An interview with Kip Thorne [1] (who recently won the Nobel Prize for physics [2]) on the science in the movie and a book about the science in the movie that he has written [3]
And a slightly breathless account of how working on developing the visuals for the film drove development of new code and led to new insights [4]
Someone admitted later than there was actually little or nothing "new" here - maybe a somewhat slicker and more cinematic visualization of expected effects around a black hole, but correct visualizations had already been done before. So the "papers" that came out of this were probably largely just a waste of ink.
I was quite disappointed in the movie myself. It claimed to be quite "sciency" but it was mostly just science fiction, IMO. I kind of liked the robots, though.
> maybe a somewhat slicker and more cinematic visualization of expected effects around a black hole, but correct visualizations had already been done before.
Yeah, if those visualizations are like most scientific visualizations, then they're likely piece of crap. They're likely some low-definition MATLAB frames or a half-assed Java applet that generates visuals comprehensible only by other astrophysicists with powerful imaginations.
There is a great value in taking such work and turning it into accurate, high-resolution renderings of cinematic quality. It makes it easier on imagination, it can reach and interest much wider audience. Hell, thanks to Interstellar's success, we can see newer works of fiction not screwing up their black hole visualizations the way pre-Interstellar fiction always did (even though "correct visualizations had already been done before").
"Science fiction" admits a wide variety of classifications. Interstellar is clearly science fiction so I don't like the grand parent's wording (I also don't like yours: what does 'science' have to do with being in the future?).
But trying to generously interpret the GP's and your comment, Interstellar was heavily promoted, and portrays itself as an accurate representation of a potential future, with correct physics and details rigorously fact checked, etc., a sub-category called "hard science ficiton." In reality there are numerous flaws in its physics, too many to count really. These aren't nits either--the most ridiculous physics-defying nonsense is in fact fundamental to the plot.
That's only the beginning of the problems. Interstellar was a terrible movie all-around, with plot holes you could fly a starship through. But it is why I think someone might say "It's not [the type of] science fiction [it claims to be]".
Science Fiction (sometimes "Speculative Fiction") asks "What if?" questions. One common formula for the question is, "What if ... in the future X?" but the "alternate history" sub-genre asks questions like "What if Germany had won in WW2?" and some asks about alternatives to the present.
When we tell stories that don't ask a "What if?" but are just set in space without asking too many awkward questions about how space works, like Star Wars, that's just called Space Opera.
In Hard SF it's inevitable that some of the specifics will be wrong. For example Greg Egan's "Schild's Ladder" relies on a completely fictional set of fundamental physics theorems concerning a "graph theory" for quantum state. In the story one element of this theorem is wrong, but of course in reality the whole theory is made up. What matters, as in most of fiction, is verisimilitude, not truth, but _plausibility_. The fictional "quantum graph theory" feels like something that theoretical fundamental physics might come up with, the proposed experiment to verify it has the sort of "If we're wrong we might all die, but we aren't wrong" vibe of many real experiments like the first test explosions of a nuclear bomb or the LHC.
Sometimes a piece of fiction might seem like bad SF but it actually wasn't intended as SF at all. Ishiguro's "Never Let Me Go" is like that. It's astonishing to me that this was put forward for SF awards. If you assume that whatever has been done/ will be done with these children makes sense, and are on board with the story on that basis, finding out what's really going on is a huge disappointment. But if you go into this knowing Ishiguro has no interest whatever in medical ethics, genetics, cloning etcetera, then you can embrace it as a metaphor about mortality (We are unable to truly accept our own inevitable death, it's explained to us but it never really sinks in, even when we see others die we always believe we're special) and it works fine.
Yes, Interstellar is a mess. It's a spectacle, I'll give it that, but well, "full of sound and fury, signifying nothing". It has at least 50% more Hans Zimmer than it needed, the plot has vast holes left in it for no apparent reason, and the larger story seems a bit aimless and underwhelming considering the setting.
Not all of the science needs to be fictional... presumably gravity will comtinue operating as it does today, tomorrow. Black holes will operate the same as well, unless the story gives it reason not to (black hole combobulators).
The "fiction" is only necessary for the stuff that doesn't exist today.
Part of the reason I love this movie is that Kip Thorne was a technical advisor. And as this paper shows, some new science resulted from the movie-making process.
Thorne's teaching abilities really get ignored. He used to TA a session of first year physics at Caltech every year and he was amazing when I had him. To teach accelerating frames of he clambered onto a table, saying "Define a frame of reference centered on the tip of my nose", then tossed it gently forward as he stepped off. It was a perfectly intuitive demonstration and he got us to laugh in the process.
