My question is about the equivalence about having an event horizon and having a singularity.
In one side the implication looks pretty obvious:
- A singularity implies having an event horizon and therefore a black hole. Since the mass is compressed in a zero volume space, if you get close enough there will be a point where the escape velocity gets bigger than the speed of light so you will get a black hole by definition.
But what about the opposite? Does having an event horizon imply the existence of a singularity?
Could it be that you have a neutron star massive enough to reach a escape velocity equal to the speed of light but not strong enough to make the matter collapse?
Even if such star can not exist because the strong force collapses before reaching an event horizon, this doesn't mean an equivalence.
It just means that for some specific value of the maximum strong force this is not possible, but image now an imaginary exotic matter that has a way bigger strong force.
For such "science fiction" matter, it would be possible to reach an event horizon without collapsing to a singularity, right?
Or is it really an equivalence between this two concepts, such that no matter how resistant matter is to collapse it will never reach an event horizon?