Well, according to the encyclopedia survey of numerical relativity, one simulation technique does indeed involve
“excising” problematic regions inside event horizons, which is valid for the precise reason you mention: for all intents and purposes nothing happening inside the hole matters.
Yet it still seems like black holes are real enough, and their interiors are real places.
(Impossible to observe, but is it that mind-bending? One is not likely to observe the core of the sun, either.)
The video says it was created on something called Space Engine. Which claims scientific accuracy, but who knows?
We do observe the core of the Sun, via neutrinos and via helioseismic waves that pass through it. It’s a very murky sort of observation, but the tech is constantly improving. The closest equivalent with a black hole is observing the “ringdown” of a merger in gravitational waves, and even that is likely analyzed using models that don’t even consider the internal regions.
When Gargantua, the black hole featured in Interstellar, was rendered, Kip Thorne, executive producer and their their cosmological consultant was as surprised as anyone.
“Is that what a black hole looks like?”
“Well, we cranked the math you gave us through our imaging software and that’s what came out.”
“…Can I borrow that?”
The prediction of Hawking radiation allows for photons, among other things, to escape the other side of the event horizon but the effect is too subtle to be observed directly.
Right, and for stellar mass black holes the temperature of their Hawking radiation is below 3K, which means that they absorb more from the background radiation than they emit. It’s going to be a long long long time before the universe cools enough for large black holes to even begin to evaporate.
Here, for instance, is described an (obviously non-classical) idea where the interior of a black hole is crammed full of strings. (Thus no classical singularities.) Anyone familiar with that one?
Not really very long at all-- A mere trillion years or so would do it.
And the fact that a trillion years can be considered “mere” tells you something about just how long black holes last.
DPRK, nobody would be particularly surprised if, once we eventually get a working theory of quantum gravity, it predicted that there weren’t any singularities after all. But the String Model is far from being a working theory of quantum gravity. In the state it’s in right now, it’d be surprising if you couldn’t support any given hypothesis in the string model.
So black holes are by definition spherical?
Well, I’ve been assuming we’re talking about non-rotating ones, for simplicity’s sake, and those are spherical (though by theorem, not by definition). But rotating ones are more common, and those are a bit squashed in shape.
If they’re rotating, then they are ellipsoidal.
Physicist Brian Cox did a BBC special on the science of Doctor Who (the TV show).
There is a segment that I think answers the OPs question pretty well.
Watch the first clip for the background setup needed for the second clip which is an explanation for the OP: