effect of the objects own intrinsic mass from its own relative perspective, or as you put it, its rest mass, so it will exhibit properties based on its rest mass even though an outside observer could see it as having much greater mass, it would still retain its rest mass properties. Correct? Would it be viewed by the outside observer as it was in a slower time frame but with more mass? Kindof like the faster an object moves from an outside perspective, the slower time seems to pass intrinsic to that object, so its like even though it would be seen as having greater mass and hence stronger gravity, so for instance it could emit 1 second of gravity from its perspective, based off of its rest mass, but the outside observer would observe 2 seconds of gravity during the same period of time. I know that is a crude way of saying it, but is that kindof the idea? I am planning on getting educated in physics when I have the money, but for now I am stuck watching Michio Kaku and Morgan Freeman while trying to put it together in my head.

Thanks,

Benjamin Ray