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If a neutron star, black hole, and regular star can all exist in the 3 solar mass range, do they have a different curve in spacetime? I always imagined the exa

If a neutron star, black hole, and regular star can all exist in the 3 solar mass range, do they have a different curve in spacetime? I always imagined the example of a ball on cellophane for a gravity well caused by massive objects. If they have similar masses, how does the black hole bend "deep" enough into space to the point where not even light can escape? What if it's some other class of object that we have yet to identify? Why black hole if not neutron star? This is not a criticism of the article, these are curiosities. It's a really good read. Fascinating science.

cgriswald 3y ago
Each mass creates a “dimple” on the cellophane but because they have different density, the shape of that dimple is different. The less dense object has a shallower cone. The infinitely dense object has a steeper one. If you’re five feet from the surface of the sun you’re hundreds of thousands of miles away from its center of mass. If you’re five feet away from the “surface” of a solar mass black hole you’re just a couple of miles away from the center of mass.
- lemonfever 3y ago
  Exactly. Also, if you are hundreds of thousands of miles from the center of mass of the sun, you'd feel the same force from gravity as if you were the same distance from the center of mass of a black hole (with the same mass). Far away, the curvature of spacetime is the same, it's just that with black holes you can get waaaay closer to the center of mass whilst still being outside of it.
- onetimeuse92304 3y ago
  Except this is not entirely true. The shape of gravitational field only differs within the body. The shape outside of the perfectly spherical body will be exactly the same regardless of how the mass is distributed (whether it is all on the surface or all in the middle of it). Or in other words, if you are on the surface of the sun, you will feel exactly the same acceleration as if entire mass of the sun was concentrated in its center. The only time you feel the difference is if you dip into the sun. As you go deeper and deeper, the pull from all the mass that is further from the center than you are will perfectly nullify each other. As you go deeper and deeper into the sun you will feel less acceleration.
  - medstrom 3y ago
    So yea, this lets you equate standing on the surface of a given star of X radius, with hovering the same X distance away from a neutron star or black hole of the same mass. The takeaway is that the cellophane dimple is more warped around the center point, but if, say, our Sun were to suddenly turn into a black hole it wouldn't change anything about our orbit.
  - deepsun 3y ago
    Nitpick: you will not feel acceleration in a freefall.
    - deleted 3y ago
      [deleted]
    - cheela 3y ago
      You’ll feel the tides, however.
      - SoftTalker 3y ago
        These analogies always fall apart for me because you'll be burnt to nothing long before you reach the surface of the sun.
        deleted 3y ago
        [deleted]
        onetimeuse92304 3y ago
        Your analogy falls apart, too. Sun does not have a surface to be reached. It just sort of gets more and more dense and that's all.
    - onetimeuse92304 3y ago
      What is "feeling"? If my senses can register changing spectra of the stars around me then yes, I will "feel" the acceleration.
- hn72774 3y ago
  Since the speed of light is a constant, mass increases towards infinity as it approaches the speed of light, and time slows for the matter relative to matter with lesser velocity, does that mean that matter accelerating towards a black hole increases the mass in the region and further increases the magnitude of the effect on the spacetime curve? Is the mass of the black hole perpetually "falling" through spacetime at near the speed of light? Would the region around an "active" black hole appear more massive when it is consuming matter vs existing in a vacuum? A big object going really fast would be almost stopped in time, while at the same moment be almost infinitely massive which is increasing the gravitational effect. The combination of these effects is what makes such a big "dent" in spacetime?
alexey-salmin 3y ago
> I always imagined the example of a ball on cellophane for a gravity well caused by massive objects. > If they have similar masses, how does the black hole bend "deep" enough into space to the point where not even light can escape? A back hole is smaller ball
superjan 3y ago
In principle, any object can become a black hole if it is made dense enough. It does not matter for the gravity at long distance: replace the earth with a black hole of the same mass, and it not change the interactions with the other bodies (sun and moon, mostly). Light does not escape in the black hole case because the black hole is smaller: in case of a black hole earth, light starting at 6370 km (current radius) can still escape. A black hole weighing the same as the earth would have a 9 millimeter radius, no light will escape from there.
- pfdietz 3y ago
  And, any material (of any density) can be made a black hole if there is enough of it. The "radius" (actually, one should properly talk about the circumference) of a black hole is proportional to its mass, so the "density" is proportional to mass^-2. M87's central black is about the same density as the air you are breathing.
  - raattgift 3y ago
    >> any object can become a black hole if it is made dense enough [big 'if'!] > any material (of any density) can be made a black hole if there is enough of it There is an awful lot of intergalactic medium out there. It's of "any density" (albeit very low). How come it's not a black hole? Isn't there "enough of it"? (cf. the "missing baryons problem"). There is an awful lot of atomic and molecular hydrogen gas in the Milky Way and practically every other galaxy. In our galaxy it totally dwarfs all the matter in our central black hole, the stellar black holes, and in all the luminous stars combined. Seems like "enough of it". It's of "any density". How come it's not a black hole? And so forth. > (actually, one should properly talk about the circumference) Why? Also, since we're being properly, what's the circumference of a spinning black hole and how does it evolve with the spin parameter? Extra credit: assume that you mean the mean density of the interior of M87*, how are you arriving at its volume? (You might cast your eyes over Bengtsson & Jakobsson's extension of work on this question by Christodoulou & Rovelli at respectively https://arxiv.org/abs/1502.01907 https://arxiv.org/abs/1502.01907 and https://arxiv.org/abs/1411.2854 https://arxiv.org/abs/1411.2854 -- when you calculate the volumes in a relativistic spirit, the interiors are very large, far too large to support your (commonly used) throwaway line about dense-as-air/less-dense-than-water). Alternatively, what do you think the BH interior modal densities are? ("In their paper CR [Christodolou & Rovelli] estimate that the black hole at the centre of the Milky Way — whose area radius they assume to be not much larger than the distance to the Moon — now contains enough space to fit a million solar systems. A decent estimate for its spin appears to be a/m ≈ 0.9 [5]. It follows that CR overestimate the volume, but only by a factor of 10 or somewhat less". And from CR: "flat space intuition does not apply to the curved geometry inside the hole [...] and the interior volume keeps growing with time"). I of course expect this comment to be thrown into a deep (gravitational) well, actually.
lrem 3y ago
A regular star has a significantly lower density. The ongoing fusion causes a pressure that keeps it from collapsing. The atoms here move chaotically through a 3d space in quite a volume. So your ball sits on too large a surface of cellophane to go really deep. That can continue for increasing masses for quite a while. Google tells me the heaviest known star is about 200 solar masses. Black holes and neutron stars are fundamentally different - there’s no space left between the matter of a neutron star. Now, the physics of that is a bit over my head, but a simplification I got from a PBS Spacetime episode is that the matter in a neutron star pretty much overlaps in 3d and stars filling up some quantum mechanics dimensions. When those cross a threshold, the last forces give way and everything collapses without a limit. So now we’re talking about a ball on your cellophane as small as physically possible for its mass (compact), pushing down significantly deeper… Until it gets replaced with pretty much a puncture, pushing it down to some abstract floor.
- lloeki 3y ago
  My understanding of it is somewhat similar, although I'd argue that's where our mental imagery breaks down: the "weight on fabric" metaphor works to a point then stops conveying what's really happening and becomes misleading. I think of it like "magnets as rubber bands", and what I call "Feynman lies": > I can't explain [magnetic] attraction in terms of anything else that's familiar to you. For example, if we’d said the magnets attract like as if they were connected by rubber bands, I would be cheating you. Because they're not connected by rubber bands, I shouldn’t be in trouble, you’d soon ask me about the nature of the bands… and secondly if you were curious enough, you'd ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I'm trying to use the rubber bands to explain, so I have cheated very badly, you see. > [...] > But I really can't do a good job, any job, of explaining magnetic force in terms of something else that you're more familiar with, because I don’t understand them in terms of anything else that you are more familiar with. direct link: https://www.youtube.com/watch?v=nYg6jzotiAc&t=1263s https://www.youtube.com/watch?v=nYg6jzotiAc&t=1263s but the whole chapter is worth a watch: https://www.youtube.com/watch?v=nYg6jzotiAc&t=894 https://www.youtube.com/watch?v=nYg6jzotiAc&t=894
pvg 3y ago
What if it's some other class of object that we have yet to identify? Why black hole if not neutron star? There's a whole science to this with a fun name: https://en.wikipedia.org/wiki/Degenerate_matter https://en.wikipedia.org/wiki/Degenerate_matter Quantum theory predicts and limits the sorts of things you can get once you really put the squeeze on and these predictions align well with observations.
deleted 3y ago
[deleted]
ordu 3y ago
If you imagine balls of different sizes but with the same mass on cellophane, and look at the shape of cellophane, then you'll see that smaller balls will make cellophane more pointed. If instead of a ball you take a point mass, then the depression will converge into a sharp point. Light can climb out from some depressions but there is a limit on a steepness it can overcome. This analogy probably is not very good for this kind of things, but it shows the idea.