I worked at Double Negative (the VFX company mentioned) during the production of Interstellar and had the pleasure of sitting in on an in-house lecture he did for the artists and R&D teams - incredibly good teaching skills. He was able to explain some very complex subjects in a 90 minute session.
For any non-scientists that are interested in this subject, he published a book about his work on the film that was quite interesting.
The abstract specifically says that no new physics resulted from the movie-making process:
"There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting."
I thought the script to Interstellar was lovely and profound, while that of Gravity (a movie with which it's often compared) was ridiculous and obviously written by someone who had no idea how physics worked.
Could a habitable planet exist in orbit around black hole? At least habitable as far as humans go? I didn't think there was another star that those planets had to feed them light and energy, and could they get enough light and energy, keep an atmosphere, and etc in orbit around a black hole?
Thank you. That made a lot more sense than I thought the movie did. At least in my layman's brain, it didn't make sense that you could get enough energy from a black hole and at the same time ... survive as a habitable planet, at least not one we'd recognize / could use for long.
There is absolutely nothing weird about a black hole in that sense. If you were to counter-factually replace our Sun with a black hole, absolutely nothing would change in terms of orbits, time dilation, spatial geometry, atmosphere, etc. It would suddenly get very dark and cold though! The black-hole-Sun wouldn't be putting off any visible light, except for the occasional bursts of energy as things impact the event horizon, bathing nearby objects in very deadly gamma rays.
So no, it wouldn't be very habitable. Everything would be cold, atmospheres frozen, and any surfaces regularly sterilized with lethal doses of gamma radiation. But you wouldn't observe any of the things you traditionally associate with black holes and which were used as plot points in Interstellar (warped space-time, funky time dilation, etc.).
> But you wouldn't observe ...(warped space-time, funky time dilation, etc.).
A survivor on Earth wouldn't notice it locally, but the presence of a very strong Einstein lens subtending ~ 100 sr on the sky would be unmistakeable.
Essentially, we'd get to observe many photons that would have crashed into the sun's surface (roughly each photon frequency having its own) travelling instead through the space between where that surface would be and very close to the event horizon. We would also see rocky and icy objects that crash into the sun (or are vapourized near some value of its surface) instead passing through a similar near region between each such object's former periastron and very close to the event horizon. Surviving Earthlings could readily test many general-relativistic predictions. The major observational problem would be that dim rocky/metallic/carbonaceous objects are already hard to see even when hot from direct illumination close to the sun, and comets would no longer throw off extremely visible tails.
> lethal doses of gamma radiation
I'm unsure this would be the case -- what would be the source? If it's matter being drawn into jets, why would those be oriented towards the Earth, when the sun's rotational axis does not point at Earth now? Also, what gets drawn into the jets other than matter in the relic fields and whatever bits of rock and ice happen to fall right in on an extremely lucky trajectory, the horizon area being so small? Do you expect a busy accretion structure? Why? And what suppresses visible light if the accretion structure is the source of gammas?
Accretion sources. I’m not saying it would happen often. But things do regularly plummet into the sun (comets, asteroids, gas from a comet tail) every few years and that would let off a burst of energy if it were a compact black hole instead. Bursts every few years or decades or centuries could be managed by people in shelters, but it would not be good for the broader ecosystem and th development of surface life.
> I'm not saying it would happen often. But things do regularly plummet into the sun
The flow of mass through the region near the black hole (and well inside the surface of our sun) is minuscule in comparison to that in binary systems where the BH's companion is a Roche lobe filling star.
The event horizon of the sun would be about 6km in diameter, assuming that we swap the sun for a black hole with little angular momentum. Within the volume 10x that diameter, one might expect violence in objects on intersecting geodesics; with a diameter 50x that of the event horizon, one can start using linearized GR safely; with a diameter 500x that of the event horizon, post-Newtonian corrrections start to become small.
The diameter of the sun is a bit more than 450 times larger than that (or about 232 000 times the diameter of the black hole).
While there are lots of objects that are known to pass within 10 solar radiuses of the sun's centre-of-mass, it's hard to be definitive about why the number falls off with decreasing radius since the sun does a good job of disintegrating comets, and non-comets are hard to observe that close to the sun. Collisions with our sun are rare, and most colliders are unlikely to have been on orbits that would take them into the central regions discussed in the paragraphs above.
