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Black hole Nuetron star paradox 
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#1
May612, 12:24 PM

P: 2

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.



#2
May612, 02:47 PM

Sci Advisor
P: 6,106

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.



#3
May612, 04:41 PM

P: 311

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.



#4
May612, 06:10 PM

Sci Advisor
P: 2,470

Black hole Nuetron star paradox
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. 


#5
May712, 01:32 AM

P: 2

Thanks, Benjamin Ray 


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