cgriswald 3y ago

Each mass creates a “dimple” on the cellophane but because they have different density, the shape of that dimple is different. The less dense object has a shallower cone. The infinitely dense object has a steeper one. If you’re five feet from the surface of the sun you’re hundreds of thousands of miles away from its center of mass. If you’re five feet away from the “surface” of a solar mass black hole you’re just a couple of miles away from the center of mass.

lemonfever 3y ago
Exactly. Also, if you are hundreds of thousands of miles from the center of mass of the sun, you'd feel the same force from gravity as if you were the same distance from the center of mass of a black hole (with the same mass). Far away, the curvature of spacetime is the same, it's just that with black holes you can get waaaay closer to the center of mass whilst still being outside of it.
onetimeuse92304 3y ago
Except this is not entirely true. The shape of gravitational field only differs within the body. The shape outside of the perfectly spherical body will be exactly the same regardless of how the mass is distributed (whether it is all on the surface or all in the middle of it). Or in other words, if you are on the surface of the sun, you will feel exactly the same acceleration as if entire mass of the sun was concentrated in its center. The only time you feel the difference is if you dip into the sun. As you go deeper and deeper, the pull from all the mass that is further from the center than you are will perfectly nullify each other. As you go deeper and deeper into the sun you will feel less acceleration.
- medstrom 3y ago
  So yea, this lets you equate standing on the surface of a given star of X radius, with hovering the same X distance away from a neutron star or black hole of the same mass. The takeaway is that the cellophane dimple is more warped around the center point, but if, say, our Sun were to suddenly turn into a black hole it wouldn't change anything about our orbit.
- deepsun 3y ago
  Nitpick: you will not feel acceleration in a freefall.
  - deleted 3y ago
    [deleted]
  - cheela 3y ago
    You’ll feel the tides, however.
    - SoftTalker 3y ago
      These analogies always fall apart for me because you'll be burnt to nothing long before you reach the surface of the sun.
      - deleted 3y ago
        [deleted]
      - onetimeuse92304 3y ago
        Your analogy falls apart, too. Sun does not have a surface to be reached. It just sort of gets more and more dense and that's all.
  - onetimeuse92304 3y ago
    What is "feeling"? If my senses can register changing spectra of the stars around me then yes, I will "feel" the acceleration.
hn72774 3y ago
Since the speed of light is a constant, mass increases towards infinity as it approaches the speed of light, and time slows for the matter relative to matter with lesser velocity, does that mean that matter accelerating towards a black hole increases the mass in the region and further increases the magnitude of the effect on the spacetime curve? Is the mass of the black hole perpetually "falling" through spacetime at near the speed of light? Would the region around an "active" black hole appear more massive when it is consuming matter vs existing in a vacuum? A big object going really fast would be almost stopped in time, while at the same moment be almost infinitely massive which is increasing the gravitational effect. The combination of these effects is what makes such a big "dent" in spacetime?

alexey-salmin 3y ago

> I always imagined the example of a ball on cellophane for a gravity well caused by massive objects. > If they have similar masses, how does the black hole bend "deep" enough into space to the point where not even light can escape? A back hole is smaller ball

superjan 3y ago

In principle, any object can become a black hole if it is made dense enough. It does not matter for the gravity at long distance: replace the earth with a black hole of the same mass, and it not change the interactions with the other bodies (sun and moon, mostly). Light does not escape in the black hole case because the black hole is smaller: in case of a black hole earth, light starting at 6370 km (current radius) can still escape. A black hole weighing the same as the earth would have a 9 millimeter radius, no light will escape from there.

