Well, I don't think any physicist believes that an actual singularity exists in the center of a black hole in physical reality. The mathematics of GR actually do predict a singularity, but this is typically viewed as a limitation of the theory, not an actual physical object.

Instead, most physicists believe that a theory of quantum gravity (a theory which accounts for gravitational interactions between quantum particles in general) would slightly modify the equations of GR to arrive at a finite solution for the interior of the black hole. Of course, such a theory eludes us so far.