The modern epoch of the understanding of black holes started in the 1950's,
partly with the introduction of additional coordinate systems in which metric
coefficients were everywhere defined.
The best known of these are the Kruskal
coordinates. Again, a change of coordinates is made and the coordinates are
valid except at r = 0.
In Kruskal coordinates,
lightlike geodesics are always represented by lines of slope +1 or -1.
The 45o lines represent the Schwarzschild radius. By looking at the
lightcones, we notice that the causality conditions described above are still
valid.
In 1963, Roy Kerr gave an exact solution for a rotating black hole. The
solution depended only on the mass and angular momentum of the black hole.
In 1968, Brandon Carter used the Kerr solution to show that
spacetime sort of "sticks" to a rotating black hole and rotates along with
the black hole - a process called frame dragging.
In the late `60's and early `70's, Brandon Carter, Werner Israel and Stephen
Hawking proved the "No Hair Theorem" which implies that the only properties
of a black hole are the mass, rotational rate, and charge.
In 1974, Stephen Hawking showed that it is possible to
associate a temperature and entropy with a black hole. He used quantum
mechanics to show that black holes can slowly radiate. The radiation is
named in his honor and is called Hawking radiation.