Objects that do find themselves only a thousand or two km from the event horizon will certainly take a post-Newtonian long time to emerge from that region, according to a surviving human observer on Earth. I'm not an expert on accretion discs (most of what I know involves the inner edge) nor astrophysical black holes, but absent a binary companion, the disc will be pretty sparse in general, and in particular maybe a factor of ten beyond the ISCO it'd be so sparse that even if it's super-hot, it's not going to do much to an asteroid or comet.
Although it's just a guess (you'd have to solve it numerically, good luck) I think tidal dismantling of a comet or asteroid would not put the debris on to many intersecting geodesics, so you need to have the debris linger around the black hole long enough for a different comet or asteroid on a significantly different orbit to add its debris. The bits of the second would almost certainly collide violently with bits of the first. I think that the timing involved for such small objects is so tight that "it would[n't] happen often" is a bit of an understatement, on human scales. :-)
Moreover, the energy densities (assuming comets, say) are small, so even being optimistic about the amount and location of inverse Compton scattering, the gamma flux at 1 AU isn't especially worrying. You're not going to destroy the Earth. (Consider a direct conversion of a pair of comets each of 6 * 10^7 kg into gammas radiated isotropically in one second; now extend the duration and reduce the amount converted, both by a lot... Then for convenience, the solid angle of the Earth from the the collision point would be about 6*10^-9 sr).
> every few years
I think maybe every few million years is more plausible, frankly.
There'd be more to see with a young star, since those tend to get a lot more things crashing onto them.
> compact black hole
Is there a non-compact black hole? :-) :-) :-)
ETA : extremely luminous events proposed to be tidal disruption events (and found at https://tde.space/ ) are almost wholly from jets from the "pancake flambé" star being disrupted close a supermassive black hole (whose diameter is much much larger than the disrupted star's). The UV emissions are largely absorbed or compton-scattered by the disrupted star's remains on their way out, and so mostly what's seen by us (or anyone outside a few tens of thousands of Schwarzschild radiuses) is in the IR.
Let me reply to your first and final sentence out of order.
> [SMBH]s can actually have really small average densities.
No kidding.
Forgive me if you know all this next three paragraphs.
Christodoulou & Rovelli (2014) (Phys. Rev. D 91, 064046 doi:0.1103/PhysRevD.91.064046) [C&R 2014] show the volume of a spherically symmetrical non-eternal BH grows significantly with time (eqn 1 of ). "The bulk of the volume turns out to be due to a region in the vicinity of a constant value of the radial coordinate. That is: inside the hole there is a long spacelike 3d cylinder with slowly varying radius, which grows longer with time ... For instance, the black hole [Sag Astar] has radius ~ 10^6 km and age ~ 10^9 years. Inside it there is space for ~ 10^34 km^3, enough to fit a million Solar Systems!" (emphasis theirs)
[C&R 2014] provoked several other papers including Begntsson & Jakobsson (2015) (Mod. Phys. Lett. A, vol 30 no. 21, doi:10.1142/S0217732315501035) extends this to black holes with significant angular momentum, whose interior volumes are much smaller, with [C&R 2014]'s non-rotating volume being an upper limit. Their results are amplified and some implications thereof considered by Ong (2015) (J. Cosmol. Astropart. Phys 04(2015)003 doi:10.1088/1475-7516/2015/04/003), delightfully titled "Never Judge a Black Hole by Its Area", which examines several other types of BH too. In particular Ong clarifies that the [C&R 2014] results are likely robust for astrophysical near-extremals like Sag. Astar.
Of course, these are studies of theoretical BHs (and mainly considered statically), but I'm pretty confident that typical stress-energy around mature astrophysical black holes won't perturb dramatically away from that.
If you like, I can quickly check with an expert on astrophysical black holes for the case of a close binary where the mass flow from the donor star is very large, or for very young BHs that still have most of their progenitor star outside the horizon, but with agreement that such a system is far from what we would have when swapping our sun with a solar-mass BH.
> Yes.
It really depends on whose definition of compact object you take. I think the majority view -- bearing in mind this is an astrophysics classification rather than a relativity one and I am in the latter camp -- is that compact objects are characterized in one or more of three ways: (a) the presence of strong gravity in the vicinity, (b) hierarchical or direct formation from gravitationally collapsing matter, (c) the presence of matter densities much higher than that of planets.
A quick survey of observational astrophysical groups (Harvard, MIT-Kavli, Cambridge-Kavli, Toronto, KTH), fails to find one that both [i] unambiguously splits supermassive black holes out from compact objects (Harvard comes close), and [ii] restricts their work to small black holes that would meet (c) in the way you want (in fact, all of the groups I quickly looked at explicitly work on SMBHs as well as NSs, white dwarfs, and stellar BHs, but perhaps my selection is unfairly biased).
