How do black holes relate to physics?
The Schwarzschild solution to Einstein's General Theory of Relativity predicted the existence of what we call a black hole.
A black hole hasn't yet been observed directly but they have been detected indirectly. There are objects which are known to be both massive and small which can only be explained by a black hole.
Cygnus X-1 is an X-ray source which was discovered in 1964. It is estimated to be a small object with a mass of 14.8 times the mass of the Sun. The only accepted explanation is that it is a black hole. A black hole with this mass would have a radius of about 44km.
Observations of stars at the centre of ours, and other galaxies, show that some stars are orbiting rapidly around a small and very massive object. Calculations show that at the centre of our galaxy is a supermassive black hole with a mass of four million solar masses which is about the size of our solar system.
General Relativity predicts that there is a singularity at the centre of a black hole. This is a point of infinite curvature of space-time and infinite density and gravity. Mathematicians and physicists hate infinities. Where physics has predicted infinities in the past, new theories were developed to eliminate them. This means that General Relativities will need to be modified to explain what is inside a black hole.
The other problem for physics in the information paradox. If something falls into a black hole information about its state is lost. This is not allowed. Stephen Hawking is working on an idea that the information is somehow stored in the event horizon of the black hole.
So, we need new laws of physics to explain black holes fully.