The risk of the TARDIS safeguard

Question

In the Christmas special "Voyage of the Damned" (Tenth Doctor), The Doctor explains the TARDIS is programmed to lock onto the nearest centre of gravity when it's adrift (in this case, Earth).

That's all great when the nearest centre of gravity is a planet. But what if it's a star or a black hole?

We know from "The Satan Pit" that:

The Time Lords invented black holes.

We also know from several other, older episodes that:

The Time Lords have been known to have a stellar manipulator which can influence the lifespan of a star.

But to the best of my knowledge, we don't know whether the TARDIS is capable of flying right through a star or a black hole. With all other type of spacecraft I'd guess the craft would perish, but the TARDIS is a bit odd.

The TARDIS has a forcefield, but I don't know whether that will hold in the extreme cases of crashing into a star or black hole (let's keep the relativistic effects of "crashing into" a black hole out of it for simplicity's sake).

The real question is of-course whether this safeguard could cause the TARDIS to destroy itself by crashing into a star, black hole or anything similar.

Any episodes confirming or disproving the TARDIS' abilities in this regard are welcome. Canon answers are preferred.

Answer 1

While we've never seen the TARDIS explicitly enter a black hole and return, there is good reason to believe that she's perfectly capable of doing so.

1: The Eye of Harmony

Though continuity is a little foggy on the Eye, it does seem clear that the Eye is a captive singularity used by the Time Lords as a power source. It's unclear whether the Eye is on Gallifrey, if there is one on every TARDIS, or somewhere in between; it is, however, clear that the Time Lords were perfectly capable of engineering black holes to meet their needs.

2: The TARDIS laughs at gravity

Gravity is simply the warping of spacetime by sufficient mass; the TARDIS bypasses any such concerns by traveling outside of spacetime itself, through the time vortex. However, even when it is in contact with the three-dimensional spacetime of the universe the TARDIS still displays the ability to ignore gravity at will. This is seen clearly when it casually pulled the Walker expedition's ship away from the black hole, or when it pulled the entire Earth across the universe at superluminal speed.

3: The TARDIS has survived worse

In Castrovalva, Peter Davidson's first story as the Doctor, the TARDIS was set an an automatic course towards "Event One" - AKA the Big Bang. This is quite literally the most energetic and gravitationally powerful event that is possible in our universe, and the Doctor was able, while suffering from post-regeneration amnesia, to pilot the TARDIS away from that event with little damage. It is hard to imagine the TARDIS being threatened by a measly little black hole after that.

And finally...

4: Stable orbits around black holes are perfectly feasible

Despite what The Doctor said about the Impossible Planet, there's nothing inherently impossible or dangerous about orbiting a black hole. Whether this position was dangerous or not would depend entirely upon how close the orbit was. It's quite likely, given the way the TARDIS achieved orbit in Voyage, that the ship is programmed to lock onto and orbit the nearest centre of gravity.