Can Dark Matter Explain Black Holes and the Mysterious Planet-Nine?

[PeterDonis]

the Schwarzschild equation for a non rotating uncharged black hole, Rs=2GM/c^2, is a reformulation of the Newtonian equation for escape velocity, Ve=sqrt(GM/r)

This is not correct. In fact, the reverse is much closer to the truth: the Newtonian equation for escape velocity can be derived from the Schwarzschild solution in GR, but the Schwarzschild solution, including the value of the horizon radius, cannot be derived from Newtonian mechanics.

There are quantum physics ramifications because the very high pressures produced by the gravitation overcomes the electrical charges in atoms crushing them.

This is not correct either. What has to be overcome by gravity for collapse to a black hole to occur is degeneracy pressure, not electromagnetic repulsion. The simplest way to see this is to observe that neutrons do not electromagnetically repel each other, yet neutron stars exist.

Newton predicted black holes, probably without realizing it

Reference, please?

 

[ProfChuck]

This is not correct. In fact, the reverse is much closer to the truth: the Newtonian equation for escape velocity can be derived from the Schwarzschild solution in GR, but the Schwarzschild solution, including the value of the horizon radius, cannot be derived from Newtonian mechanics.
This is not correct either. What has to be overcome by gravity for collapse to a black hole to occur is degeneracy pressure, not electromagnetic repulsion. The simplest way to see this is to observe that neutrons do not electromagnetically repel each other, yet neutron stars exist.
Reference, please?

Item 1: The Newtonian equation for escape velocity is, Ve=sqrt(GM/r). Set Ve to to the speed of light and solve for r.

Item 2: You are of course correct. I should have included that in my response.

Item 3: It is my opinion. In Newtons time the speed of light was not well known so there was no particular reason for him to include the ramifications in his thinking.

 

[PeterDonis]

The Newtonian equation for escape velocity is, Ve=sqrt(GM/r). Set Ve to to the speed of light and solve for r.

Yes, but that has nothing to do with the Schwarzschild solution in GR. So it doesn't support what you originally said.

It is my opinion.

Then it's off topic here.

 

[phinds]

I wonder if science and/or industry will ever be able to create a video camera that would remain intact so we can find out exactly what happens inside, or what causes black holes or spheres.

I don't know if you are joking or serious but I'll assume you are serious. It is irrelevant whether a camera stay intact inside of the Event Horizon since it is removed from causal connection with the rest of the universe other than the fact that it would add a trivial amount of mass to the BH and thus cause a trivial increase in its gravitational strength. That this is such a basic fact about black holes is why I can't tell if you are joking or serious.

 

[Comeback City]

or what causes black holes or spheres.

We know what causes black holes. They are formed due to a massive star running out of nuclear energy and not being able to support its own mass. It then collapses to a singularity where all mass of the previous star is centralized.

 

[phinds]

We know what causes black holes. They are formed due to a massive star running out of nuclear energy and not being able to support its own mass. It then collapses to a singularity where all mass of the previous star is centralized.

Not ALL the mass of the star. Some of it is blown off in the explosion.

 

[Comeback City]

Not ALL the mass of the star. Some of it is blown off in the explosion.

That is true. Would most of the mass still remain though?

 

[phinds]

That is true. Would most of the mass still remain though?

Good question. I've read the answer to that but do not remember. My memory is not what it used to be. Actually, my memory was never what it used to be.

 

[PeterDonis]

Would most of the mass still remain though?

Not necessarily. As long as enough mass remains to exceed the maximum mass limit for a white dwarf or neutron star, the object will still collapse to a black hole, even if a large fraction of its original mass is ejected in the explosion.

 

[Comeback City]

Not necessarily. As long as enough mass remains to exceed the maximum mass limit for a white dwarf or neutron star, the object will still collapse to a black hole, even if a large fraction of its original mass is ejected in the explosion.

So would it be more likely that larger collapsed stars will lose a larger percentage of their mass in the explosion than smaller collapsed stars? Or is roughly the same percentage lost regardless of the star's mass?

 

[PeterDonis]

would it be more likely that larger collapsed stars will lose a larger percentage of their mass in the explosion than smaller collapsed stars?

I think that is generally expected, but I don't know how much actual data we have to back up that expectation.

 

[stoomart]

That is true. Would most of the mass still remain though?

There is the case of failed supernovas, which do not explode but still form a BH; I assume they would retain most, if not all their mass.

 

[BL4CKB0X97]

If the mass supposedly orbiting our solar system was a black hole, we would begin orbiting it and eventually get "sucked into" it. That itself basically rules out the black hole possibility. I'm not sure how this relates to dark matter and dark energy, though.

If the Bh was far enough away and the gravitational effects weak enough, surely the effects would be negligible. The sun would have a much stronger gravitational effect on the solar system, enough to prevent the outer planets being dragged away.

