Is there a connection between exclusion principle and the speed of light? As far as I know exotic stars are composed of degenerate matter created by the balance between gravity and pressure of exclusion principle and as the mass of the star grows it goes into more compressed stages. At the same time with growing density of the star gravitational pull rises and so does its escape velocity. 
The thing I don't understand is why the point at which escape velocity reaches the speed of light is the same point as the one at which star becomes a black hole? Why there are no "black stars" which hadn't collapsed? Is there some connection between exclusion principle and the speed of light?
 A: Before the escape velocity reach the light speed, photons, which are produced on the star can escape from there and therefore star can shine (it does not have to be a visible light, though).
As you have pointed out, while the mass of the star increases the escape velocity rires too. At some point of time, this velocity, as calculated, is higher then the speed of light. And that means, that any single object which starts from the star surface needs to have starting velocity higher than the speed of light, which is impossible. Therefore, even photons can not escape from the star. That's why this star can not shine - it becomes "black".


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*Although photon has no rest mass, the gravitational field acts on it, that's another reason why photons can not leave such a strong gravitational field - their paths are curved way too much to escape.

*Although star can not produce light from it's own, there is theoretically predicted, that black holes irradiate - this is called Hawking's radiation, but it's mechanism is way different.

*Recently Hawking pointed out, that black holes may actually not exist...

