<p><em>Two</em> stars are not &quot;a sphere&quot;.  So their combined gravitation field is not that of a single black hole at their barycentre.</p>
<p>To give an idea of just <em>how</em> wrong this is, below is the Newtonian gravitational potential for two uniform spheres (in purple) and a single point mass at their barycentre (in green).  Note that at the gravitational potential of the point mass (&quot;a black hole&quot;) is not the same as the gravitation potential of the two uniform spheres.  This is particularly apparent at the barycentre, in the middle.</p>
<p><a href="https://i.sstatic.net/aMnr9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/aMnr9.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-08-16T18:14:53.603Z
To be honest I'd wonder if this was some kind of joke.  I can't imagine anyone seriously proposing it.
James K
CC BY-SA 4.0
2021-08-17T09:43:15.523Z
The question is why these 'virtual ' black holes are unobserved.If a gravitational system acts as if its entire mass(sum of the masses of its members) is concentrated at the barycenter,then what prevents a barycenter of sufficient mass from having the characteristics of a black hole/neutron star(event-horizon et cetera)?To put it another way,is a barycenter of sufficient 'mass' distinguishable from a black hole of equal mass ?Are these barycentric/virtual singularities nonobserved by noneexistence or simply by nobody  looking out for them,since they are unexpected?
AnnexRemotelearn
CC BY-SA 4.0
2021-08-17T10:49:54.727Z
"If a gravitational system acts as if its entire mass is concentrated at the barycenter,"..... **It doesn't**.   The gravitational potential surrounding and between two stars is ***very*** different from the potential surrounding a single black hole.  Barycentres don't have "mass".  And yes, two stars is distinguishable from one black hole.  They are "nonobserved" by "nonexistence."
James K
CC BY-SA 4.0
2021-08-17T11:36:38.470Z
@AnnexRemotelearn "The question is why these 'virtual ' black holes are unobserved.", did you even read this answer? It is not that something is missing from our observations, but your understanding of physics that is flawed. You just can't combine two point masses and pretend they are one different point mass. That only works for a spherical distribution of point masses.
AtmosphericPrisonEscape
CC BY-SA 4.0
2021-08-17T12:40:30.730Z
You said you can't combine two point masses,and their barycenter doesn't act as if the mass of the system is concentrated there.Could you give me some of your citations/reference to support this?Though I was from the math faculty,rather than physics,high school physics said so.And our textbooks came from reputable publishers in/from Europe and America.
AnnexRemotelearn
CC BY-SA 4.0
2021-08-17T13:47:18.470Z
**See picture**.  I'm getting rather bored of this nonsense now. This is gravitational equivalent of "Elephants are actually plants". or "Substances can't mix if they are made of atoms".  What is this "Institution?"  Where can we see this "paper".  Who are the authors?  This is deep crackpot material, if it is as you describe.
James K
CC BY-SA 4.0
2021-08-17T19:41:16.680Z
@AnnexRemotelearn the gravitational potential for a binary system is known as the Roche potential https://en.wikipedia.org/wiki/Roche_lobe
Daddy Kropotkin
CC BY-SA 4.0
2021-08-16T18:13:50.177Z
2021-08-17T11:42:52.150Z
2021-08-17T11:42:52.150Z
James K
<p>If a sphere acts as if its entire mass is at it's center, then you have to form a sphere to have a black hole.</p>
<p>If there are two stars, there are two spheres, separated from each other by miles, or by AUs, or by light years.  Not one sphere of matter.</p>
<p>I note that a black hole with a radius of ten solar masses would have an event horizon radius of about 30 kilometers and thus a diameter of about 60 kilometers.  To be a black hole all of its mass would have to be within that diameter of about 60 kilometers.</p>
<p>So a line connecting the centers of the two stars would go from the outer surface of  star A, through the center of star A, to the inner surface (facing star B) of Atar A, through empty space, through the barycenter of the two stars, through empty space, through the inner surface of star B, thorugh the center of star B, and to the other surface of star B, in 60 kilometers or less.</p>
<p>And a black hole with 4 solar masses would have a smaller radius and diameter than 60 kilometers.</p>
