That is great advice

Please add me to the physics list, thanks :)

Thanks Jerry for inviting me here and for the suggestions!

Penrose's work started off what came to called 'the golden age of general relativity', whence Penrose and other relativists (most notably Stephen Hawking) proved many general results about spacetime singularities. Happy birthday to Roger Penrose!

Combining tools of topology and some earlier work by Raychaudhuri and others, Penrose proved a powerful theorem to show that under reasonable physical assumptions, singularities were inevitable! Put differently, black holes are inevitably formed when a star collapses.

But no real star is perfectly symmetrical! Solving the exact differential equations for an arbitrarily-shaped star was impossible. One could at best study stars that were almost spherical. Penrose brought a new mathematical tool to bear on this problem - topology.

Before Penrose, the chief tool of general relativity was differential equations. They gave detailed predictions, but only for idealized situations. From solving differential equations, it had been known that if a perfectly spherical star collapsed, it would form a black hole.

Even though black hole solutions were known for a while, experts were not convinced they were real. They had good reason. Only for some very special cases could it be proven that the collapse of a star would form a black hole.