[Bryan See]

Well, except for Capella having several large planets within less than 0.1 AU, more than half of which is occupied by the star itself.

Any planet orbits at 0.1 AU close to that kind of star is considered hot. Hot Jupiters and hot Neptunes normally reside in that region. These are the ones discovered by Earth-based observations and Kepler space telescope. Think about the tenth transiting "Tatooine" exoplanet Kepler-453b.

[Phantom Hoover]

The singularity is a one-dimensional point which contains infinite mass in an infinitely small space, where gravity become infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate. The singularity is at the center of the black hole, beyond the event horizon.

I don't think physicists actually expect the singularity to have infinite mass, they expect weird physics to happen at it.

[watsisname]

The quantity that really becomes infinite at the singularity is the strength of the space-time curvature, AKA the tidal forces.  You can think of this as a consequence of having finite mass in zero volume -- in other words a point mass.  It's just like how the strength of electric field is infinite at a point charge.

All allowed paths through space-time terminate at the singularity in finite proper time, so this implies that all matter that falls into the hole is utterly destroyed there, essentially the mass becoming manifest only as gravitational field.  Think of the black hole as being completely empty.  It is made not of matter but of warped space-time.

[GhylTarvoke]

(Disclaimer: I study mathematics, not physics.) I agree with PH - I don't think the concepts of "infinity" and "point" exist in the real world. When physicists use those words to describe black holes, they're actually saying that our understanding of physics breaks down inside an event horizon.

[watsisname]

Our understanding of physics is actually okay even deep inside the horizon.  It only breaks down when you get really close to the singularity (like on subatomic scales), where quantum gravitational effects become important.  General relativity, as a classical theory, predicts infinite quantities there, but the reality probably just "approaches" infinity.

[Phantom Hoover]

Yeah, that's exactly what I was referring to.