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What breaks my brain is that if the Sun were compressed into a black hole, its Schwarzschild radius would be less than 2 miles, but the biggest black hole we kn

What breaks my brain is that if the Sun were compressed into a black hole, its Schwarzschild radius would be less than 2 miles, but the biggest black hole we know about so far, Phoenix A, has a Schwarzschild radius of almost 2,000 AU. The radius of Neptune's orbit is "only" about 30 AU, so Phoenix A's Schwarzschild radius is almost 70 times longer. Illustration here: https://upload.wikimedia.org/wikipedia/commons/d/d3/Phoenix_A_compared_to_Ton_618_and_the_Orbit_of_Neptune.jpg https://upload.wikimedia.org/wikipedia/commons/d/d3/Phoenix_... . And of course, volume increases cubically with radius. I have a hard time contemplating that you could make a black hole that ridiculously ginormous even if you crammed the entire universe into one black hole, and yet Phoenix A is far from the only supermassive black hole out there.

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pdonis 3y ago
> volume increases cubically with radius This intuition does not work in curved spacetime, particularly not for black holes. Black holes do not even have a well-defined volume at all.
- denton-scratch 3y ago
  Well, a sphere with some Schwarzschild radius has a volume. I was uncomfortable with the conflation of the "volume of a black hole" with the volume of that sphere.
  - pdonis 3y ago
    > a sphere with some Schwarzschild radius ...is not what a black hole is. It is not even "something kinda sorta like a sphere with some Schwarzschild radius". It is nothing like any ordinary object you're used to. It doesn't have a well-defined "radius" any more than it has a well-defined volume; the Schwarzschild "radius" is actually sqrt(A / 4 pi), where A is the surface area of the hole's horizon (which in turn is calculated from the mass of the hole).
    - mr_toad 3y ago
      It’s still useful to talk about the density of matter inside a volume that is equivalent to the volume defined by the sphere with a Schwartzchild radius because it sets an upper limit on the density that a given mass could be before an event horizon would form. This is relevant to the discussion at hand because for these very large black holes that density is not very high and conceivably a gas cloud of sufficient mass could contract to that density and have an event horizon form without collapsing into Stars.
      - pdonis 3y ago
        > It’s still useful to talk about the density of matter inside a volume that is equivalent to the volume defined by the sphere with a Schwartzchild radius because it sets an upper limit on the density that a given mass could be before an event horizon would form. No, it doesn't. There are indeed upper limits on the mass of objects that are formed from stars that run out of nuclear fuel, before the objects collapse to black holes (the Chandrasekhar limit for white dwarfs and the Tolman-Oppenheimer-Volkoff limit for neutron stars), but those limits are not based on density. It is true that, especially in the early universe, gas clouds forming very massive black holes without going through the intermediate stage of forming stars is considered possible; but that is not based on the kind of simplistic calculation that you describe. It's based on numerical simulations of the Einstein Field Equation with relevant initial conditions. Another factor you are not considering is that the universe is expanding, and the early universe was expanding much more rapidly than our current universe is. So gas clouds contracting to form very massive black holes had to work against the expansion to do so. That further complicates the calculations.
        denton-scratch 3y ago
        > So gas clouds contracting to form very massive black holes had to work against the expansion to do so. Is that correct? My understanding is that the expansion of the Universe occurs away from large concentrations of mass; expansion doesn't cause the stars in a galaxy to move apart.
infogulch 3y ago
The weird thing about supermassive black holes is that their average density at the Schwarzschild radius actually goes down as they grow bigger. E.g. I just calculated Phoenix A's density is shockingly low at 2*10^-6 g/cm³ which is similar to high altitude in the earth's atmosphere.
- Tommstein 3y ago
  > The weird thing about supermassive black holes is that their average density at the Schwarzschild radius actually goes down as they grow bigger. What does that mean? The Schwarzschild radius is just the distance at which even light can no longer escape, the only matter there is the matter that happens to be falling in at that moment. Unless you mean the average density within the Schwarzschild volume (a term I just made up as far as I know, but you know what I mean) if all the mass of the black hole were spread out evenly throughout it.
  - The_Colonel 3y ago
    > if all the mass of the black hole were spread out evenly throughout it. That seems like a weird condition. "Average density" is pretty well-defined and doesn't need even spreading. Even more, isn't the distribution of mass within a black hole a meaningless question? There's no information coming from the black hole, for an external observer it literally doesn't matter how the matter is arranged within.
    - lumost 3y ago
      This assumes the mass forms a perfect sphere with no thermal oscillations or other deformities.
      - The_Colonel 3y ago
        What claim needs an assumption of being perfectly spherical? A rotating (or merging) black hole can be deformed (non-spherical), but that doesn't stop you to calculate average density.