<p>according to a table in an answer by user177107 to the question: <a href="https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe/40758#40758%5B1%5D">https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe/40758#40758[1]</a></p>
<p>A star with a mass of 2.05 solar masses would be spectral type A2V with a radius 1.97 times that of the Sun.  The Sun has an equitorial radius of about 695,000 kilometers and thus a diameter of 1,390,000 kilometers.  So two spectral class A2V stars would each have diameters of about 2,738,300 kilometers.  So even if the two stars were touching each other, there would be about 5,476,600 kilometers from the outer surface of star A to the outer surface of star B, which is about 9,127 times as large as the radius of a black hole of 10 solar masses.</p>
<p>So it is impossible for two stars each with two solar masses to get close enough to each other to form a black hole.</p>
<p>What if the two stars are white dwarfs?  The smallest white dwarf star known was discovered in 2021 with a radius of 2,100 kilometers (1,305 miles) and a diameter of  4,200 kilometers.</p>
<p><a href="https://www.sciencenewsforstudents.org/article/white-dwarf-star-smallest-ever-found-moon-size-most-massive%5B2%5D" rel="nofollow noreferrer">https://www.sciencenewsforstudents.org/article/white-dwarf-star-smallest-ever-found-moon-size-most-massive[2]</a></p>
<p>Thus two such white dwarfs would have a total diameter of 8,400 klometers even if they were touching each other, which is 140 times the diameter of a 10-slar-mass black hole.</p>
<p>The more massive a white dwarf is, the smaller it will be.  In fact, calculations show that a white dwarf about with 1.2 solar masses would be infintely small. Thus it is impossible to have two white dwart stars with a total mass above 2.4 solar masses, let alone 4 solar masses.</p>
<p>Neutron stars are believed to have masses in the range of 1.4 solar masses to 2.14 solar masses.  Thus it is possible for two neutron stars to have a total mass of 4 solar masses.</p>
<p>In 2020 a study calculated that neutron stars should have diameters between 13 and 15 miles, or 21 to 24 kilometers.</p>
<p><a href="https://astronomy.com/news/2020/03/how-big-are-neutron-stars%5B3%5D" rel="nofollow noreferrer">https://astronomy.com/news/2020/03/how-big-are-neutron-stars[3]</a></p>
<p>Thus two neutral stars which would touching each other would have a total diameter of 42 to 48 kilometers.  It may be possible that two neutron stars each with 2 solar masses could orbit each other closely enough to form an event horizon around the pair of neutraon stars.</p>
<p>But even though calculatins suggest a mass above 2.16 solar masses would enough to form a black hole - thus indicating that two neutron stars each with 1.1 solar mass would be enough to forma black hole if they orbited closely enough, there are no known black holes with only 2.17 solar masses.</p>
<p>I guess that is why the question specifies 4 solar masses as the minimum mass of a black hole.</p>
<p>But actually the least massive known black holes have masses of about 5 solar masses.</p>
<blockquote>
<p>It is thought that beyond 2.16 M☉ the stellar remnant will overcome the strong force repulsion and neutron degeneracy pressure so that gravitational collapse will occur to produce a black hole, but the smallest observed mass of a stellar black hole is about 5 M☉.[b] Between 2.16 M☉ and 5 M☉, hypothetical intermediate-mass stars such as quark stars and electroweak stars have been proposed, but none have been shown to exist.[b]</p>
</blockquote>
<p><a href="https://en.wikipedia.org/wiki/Neutron_star#Mass_and_temperature%5B4%5D" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Neutron_star#Mass_and_temperature[4]</a></p>
<p>So possibly two hypothetical quark stars or electroweak stars could be close enough to each other that an event horizon forms around them, making them a black hole.</p>
<p>So it may be theoretically possible for two neutron stars or quark stars or electroweak stars to be close enough to each other for an event horizon be around the two objects, making them a black hole.  But they would have to be very close, separated by just a few kilometers at most, to have sufficient matter density for a black hole.</p>
<p>Added 08-17-2021</p>