pfdietz 3y ago
And, any material (of any density) can be made a black hole if there is enough of it. The "radius" (actually, one should properly talk about the circumference) of a black hole is proportional to its mass, so the "density" is proportional to mass^-2. M87's central black is about the same density as the air you are breathing.
- raattgift 3y ago
  >> any object can become a black hole if it is made dense enough [big 'if'!] > any material (of any density) can be made a black hole if there is enough of it There is an awful lot of intergalactic medium out there. It's of "any density" (albeit very low). How come it's not a black hole? Isn't there "enough of it"? (cf. the "missing baryons problem"). There is an awful lot of atomic and molecular hydrogen gas in the Milky Way and practically every other galaxy. In our galaxy it totally dwarfs all the matter in our central black hole, the stellar black holes, and in all the luminous stars combined. Seems like "enough of it". It's of "any density". How come it's not a black hole? And so forth. > (actually, one should properly talk about the circumference) Why? Also, since we're being properly, what's the circumference of a spinning black hole and how does it evolve with the spin parameter? Extra credit: assume that you mean the mean density of the interior of M87*, how are you arriving at its volume? (You might cast your eyes over Bengtsson & Jakobsson's extension of work on this question by Christodoulou & Rovelli at respectively https://arxiv.org/abs/1502.01907 https://arxiv.org/abs/1502.01907 and https://arxiv.org/abs/1411.2854 https://arxiv.org/abs/1411.2854 -- when you calculate the volumes in a relativistic spirit, the interiors are very large, far too large to support your (commonly used) throwaway line about dense-as-air/less-dense-than-water). Alternatively, what do you think the BH interior modal densities are? ("In their paper CR [Christodolou & Rovelli] estimate that the black hole at the centre of the Milky Way — whose area radius they assume to be not much larger than the distance to the Moon — now contains enough space to fit a million solar systems. A decent estimate for its spin appears to be a/m ≈ 0.9 [5]. It follows that CR overestimate the volume, but only by a factor of 10 or somewhat less". And from CR: "flat space intuition does not apply to the curved geometry inside the hole [...] and the interior volume keeps growing with time"). I of course expect this comment to be thrown into a deep (gravitational) well, actually.

lrem 3y ago

A regular star has a significantly lower density. The ongoing fusion causes a pressure that keeps it from collapsing. The atoms here move chaotically through a 3d space in quite a volume. So your ball sits on too large a surface of cellophane to go really deep. That can continue for increasing masses for quite a while. Google tells me the heaviest known star is about 200 solar masses. Black holes and neutron stars are fundamentally different - there’s no space left between the matter of a neutron star. Now, the physics of that is a bit over my head, but a simplification I got from a PBS Spacetime episode is that the matter in a neutron star pretty much overlaps in 3d and stars filling up some quantum mechanics dimensions. When those cross a threshold, the last forces give way and everything collapses without a limit. So now we’re talking about a ball on your cellophane as small as physically possible for its mass (compact), pushing down significantly deeper… Until it gets replaced with pretty much a puncture, pushing it down to some abstract floor.

lloeki 3y ago
My understanding of it is somewhat similar, although I'd argue that's where our mental imagery breaks down: the "weight on fabric" metaphor works to a point then stops conveying what's really happening and becomes misleading. I think of it like "magnets as rubber bands", and what I call "Feynman lies": > I can't explain [magnetic] attraction in terms of anything else that's familiar to you. For example, if we’d said the magnets attract like as if they were connected by rubber bands, I would be cheating you. Because they're not connected by rubber bands, I shouldn’t be in trouble, you’d soon ask me about the nature of the bands… and secondly if you were curious enough, you'd ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I'm trying to use the rubber bands to explain, so I have cheated very badly, you see. > [...] > But I really can't do a good job, any job, of explaining magnetic force in terms of something else that you're more familiar with, because I don’t understand them in terms of anything else that you are more familiar with. direct link: https://www.youtube.com/watch?v=nYg6jzotiAc&t=1263s https://www.youtube.com/watch?v=nYg6jzotiAc&t=1263s but the whole chapter is worth a watch: https://www.youtube.com/watch?v=nYg6jzotiAc&t=894 https://www.youtube.com/watch?v=nYg6jzotiAc&t=894

pvg 3y ago

What if it's some other class of object that we have yet to identify? Why black hole if not neutron star? There's a whole science to this with a fun name: https://en.wikipedia.org/wiki/Degenerate_matter https://en.wikipedia.org/wiki/Degenerate_matter Quantum theory predicts and limits the sorts of things you can get once you really put the squeeze on and these predictions align well with observations.

deleted 3y ago

[deleted]

ordu 3y ago

If you imagine balls of different sizes but with the same mass on cellophane, and look at the shape of cellophane, then you'll see that smaller balls will make cellophane more pointed. If instead of a ball you take a point mass, then the depression will converge into a sharp point. Light can climb out from some depressions but there is a limit on a steepness it can overcome. This analogy probably is not very good for this kind of things, but it shows the idea.