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pdonis 3y ago

> volume increases cubically with radius This intuition does not work in curved spacetime, particularly not for black holes. Black holes do not even have a well-defined volume at all.

denton-scratch 3y ago
Well, a sphere with some Schwarzschild radius has a volume. I was uncomfortable with the conflation of the "volume of a black hole" with the volume of that sphere.
- pdonis 3y ago
  > a sphere with some Schwarzschild radius ...is not what a black hole is. It is not even "something kinda sorta like a sphere with some Schwarzschild radius". It is nothing like any ordinary object you're used to. It doesn't have a well-defined "radius" any more than it has a well-defined volume; the Schwarzschild "radius" is actually sqrt(A / 4 pi), where A is the surface area of the hole's horizon (which in turn is calculated from the mass of the hole).
  - mr_toad 3y ago
    It’s still useful to talk about the density of matter inside a volume that is equivalent to the volume defined by the sphere with a Schwartzchild radius because it sets an upper limit on the density that a given mass could be before an event horizon would form. This is relevant to the discussion at hand because for these very large black holes that density is not very high and conceivably a gas cloud of sufficient mass could contract to that density and have an event horizon form without collapsing into Stars.
    - pdonis 3y ago
      > It’s still useful to talk about the density of matter inside a volume that is equivalent to the volume defined by the sphere with a Schwartzchild radius because it sets an upper limit on the density that a given mass could be before an event horizon would form. No, it doesn't. There are indeed upper limits on the mass of objects that are formed from stars that run out of nuclear fuel, before the objects collapse to black holes (the Chandrasekhar limit for white dwarfs and the Tolman-Oppenheimer-Volkoff limit for neutron stars), but those limits are not based on density. It is true that, especially in the early universe, gas clouds forming very massive black holes without going through the intermediate stage of forming stars is considered possible; but that is not based on the kind of simplistic calculation that you describe. It's based on numerical simulations of the Einstein Field Equation with relevant initial conditions. Another factor you are not considering is that the universe is expanding, and the early universe was expanding much more rapidly than our current universe is. So gas clouds contracting to form very massive black holes had to work against the expansion to do so. That further complicates the calculations.
      - denton-scratch 3y ago
        > So gas clouds contracting to form very massive black holes had to work against the expansion to do so. Is that correct? My understanding is that the expansion of the Universe occurs away from large concentrations of mass; expansion doesn't cause the stars in a galaxy to move apart.

infogulch 3y ago

The weird thing about supermassive black holes is that their average density at the Schwarzschild radius actually goes down as they grow bigger. E.g. I just calculated Phoenix A's density is shockingly low at 2*10^-6 g/cm³ which is similar to high altitude in the earth's atmosphere.

Tommstein 3y ago
> The weird thing about supermassive black holes is that their average density at the Schwarzschild radius actually goes down as they grow bigger. What does that mean? The Schwarzschild radius is just the distance at which even light can no longer escape, the only matter there is the matter that happens to be falling in at that moment. Unless you mean the average density within the Schwarzschild volume (a term I just made up as far as I know, but you know what I mean) if all the mass of the black hole were spread out evenly throughout it.
- The_Colonel 3y ago
  > if all the mass of the black hole were spread out evenly throughout it. That seems like a weird condition. "Average density" is pretty well-defined and doesn't need even spreading. Even more, isn't the distribution of mass within a black hole a meaningless question? There's no information coming from the black hole, for an external observer it literally doesn't matter how the matter is arranged within.
  - lumost 3y ago
    This assumes the mass forms a perfect sphere with no thermal oscillations or other deformities.
    - The_Colonel 3y ago
      What claim needs an assumption of being perfectly spherical? A rotating (or merging) black hole can be deformed (non-spherical), but that doesn't stop you to calculate average density.