As for our local sun, you can tell him that a lot of people think that its center is composed of a superconducting superfluid surrounding a black hole. Some people think the Earth and many of the solar planets and some moons ( ie IO ) have black holes in them that were created during the big bang.
No, no, no! Our sun and the Earth do not have black holes inside of them! Any object can have a Schwarzschild radius. It is merely a ratio of the mass for a given volume... i.e. a density. If an object reaches a certain density, then the gravitational energy will cause it to collapse into a black hole. The sun and the Earth have a certain amount of mass. If you squeeze all of the mass of the sun, for instance, into a sphere of radius =3 kilometer, then our sun would gravitationally collapse into a black hole. The Earth's mass would have to be squeezed into a 9mm sphere in order to generate a black hole.
Trust me, it's not gonna happen anytime soon!