Astrophysicists and relativists can be surprisingly different beasts, but I think few of the former would insist on inserting "mean" into (c) and then exclude very massive BHs as not compact on that basis, especially given [C&R 2015] and subsequent results for spherically symmetrical non-rotating stellar-mass BHs.
It also seems like it would be a pretty strange exclusion since SMBHs -- however you define their mean density -- certainly exhibit relevant-to-astrophysicists general-relativistic phenomena near the horizon, and would still do so even if (for a sufficiently massive BH) the curvature just outside the horizon falls below the curvature we experience here on the surface of Earth.
Finally, I object if your definition of average density depends on any definition of internal volume, as that would depend on a choice of spatial section, which in turn depends on a choice of coordinates, and thus cannot be other than an observer-dependent quantity. In general, an observer can be found that makes a complete mess of one's expectation for such a quantity.
That movie has certain black-hole like properties I guess. For example when you are stuck in the theater watching it it feels like you've been there for 30 hours. But you come out and it has only been 3 hours.
And a slightly breathless account of how working on developing the visuals for the film drove development of new code and led to new insights [4]
Needless to say, I'm a fan of the film.. :D
[1] https://blogs.scientificamerican.com/observations/parsing-th...
[2] https://www.nobelprize.org/nobel_prizes/physics/laureates/20...
[3] https://en.m.wikipedia.org/wiki/The_Science_of_Interstellar
[4] https://www.wired.com/2014/10/astrophysics-interstellar-blac...
I was quite disappointed in the movie myself. It claimed to be quite "sciency" but it was mostly just science fiction, IMO. I kind of liked the robots, though.
Yeah, if those visualizations are like most scientific visualizations, then they're likely piece of crap. They're likely some low-definition MATLAB frames or a half-assed Java applet that generates visuals comprehensible only by other astrophysicists with powerful imaginations.
There is a great value in taking such work and turning it into accurate, high-resolution renderings of cinematic quality. It makes it easier on imagination, it can reach and interest much wider audience. Hell, thanks to Interstellar's success, we can see newer works of fiction not screwing up their black hole visualizations the way pre-Interstellar fiction always did (even though "correct visualizations had already been done before").
But trying to generously interpret the GP's and your comment, Interstellar was heavily promoted, and portrays itself as an accurate representation of a potential future, with correct physics and details rigorously fact checked, etc., a sub-category called "hard science ficiton." In reality there are numerous flaws in its physics, too many to count really. These aren't nits either--the most ridiculous physics-defying nonsense is in fact fundamental to the plot.
That's only the beginning of the problems. Interstellar was a terrible movie all-around, with plot holes you could fly a starship through. But it is why I think someone might say "It's not [the type of] science fiction [it claims to be]".
When we tell stories that don't ask a "What if?" but are just set in space without asking too many awkward questions about how space works, like Star Wars, that's just called Space Opera.
In Hard SF it's inevitable that some of the specifics will be wrong. For example Greg Egan's "Schild's Ladder" relies on a completely fictional set of fundamental physics theorems concerning a "graph theory" for quantum state. In the story one element of this theorem is wrong, but of course in reality the whole theory is made up. What matters, as in most of fiction, is verisimilitude, not truth, but _plausibility_. The fictional "quantum graph theory" feels like something that theoretical fundamental physics might come up with, the proposed experiment to verify it has the sort of "If we're wrong we might all die, but we aren't wrong" vibe of many real experiments like the first test explosions of a nuclear bomb or the LHC.
Sometimes a piece of fiction might seem like bad SF but it actually wasn't intended as SF at all. Ishiguro's "Never Let Me Go" is like that. It's astonishing to me that this was put forward for SF awards. If you assume that whatever has been done/ will be done with these children makes sense, and are on board with the story on that basis, finding out what's really going on is a huge disappointment. But if you go into this knowing Ishiguro has no interest whatever in medical ethics, genetics, cloning etcetera, then you can embrace it as a metaphor about mortality (We are unable to truly accept our own inevitable death, it's explained to us but it never really sinks in, even when we see others die we always believe we're special) and it works fine.
Yes, Interstellar is a mess. It's a spectacle, I'll give it that, but well, "full of sound and fury, signifying nothing". It has at least 50% more Hans Zimmer than it needed, the plot has vast holes left in it for no apparent reason, and the larger story seems a bit aimless and underwhelming considering the setting.
