I am skeptical about black holes, because they involve infinity. There is an opinion that they don't actually solve Einstein's equations.There is a lot of evidence for black holes, where they are defined:
A black hole is a region of spacetime from which gravity prevents anything, including light, from escaping.Belief in such objects dates back two centuries, and has little to do with relativity. If the mass is sufficiently concentrated, the gravity will be sufficiently strong to contain light.
Relativity teaches that the black hole has a boundary, called the event horizon or Schwarzschild radius, and a singularity at the middle. Furthermore, nothing inside the event horizon is observable to anyone on the outside. In particular, the singularity is not observable.
Physics has other infinities that are not observable. For example, the electron is widely assumed to be a point particle, in which case it has infinite density, and the charge concentration gives it infinite energy. These infinities are not observable, and the usual explanation is QED renormalization.
Getting back to my reader's comment, does a rational skeptic really need to believe in physical infinities that can never be observed? I say no. I believe in black holes right up to that event horizon. Discussion of what happens inside the event horizon is just metaphysical fluff that is outside the scope of science. You can say anything you want, and no one can ever prove you right or wrong. Not even in principle, according to relativity.
Likewise, there is no real reason for anyone to believe in the electron infinities. The infinity renormalization schemes may be the most convenient way to calculate electron scattering, but there could well be new physics on other scales to prevent the infinities, such as string theory. As long as the infinities are not observable and not truly required by the theory, there is no reason anyone has to believe in them.