Black holes are common phenomenon within our universe. Their centers are referred to as singularities, where mathematics and models are said to breakdown. This is because quantities of infinite are returned within the mathematical equations. But does this necessarily mean that in reality blackholes exhibit the qualities put forward by the math? The answer most likely is no, for several reasons. Einstein’s Theory of Relativity states that the mass and energy of any particle are equivalent: E=mc2. Blackholes are born from dying stars, stars which are finite in mass. Given the 2nd Law of Thermodynamics where energy is neither created nor destroyed, it would be unusual for a finite star with a finite density and mass to later become a blackhole with an infinite density and mass.
So where do the infinities come from? We have to remember that mathematical and physical models of the universe are just that: models. They are not the universe or actual reality. In 1936 Einstein wrote the essay Physics and Reality, in which he grapples with the question of how to consider and contextualize the “real external world.” He would often debate with fellow Physicist Einstein also wrote in his writings on Relativity that a coordinate-system is always used in measuring anything in the universe, and that the coordinate system is how we measure phenomenon. Coordinate systems are really just the tools scientist use to measure space and time.
So as a physicist, Einstein talked at length about how all motion that is measured is measured in relation to a coordinate system. Sometimes in mathematics singularities occur with certain values in functions. Sometimes coordinate singularities occur where a singularity is said to occur in one coordinate frame but isn’t seen when viewed from a different coordinate frame. The singularities that occur in Physics in the relation to space, time, and density at the centers of Black Holes and at the beginning of our Universe before the occurrence of the Big Bang are not being disputed. What is being said is that these singularities are only coordinate singularities and in the real universe in which we exist. They exist within the equations used by physicists, but like other singularities, their existence is only within the equations and not the actual universe itself. While equations say the Universe at the time of the Big Bang was smaller than even a grapefruit and had an infinite density, the actual size and density may well have not been infinite small or infinitely dense.
Just as Black Holes have real size and real density, so to should the universe during it’s time before the Big Bang. Popular Astrophysicists nowadays do not often differentiate between the models of the universe, space, and time, essentially the coordinate-system which we use as part of our observations of the universe, and the actual real universe in which we live. It’s not up to me to change their minds or their methods of explaining Physics. It’s enough to know that some physicists think about these differences and these aspects of reality and science and others do not.