Let's suppose a nutron star(because it directly collapses into black hole afterwards) , if we move with velocity near speed of light than in our frame neutron star will also move with velocity near speed of light in opposite direction So my question is , as it's relativistic mass will increase (because it is having velocity in our frame) will it collapse into black hole because of its own gravity? If yes then will it become black hole only for us (who is moving with velocity near $c $) or even for observer for which neutron start is at rest (I don't think it will happen)?
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1Does this answer your question? If a mass moves close to the speed of light, does it turn into a black hole? – John Rennie Aug 08 '23 at 07:35