Thirdly, the mass would produce so much curvature of the space-time metric that space would close up around the star, leaving us outside i.
These infinitely dense points in space will spaghettify anything that ventures too close. The gravitational force becomes so strong that nothing can escape it, even photons of light, hence the name "black" hole. One black hole is not like the others Supermassive black holes, predicted by Einstein's general theory of relativity, can have masses equal to billions of suns; these cosmic monsters likely hide at the centers of most galaxies.
Much like everything else about black holes, the gravitational singularity is a source of endless debate. Cambridge University Press. The result of this amount of matter squeezed into a small area results in a gravitational field so strong that nothing, not even light, can escape.
For example, if our sun was suddenly replaced by a black hole of similar mass, our planetary family would continue to orbit unperturbed, if much less warm and illuminated.