"To a mathematician infinity is simply a number without limit, to a physicist it's a monstrosity" says Prof Michio Kaku (the one with the long silver hair) on the occasion of deriving infinity from black hole tensor equations when distance from the centre = 0. "It means that gravity is infinite at the centre of a black hole, that time stops, space has no sense. It means the collapse of everything we know about the physical universe. In the real world there is no such thing as infinity. Therefore there is a fundamental flaw in the formulation of Einstein's theory." (“Who’s afraid of a big black hole” BBC, Horizon, YouTube)
Yet surely it is just the very impossibility of infinity that enables and explains a central proposition of relativity – the impossibility of accelerating an object with mass to the speed of light. So it seems to have been a useful monstrosity.
For Daniele Faccio however, engineering mini black holes in his lab at Heriot – Watt, they are “where all the new physics is hiding”. (“Strip the cosmos: Black Holes”, YouTube)