<p>It seems inuitively very doubtful that two objects that are not dense enough to have event horizons could get close enough to form an event horizon around the pair of them.  So if someone wanted to convince physicists that was possible they would have to do more complex math to find out whether it was possible.</p>
<p>The only two ways I can think of for two ultra dense and ultra compact stars to get so close together would be:</p>
<p>One)  They were on a collision course.  So soon after getting close enough to hypothetically form an event horizon around the pair, they could collide and their mass would probably combine to form a single singlelarity.</p>
<p>Two)  They were originally a binary star with the two normal stars separated by millions or billions of kilometers. Over ages, as the two normal stars gradually developed into neutron stars or other compact stars, some force caused their orbit around their barycenter to decay.  And eventually, after they both became compact stars, their obit decayed enough for them to get close enough to form an event horizon around the pair. And then either that force would cause their orbits to continue shrining until they eventually merged into one object, or else the event horizon  would prevent the interactions causing orbital decay, and the orbits would stabilize.</p>
<p>End of addition 08-17-2021</p>
<p>I note that the more massive a black hole is the wider its event horizon will be, and the less dense it has to be to still be dense enough to be a black hole.</p>
<p>So it might possibly be possible that the entire universe is within the event horizon of a gigantic black hole formed by the gravity of all the stars and other objects within it combined.</p>
<p>Here is a link to an article mentioning a suggestion that the entire universe could be within a black hole.</p>
<p><a href="https://matrixdisclosure.com/black-holes-entire-universe-inside/#:%7E:text=Moreover%2C%20says%20a%20physicist%2C%20even%20our%20universe%20is,Hole%2C%20our%20particles%20would%20reach%20a%20parallel%20universe.%5B5%5D" rel="nofollow noreferrer">https://matrixdisclosure.com/black-holes-entire-universe-inside/#:~:text=Moreover%2C%20says%20a%20physicist%2C%20even%20our%20universe%20is,Hole%2C%20our%20particles%20would%20reach%20a%20parallel%20universe.[5]</a></p>

CC BY-SA 4.0
2021-08-17T09:25:42.580Z
Golding,I greatly appreciate the comprehensiveness of your reply,backed with URL citations.As somebody from a country where the intellectual tradition is sparse,it is encouraging.I was also amazed you cited the notion the Universe could be part of a singularity created by the mass-energy in it;this concept was mooted in a previous colloquim in physics,but was laughed out of court.I'll get back to you shortly with som clarification.
AnnexRemotelearn
CC BY-SA 4.0
2021-08-17T16:22:50.557Z
@AnnexRemotelearn  I read abuut an idea the whole universe cold be a black hole as a rather far out idea long ago.  And here is a link to an article discussing whether the whole universe could be within a black hole.  https://matrixdisclosure.com/black-holes-entire-universe-inside/#:~:text=Moreover%2C%20says%20a%20physicist%2C%20even%20our%20universe%20is,Hole%2C%20our%20particles%20would%20reach%20a%20parallel%20universe.     I expect that the more scientific discussions of that idea would involve a lot of math.
M. A. Golding
CC BY-SA 4.0
2021-08-17T19:40:03.023Z
" It may be possible that two neutron stars each with 2 solar masses could orbit each other closely enough to form an event horizon around the pair of neutraon stars." Can you provide a source or at least some reasoning for this? Just simply stating that it happens, as you did in your "Edit", is not sufficient...
Daddy Kropotkin
CC BY-SA 4.0
2021-08-17T19:40:07.627Z
Also, when you say that " And eventually, after they both became compact stars, their obit decayed enough for them to get close enough to form an event horizon around the pair.".... this is generally due to common envelope evolution which is observationally unavoidable, not due to some magical gravitational collapse scenario....
Daddy Kropotkin
CC BY-SA 4.0
2021-08-19T00:34:41.693Z
@Daddy Kropotkin  I wrote that "It may be possible".  I didn't write that it happens.  There is a big difference between writing that something might possibly or cceivably be possible and writing that it actually has happened, which requires that it is certainly possible.
M. A. Golding
CC BY-SA 4.0
2021-08-19T01:12:30.257Z
And I'm simply asking you to justify why you think that is possible.