 

[Comeback City]

If the Bh was far enough away and the gravitational effects weak enough, surely the effects would be negligible. The sun would have a much stronger gravitational effect on the solar system, enough to prevent the outer planets being dragged away.

If it is small enough, yes. But this planet nine has an estimated radius of about 13,000 + km. If it were a bh, it would have a mass of about 4000+ solar masses. @Drakkith pointed out the effects would be huge.

 

[Drakkith]

If the Bh was far enough away and the gravitational effects weak enough, surely the effects would be negligible. The sun would have a much stronger gravitational effect on the solar system, enough to prevent the outer planets being dragged away.

If it is small enough, yes. But this planet nine has an estimated radius of about 13,000 + km. If it were a bh, it would have a mass of about 4000+ solar masses. @Drakkith pointed out the effects would be huge.

The radius is irrelevant here. It is the mass that's key. The researchers proposing the existence of planet 9 don't put the radius of the planet into their models, they put in the mass. This is because observations constrain the mass to a certain range, about 7-10 Earth masses. Whatever the object may be, if it exists at all, it cannot be far above this range or its gravitational effects would already have been noticed and it wouldn't match the proposed model.

 

[Comeback City]

The radius is irrelevant here.

If it was a black hole, the radius would be relevant.

This is because observations constrain the mass to a certain range, about 7-10 Earth masses.

If they are estimating the mass in this range, then the answer to the question in the original post is no, it cannot be a black hole.

 

[phinds]

If it was a black hole, the radius would be relevant.

Why? I don't understand why you think this.

If they are estimating the mass in this range, then the answer to the question in the original post is no, it cannot be a black hole.

Not true. It would be on the low end of BH size, but not impossible

 

[Drakkith]

If it was a black hole, the radius would be relevant.

The radius is directly proportional to the mass of the black hole, which is what is actually being measured/modeled. The object, whatever it is, is constrained by how much mass it has, not its radius. So no, the radius is not relevant. The mass is.

If they are estimating the mass in this range, then the answer to the question in the original post is no, it cannot be a black hole.

It could if the black hole was within this mass range, but there just isn't any known way for a black hole of this mass to exist. And even if there were a way, the chances of one existing in our solar system would be exceptionally small.

 

[Comeback City]

Why? I don't understand why you think this.

Mass and radius of bh are directly related through
r=2GM/c²
If one is relevant, the other should be also.
If it isn't a black hole, then it would not be relevant.

 

[Comeback City]

Not true. It would be on the low end of BH size, but not impossible

It could if the black hole was within this mass range, but there just isn't any known way for a black hole of this mass to exist. And even if there were a way, the chances of one existing in our solar system would be exceptionally small.

 

[Drakkith]

Mass and radius of bh are directly related through
r=2GM/c²
If one is relevant, the other should be also.
If it isn't a black hole, then it would not be relevant.

The fact that they are related does not make both relevant. The radius does not appear in the model under discussion here.

 

[phinds]

Mass and radius of bh are directly related through
r=2GM/c²
If one is relevant, the other should be also.
If it isn't a black hole, then it would not be relevant.

I disagree. Only the mass is relevant, in either case. The diameter has no affect on the rest of the universe (unless you are really close to the surface)

 

[Comeback City]

The fact that they are related does not make both relevant. The radius does not appear in the model under discussion here.

I disagree. Only the mass is relevant, in either case. The diameter has no affect on the rest of the universe (unless you are really close to the surface)

Ok. I see your point(s). I was trying to show that if the mass of a bh can be derived from its radius, then the radius itself is relevant.

 

[Drakkith]

Ok. I see your point(s). I was trying to show that if the mass of a bh can be derived from its radius, then the radius itself is relevant.

It certainly would be if, as phinds said, you were worried about the behavior of things very close to the black hole. But we're talking about the behavior of small objects many millions of kilometers away even at their closest approach to this object. In such a situation the radius doesn't matter since nothing approaches this object close enough to worry about it.

 

[PeterDonis]

if the mass of a bh can be derived from its radius

The point Drakkith is making is that this is only relevant if the radius is what you are actually measuring, or constraining via other measurements. But in the models under discussion, what is being constrained is the mass of the object, not the radius; so the mass is the observable and the radius is derived. Therefore the radius is not relevant; the mass is.

 

[BL4CKB0X97]

If it was a black hole, the radius would be relevant.

If they are estimating the mass in this range, then the answer to the question in the original post is no, it cannot be a black hole.

I believe the radius is estimated by mass, so it would be irrelevant should the mass match the model.

 

[Comeback City]

I believe the radius is estimated by mass, so it would be irrelevant should the mass match the model.

I think it can go either way. Mass and radius are related through the Schwarzschild radius equation,
r_s=2GM/c²
In my case, I used the estimated radius of "planet nine" to find the mass of this object if it was a black hole, like the OP predicted. That is why I thought the radius would be relevant, since I used it to find the mass in the first place.

