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> it's the concentration of mass (density) that defines neutron stars and black holes. Not really, no. What defines a neutron star is that it is in hydrostatic

by pdonis 2y ago

> it's the concentration of mass (density) that defines neutron stars and black holes. Not really, no. What defines a neutron star is that it is in hydrostatic equilibrium supported by neutron degeneracy pressure. If we include the quark-gluon plasma phase, we can just amend that to being supported by quark degeneracy pressure (and noting that "neutron" is just a special case of "quark" for this purpose). Whereas a normal star is in hydrostatic equilibrium supported by thermal pressure (with fusion reactions providing the heat source). And a galaxy is not in hydrostatic equilibrium at all, it's composed of stars in free-fall orbits. The average densities of the objects in all three of these cases are consequences of the above. A black hole is defined by having an event horizon and being vacuum. There is no well-defined concept of "density" for a black hole, nor is there "concentration of mass" in the sense of the hole being made of matter; it's not, it's vacuum. The "mass" of a black hole is a global feature of its spacetime geometry.

itishappy 2y ago
Right, but are those phenomenon not also consequences of density? If we compressed stellar or even terrestrial material down the density of a neutron star, would we not get neutronium as a result? I agree that the density of a black hole will depend on choice of observer, but nothing stops us from picking a reasonable one, such as a Schwarzschild observer. Mass (as you've mentioned) and volume (Schwarzschild radius) are both we enough for us to define a global average density. It does not behave intuitively though, increasing mass actually decreases density, which does seems to contradict my earlier point...
- pdonis 2y ago
  > are those phenomenon not also consequences of density? No, density is a consequence of the object's structure. Hydrostatic equilibrium supported by degeneracy pressure leads to higher density than hydrostatic equilibrium supported by thermal pressure. > I agree that the density of a black hole will depend on choice of observer That's not what I said. I said there is no well-defined density of a black hole at all. That's because the hole is vacuum and has no well-defined spatial volume. > nothing stops us from picking a reasonable one, such as a Schwarzschild observer There are no Schwarzschild observers inside a black hole. Schwarzschild coordinates in the interior of a black hole give an infinite answer for the "spatial volume", which, of course, is not well-defined. > volume (Schwarzschild radius) The Schwarzschild radius is derived from the surface area of the hole's horizon. It does not mean the hole has a well-defined volume. It doesn't.
  - itishappy 2y ago
    > No, density is a consequence of the object's structure. Which is a consequence of the gravitational pressure, no? Quark degenerate matter without a confining potential would not be at equilibrium. > There are no Schwarzschild observers inside a black hole. Of course not, but the definition of the Schwarzschild radius does not require a black hole, just mass. For example, we define the Schwarzschild radius of the Sun to be about 3km. Outside of black hole dynamics, this defines a volume of space, and we call an object whose radius is smaller than its Schwarzschild radius a black hole. I understand that black holes are fundamentally dynamic processes, but can we not define the behavior at the limit?
    - pdonis 2y ago
      > Which is a consequence of the gravitational pressure, no? Not just gravity alone, no. (And "gravitational pressure" is not a good description of gravity's effect.) Gravity plus the fact that the object does not have a heat source inside it (fusion) to provide thermal pressure. With thermal pressure an object with the same number of particles in it would be much larger--an ordinary star--and its average density would be much smaller. > the definition of the Schwarzschild radius does not require a black hole But if the object is not a black hole the Schwarzschild radius is physically meaningless. It only has physical meaning for a black hole, and its physical meaning, as I said, has to do with the area of the hole's horizon, and only that. > this defines a volume of space, and we call an object whose radius is smaller than its Schwarzschild radius a black hole No, this is not correct. We call an object a black hole if it has an event horizon. A black hole doesn't have a well-defined "radius" in space any more than it has a well-defined volume. A black hole is certainly not just an object "made of stuff", like a neutron star, that just happens to have collapsed further. It is a different kind of thing from any ordinary object. > I understand that black holes are fundamentally dynamic processes, but can we not define the behavior at the limit? What you are describing is not a "limit" of anything. It's simply a wrong description of the physics of a black hole. If by "dynamic" you are talking about the process of forming a black hole from the collapse of a massive object, you're still not correctly describing the end point of that process.

by pdonis 2y ago

itishappy 2y ago

Right, but are those phenomenon not also consequences of density? If we compressed stellar or even terrestrial material down the density of a neutron star, would we not get neutronium as a result? I agree that the density of a black hole will depend on choice of observer, but nothing stops us from picking a reasonable one, such as a Schwarzschild observer. Mass (as you've mentioned) and volume (Schwarzschild radius) are both we enough for us to define a global average density. It does not behave intuitively though, increasing mass actually decreases density, which does seems to contradict my earlier point...

pdonis 2y ago
> are those phenomenon not also consequences of density? No, density is a consequence of the object's structure. Hydrostatic equilibrium supported by degeneracy pressure leads to higher density than hydrostatic equilibrium supported by thermal pressure. > I agree that the density of a black hole will depend on choice of observer That's not what I said. I said there is no well-defined density of a black hole at all. That's because the hole is vacuum and has no well-defined spatial volume. > nothing stops us from picking a reasonable one, such as a Schwarzschild observer There are no Schwarzschild observers inside a black hole. Schwarzschild coordinates in the interior of a black hole give an infinite answer for the "spatial volume", which, of course, is not well-defined. > volume (Schwarzschild radius) The Schwarzschild radius is derived from the surface area of the hole's horizon. It does not mean the hole has a well-defined volume. It doesn't.
- itishappy 2y ago
  > No, density is a consequence of the object's structure. Which is a consequence of the gravitational pressure, no? Quark degenerate matter without a confining potential would not be at equilibrium. > There are no Schwarzschild observers inside a black hole. Of course not, but the definition of the Schwarzschild radius does not require a black hole, just mass. For example, we define the Schwarzschild radius of the Sun to be about 3km. Outside of black hole dynamics, this defines a volume of space, and we call an object whose radius is smaller than its Schwarzschild radius a black hole. I understand that black holes are fundamentally dynamic processes, but can we not define the behavior at the limit?
  - pdonis 2y ago
    > Which is a consequence of the gravitational pressure, no? Not just gravity alone, no. (And "gravitational pressure" is not a good description of gravity's effect.) Gravity plus the fact that the object does not have a heat source inside it (fusion) to provide thermal pressure. With thermal pressure an object with the same number of particles in it would be much larger--an ordinary star--and its average density would be much smaller. > the definition of the Schwarzschild radius does not require a black hole But if the object is not a black hole the Schwarzschild radius is physically meaningless. It only has physical meaning for a black hole, and its physical meaning, as I said, has to do with the area of the hole's horizon, and only that. > this defines a volume of space, and we call an object whose radius is smaller than its Schwarzschild radius a black hole No, this is not correct. We call an object a black hole if it has an event horizon. A black hole doesn't have a well-defined "radius" in space any more than it has a well-defined volume. A black hole is certainly not just an object "made of stuff", like a neutron star, that just happens to have collapsed further. It is a different kind of thing from any ordinary object. > I understand that black holes are fundamentally dynamic processes, but can we not define the behavior at the limit? What you are describing is not a "limit" of anything. It's simply a wrong description of the physics of a black hole. If by "dynamic" you are talking about the process of forming a black hole from the collapse of a massive object, you're still not correctly describing the end point of that process.