If they existed they could exist, but it's impossible for them to form.
I've asked many many physicists this very same question, and none could answer me (or I've gotten hand-wavy non answers). It's like no one wants to be the first to declare this well accepted thing as non-existing.
The black holes observed by astronomers are not actually black holes, but rather super massive neutron starts. It's not possible to distinguish between these two objects, astronomers assume a black holes based on size, not based on observed phenomena.