 

[Bandersnatch]

The point that everybody here is trying to convey is that the radius of the object as given in one of the earlier posts is there for a particular reason other than observations, and as such comes burdened with certain assumptions.

The observations gave only the mass estimate.
Now, to get the radius, we have to make an informed guess as to what is the object made of. There are a few options:
1. It's made of normal matter (like planets and stars).
2. It's made of degenerate matter (like a white dwarf).
3. It's made of neutronium (like a neutron star).
4. It's a black hole.

Each of these options is in principle viable, in the sense that one can imagine objects made out of those materials. Each gives a different radius estimate for the same (observed) mass with identical gravitational effects.
But since we're making an informed guess, we can use our knowledge to eliminate some options. In particular, we can ask:
1) whether there is a way for either of the objects to form while having such low mass
2) whether such objects should produce additional observables that aren't there
...which eliminates all but the normal matter object, i.e. a planet. Plugging in a range of possible densities of normal matter (depending on possible compositions and using models for gravitational compression), you get a range of radii.

So, if you then take that radius and try to plug it into an equation for calculating a black hole mass, you're making two mistakes:
- you're ignoring the fact that the mass is what is already known and can't be anything else
- you're using the radius that was a guess based on the idea that the object is definitely not a black hole

 

[Comeback City]

The point that everybody here is trying to convey is that the radius of the object as given in one of the earlier posts is there for a particular reason other than observations, and as such comes burdened with certain assumptions.

The observations gave only the mass estimate.
Now, to get the radius, we have to make an informed guess as to what is the object made of. There are a few options:
1. It's made of normal matter (like planets and stars).
2. It's made of degenerate matter (like a white dwarf).
3. It's made of neutronium (like a neutron star).
4. It's a black hole.

Each of these options is in principle viable, in the sense that one can imagine objects made out of those materials. Each gives a different radius estimate for the same (observed) mass with identical gravitational effects.
But since we're making an informed guess, we can use our knowledge to eliminate some options. In particular, we can ask:
1) whether there is a way for either of the objects to form while having such low mass
2) whether such objects should produce additional observables that aren't there
...which eliminates all but the normal matter object, i.e. a planet. Plugging in a range of possible densities of normal matter (depending on possible compositions and using models for gravitational compression), you get a range of radii.

So, if you then take that radius and try to plug it into an equation for calculating a black hole mass, you're making two mistakes:
- you're ignoring the fact that the mass is what is already known and can't be anything else
- you're using the radius that was a guess based on the idea that the object is definitely not a black hole

If we only have observed the mass, it is around 7-10 Earth masses, and we are pretty sure there is no way for a black hole that small to form, then we have the answer to the original question: It cannot be a black hole. Thanks for pointing out the mistakes, though; I didn't realize that was the problem.

 

[Bandersnatch]

there is no way for a black hole that small to form, then we have the answer to the original question: It cannot be a black hole

There actually is a way for a black hole of just about that mass to form - it could have been formed at the very early stages in the evolution of the universe (cf: primordial black holes). But it would have a strong observable radiation signature - via accretion disc and Hawking radiation.

 

[Comeback City]

There actually is a way for a black hole of just about that mass to form - it could have been formed at the very early stages in the evolution of the universe (cf: primordial black holes). But it would have a strong observable radiation signature - via accretion disc and Hawking radiation.

And that is what @Chronos pointed in #15. We most likely would've detected its radiation emissions by this point in time.

 

[BL4CKB0X97]

I think it can go either way. Mass and radius are related through the Schwarzschild radius equation,
r_s=2GM/c²
In my case, I used the estimated radius of "planet nine" to find the mass of this object if it was a black hole, like the OP predicted. That is why I thought the radius would be relevant, since I used it to find the mass in the first place.

What Bandersnatch said. [emoji106]

 

[Physics_Kid]

this is awesome, my "simple" Q turns into a good discussion.

so, something i don't understand is, the planet-9 model makes the prediction of a mass & location based on the known things about the other orbiting objects in the solar system. so if a location is known then why can't they look there with Hubble or similar?

so, a BH = ~10 Earth's is possible, but we would have other observable things to identify such, but now i have to ask, if a BH is small, in the kuiper belt, would non-directional sensors be able to identify it, or would you need to have a sensor pointing right at it?

 

[Drakkith]

so, something i don't understand is, the planet-9 model makes the prediction of a mass & location based on the known things about the other orbiting objects in the solar system. so if a location is known then why can't they look there with Hubble or similar?

The model only gives a prediction of the orbit of the planet, not the location along the orbit. There's still a large area of sky to search and this hypothetical planet would be very dim.

 

[Physics_Kid]

i thought the prediction of the mass was based on all orbits, even the orbit of planet-9 mass. you would need an orbital location of a mass to be able to predict the affects of the other orbits, and vice-versa. so doesn't the model predict the mass required, and its orbit?