Final answer:
The region of infinite density predicted by the Schwarzschild and Kerr solutions is known as a singularity, with the Schwarzschild radius acting as the event horizon of a black hole.
Step-by-step explanation:
The region of infinite density predicted by the Schwarzschild and Kerr solutions in general relativity is called a singularity. In the Schwarzschild solution, this singularity is a point, whereas in the Kerr solution, it takes the form of an infinitely thin ring. The Schwarzschild radius, also known as the event horizon, is the critical radius beyond which the gravitational pull of a mass becomes so strong that not even light can escape, effectively marking the boundary of a black hole.