Final answer:
The Sun isn't a black hole despite having a Schwarzschild radius because its actual size is far larger than this theoretical limit and its core is not massive enough to cause a collapse into a black hole.
Step-by-step explanation:
The Schwarzschild radius, also known as the event horizon of a black hole, is the radius at which the escape velocity becomes equal to the speed of light. For an object to become a black hole, its mass must be within its Schwarzschild radius. The Sun, while having a theoretical Schwarzschild radius, isn't a black hole because its actual radius is much larger than this critical radius.
In contrast, an object like a neutron star, even though having a high distortion of space-time, has a radius that is also larger than its Schwarzschild radius, allowing objects to escape from its surface. For a star to collapse into a black hole after a supernova, it must have a stellar core that is more massive than three times the mass of the Sun. The Sun does not meet this criterion, which is why it does not collapse into a black hole.