The "fiction" is only necessary for the stuff that doesn't exist today.
Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar
For any non-scientists that are interested in this subject, he published a book about his work on the film that was quite interesting.
"There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting."
I liked the visuals, but I think the script was a disaster, and the movie itself was only middling.
To each their own.
Could a habitable planet exist in orbit around black hole? At least habitable as far as humans go? I didn't think there was another star that those planets had to feed them light and energy, and could they get enough light and energy, keep an atmosphere, and etc in orbit around a black hole?
[1] https://www.popularmechanics.com/space/a19032/how-life-could...
So no, it wouldn't be very habitable. Everything would be cold, atmospheres frozen, and any surfaces regularly sterilized with lethal doses of gamma radiation. But you wouldn't observe any of the things you traditionally associate with black holes and which were used as plot points in Interstellar (warped space-time, funky time dilation, etc.).
A survivor on Earth wouldn't notice it locally, but the presence of a very strong Einstein lens subtending ~ 100 sr on the sky would be unmistakeable.
Essentially, we'd get to observe many photons that would have crashed into the sun's surface (roughly each photon frequency having its own) travelling instead through the space between where that surface would be and very close to the event horizon. We would also see rocky and icy objects that crash into the sun (or are vapourized near some value of its surface) instead passing through a similar near region between each such object's former periastron and very close to the event horizon. Surviving Earthlings could readily test many general-relativistic predictions. The major observational problem would be that dim rocky/metallic/carbonaceous objects are already hard to see even when hot from direct illumination close to the sun, and comets would no longer throw off extremely visible tails.
> lethal doses of gamma radiation
I'm unsure this would be the case -- what would be the source? If it's matter being drawn into jets, why would those be oriented towards the Earth, when the sun's rotational axis does not point at Earth now? Also, what gets drawn into the jets other than matter in the relic fields and whatever bits of rock and ice happen to fall right in on an extremely lucky trajectory, the horizon area being so small? Do you expect a busy accretion structure? Why? And what suppresses visible light if the accretion structure is the source of gammas?
The flow of mass through the region near the black hole (and well inside the surface of our sun) is minuscule in comparison to that in binary systems where the BH's companion is a Roche lobe filling star.
The event horizon of the sun would be about 6km in diameter, assuming that we swap the sun for a black hole with little angular momentum. Within the volume 10x that diameter, one might expect violence in objects on intersecting geodesics; with a diameter 50x that of the event horizon, one can start using linearized GR safely; with a diameter 500x that of the event horizon, post-Newtonian corrrections start to become small.
The diameter of the sun is a bit more than 450 times larger than that (or about 232 000 times the diameter of the black hole).
While there are lots of objects that are known to pass within 10 solar radiuses of the sun's centre-of-mass, it's hard to be definitive about why the number falls off with decreasing radius since the sun does a good job of disintegrating comets, and non-comets are hard to observe that close to the sun. Collisions with our sun are rare, and most colliders are unlikely to have been on orbits that would take them into the central regions discussed in the paragraphs above.
Objects that do find themselves only a thousand or two km from the event horizon will certainly take a post-Newtonian long time to emerge from that region, according to a surviving human observer on Earth. I'm not an expert on accretion discs (most of what I know involves the inner edge) nor astrophysical black holes, but absent a binary companion, the disc will be pretty sparse in general, and in particular maybe a factor of ten beyond the ISCO it'd be so sparse that even if it's super-hot, it's not going to do much to an asteroid or comet.
Although it's just a guess (you'd have to solve it numerically, good luck) I think tidal dismantling of a comet or asteroid would not put the debris on to many intersecting geodesics, so you need to have the debris linger around the black hole long enough for a different comet or asteroid on a significantly different orbit to add its debris. The bits of the second would almost certainly collide violently with bits of the first. I think that the timing involved for such small objects is so tight that "it would[n't] happen often" is a bit of an understatement, on human scales. :-)
Moreover, the energy densities (assuming comets, say) are small, so even being optimistic about the amount and location of inverse Compton scattering, the gamma flux at 1 AU isn't especially worrying. You're not going to destroy the Earth. (Consider a direct conversion of a pair of comets each of 6 * 10^7 kg into gammas radiated isotropically in one second; now extend the duration and reduce the amount converted, both by a lot... Then for convenience, the solid angle of the Earth from the the collision point would be about 6*10^-9 sr).
> every few years
I think maybe every few million years is more plausible, frankly.
There'd be more to see with a young star, since those tend to get a lot more things crashing onto them.
> compact black hole
Is there a non-compact black hole? :-) :-) :-)
ETA : extremely luminous events proposed to be tidal disruption events (and found at https://tde.space/ ) are almost wholly from jets from the "pancake flambé" star being disrupted close a supermassive black hole (whose diameter is much much larger than the disrupted star's). The UV emissions are largely absorbed or compton-scattered by the disrupted star's remains on their way out, and so mostly what's seen by us (or anyone outside a few tens of thousands of Schwarzschild radiuses) is in the IR.
Yes. The radius of a black hole increases linearly with mass. Supermassive black holes can actually have really small average densities.
> [SMBH]s can actually have really small average densities.
No kidding.
Forgive me if you know all this next three paragraphs.
Christodoulou & Rovelli (2014) (Phys. Rev. D 91, 064046 doi:0.1103/PhysRevD.91.064046) [C&R 2014] show the volume of a spherically symmetrical non-eternal BH grows significantly with time (eqn 1 of ). "The bulk of the volume turns out to be due to a region in the vicinity of a constant value of the radial coordinate. That is: inside the hole there is a long spacelike 3d cylinder with slowly varying radius, which grows longer with time ... For instance, the black hole [Sag Astar] has radius ~ 10^6 km and age ~ 10^9 years. Inside it there is space for ~ 10^34 km^3, enough to fit a million Solar Systems!" (emphasis theirs)
[C&R 2014] provoked several other papers including Begntsson & Jakobsson (2015) (Mod. Phys. Lett. A, vol 30 no. 21, doi:10.1142/S0217732315501035) extends this to black holes with significant angular momentum, whose interior volumes are much smaller, with [C&R 2014]'s non-rotating volume being an upper limit. Their results are amplified and some implications thereof considered by Ong (2015) (J. Cosmol. Astropart. Phys 04(2015)003 doi:10.1088/1475-7516/2015/04/003), delightfully titled "Never Judge a Black Hole by Its Area", which examines several other types of BH too. In particular Ong clarifies that the [C&R 2014] results are likely robust for astrophysical near-extremals like Sag. Astar.
Of course, these are studies of theoretical BHs (and mainly considered statically), but I'm pretty confident that typical stress-energy around mature astrophysical black holes won't perturb dramatically away from that.
If you like, I can quickly check with an expert on astrophysical black holes for the case of a close binary where the mass flow from the donor star is very large, or for very young BHs that still have most of their progenitor star outside the horizon, but with agreement that such a system is far from what we would have when swapping our sun with a solar-mass BH.
> Yes.
It really depends on whose definition of compact object you take. I think the majority view -- bearing in mind this is an astrophysics classification rather than a relativity one and I am in the latter camp -- is that compact objects are characterized in one or more of three ways: (a) the presence of strong gravity in the vicinity, (b) hierarchical or direct formation from gravitationally collapsing matter, (c) the presence of matter densities much higher than that of planets.
A quick survey of observational astrophysical groups (Harvard, MIT-Kavli, Cambridge-Kavli, Toronto, KTH), fails to find one that both [i] unambiguously splits supermassive black holes out from compact objects (Harvard comes close), and [ii] restricts their work to small black holes that would meet (c) in the way you want (in fact, all of the groups I quickly looked at explicitly work on SMBHs as well as NSs, white dwarfs, and stellar BHs, but perhaps my selection is unfairly biased).
Astrophysicists and relativists can be surprisingly different beasts, but I think few of the former would insist on inserting "mean" into (c) and then exclude very massive BHs as not compact on that basis, especially given [C&R 2015] and subsequent results for spherically symmetrical non-rotating stellar-mass BHs.
It also seems like it would be a pretty strange exclusion since SMBHs -- however you define their mean density -- certainly exhibit relevant-to-astrophysicists general-relativistic phenomena near the horizon, and would still do so even if (for a sufficiently massive BH) the curvature just outside the horizon falls below the curvature we experience here on the surface of Earth.
Finally, I object if your definition of average density depends on any definition of internal volume, as that would depend on a choice of spatial section, which in turn depends on a choice of coordinates, and thus cannot be other than an observer-dependent quantity. In general, an observer can be found that makes a complete mess of one's expectation for such a quantity.
(ETA: Ong makes exactly this point at the even more delightful discussion of his paper op. cit. at https://www.kth.se/profile/ycong/page/the-interior-volumes-o... )
(longer version of the one posted by evo_9)