Daddy Kropotkin
CC BY-SA 4.0
2021-08-16T18:34:05.623Z
2021-08-17T17:04:22.093Z
2021-08-17T17:04:22.093Z
M. A. Golding
<p>A paper('A QuasiHeuristic View On The Occurrence Of Singularity Forms of Ordinary Matter') discussed at a recent colloqium at our institution postulated,since 4 Solar masses is what is needed for black hole formation ,then at the center of mass between 2 ordinary stars,each double the Sun in mass, there should always be a black hole.(There were also about five other consistent predictions)If we view a binary system of such stars 5 million kilometers apart,then the barycenter should be located at the point precisely  2.5 kilometers between the pair.This point should act as if there were a body of 4 Solar masses concentrated at it,and the stars orbit it.</p>
<p>Or Newton's theory has to be reviewed.So where are those 'ordinary' black holes out there?No mention I have seen of any yet</p>
<p><strong>Note</strong> ;On submitting the paper to informal peer-review,most of the objections were about singularities depending crucially on density rather than just mass.Also,they said if this were the case,objects on earth would be attracted towards the Sun-Earth center-of-mass rather than to the Earth's center.The authors countered by saying</p>
<p>*The density requirement actually favours a barycenter.Between say, two ordinary stars of mass 2 Solar-Masses each(where a Solar Mass is the mass of the Sun),the barycenter of it simply is a point in space which acts as if 4 solar masses are concentrated there.Since points have no extension,there should result a situation of such density a singularity would appear.</p>
<p>*Objects on Earth should appear to be attracted to the Sun-Earth barycenter and fall towards/into it,but do not for the same reason the Earth doesn't;the objects together,with the Earth, are in orbit around it,so this vitiates the attraction of the barycenter .</p>
<p>Edit;The question is why these 'virtual' black holes are unobserved.If a gravitational system acts as if its entire mass(sum of the masses of its members) is concentrated at the barycenter,then what prevents a barycenter of sufficient mass from having the characteristics of a black hole/neutron star(event-horizon, et cetera)?To put it another way,is a barycenter of sufficient 'mass' distinguishable from a black hole of equal mass ?Are these barycentric/virtual singularities unobserved by noneexistence or simply by nobody looking out for them,since they are unexpected?</p>
<p>Note,as the authors wrote in their synopsis(and in the paper title,their paper is heuristic;they insist they are proposing something which should occur,and in its absence,a revision to conventional (Newtonian?)theory may be needed.Both authors,though physicists,have no actual physical experience at an observatory.</p>

CC BY-SA 4.0
2021-08-16T17:46:29.903Z
Re *then at the center of mass between 2 ordinary stars,each double the Sun in mass, there should always be a black hole*: This is completely bogus and displays an ignorance of Newtonian mechanics.
David Hammen
CC BY-SA 4.0
2021-08-16T19:58:17.397Z
Why $would$ a black hole form in between two stars that are widely separated?
Daddy Kropotkin
CC BY-SA 4.0
2021-08-16T20:00:19.160Z
Mixing relativity and Newtonian physics with black holes.  Any "result" of thinking like that will be useless.
StephenG - Help Ukraine
CC BY-SA 4.0
2021-08-17T17:12:47.577Z
I’m voting to close this question because it doesn't look like it is about science, but about a crackpot theory. Another possibility is that the article mentioned is indeed a valid article, but has been misinterpreted by the OP. In this case, the question would be about the misconception and would be valid on this site. Please, provide a reference for the cited article and/or the author's names. If it turns out it is a valid paper I will retract my vote.
Prallax
CC BY-SA 4.0
2021-08-17T18:41:08.503Z
@prallax,Hi the paper,we were told, has been sent to a peer-reviewed journal(which in its editorial policy allows informal group discussions of papers in consideration)Am I misinterpreting it?I don't think so,though I am from math faculty rather than physics.No reply from journal editors yet on review results.However,it is your prerogative to view the concept in the paper what you wish.I don't get what your objection is,perhaps you could itemise it.Most of the informal review disputed it,but they also said what they objected to ,as shown in my clarification.
AnnexRemotelearn
CC BY-SA 4.0
2021-08-17T19:21:05.757Z
@AnnexRemotelearn do you have a link to a pre-print of the paper? Or the names of the authors? Perhaps they published it on [arXiv](https://arxiv.org/)? +1 from me. Even if it's ultimately wrong, it's still an interesting question.
franz_lyre
<star><black-hole>
If Newton said a sphere acts as if its entire mass is at its center,why are there no black holes between any two ordinary stars of 4 Solar Masses?
AnnexRemotelearn
# If Newton said a sphere acts as if its entire mass is at its center,why are there no black holes between any two ordinary stars of 4 Solar Masses?

(Asked by: username_0 on 2021-08-16)

A paper('A QuasiHeuristic View On The Occurrence Of Singularity Forms of Ordinary Matter') discussed at a recent colloqium at our institution postulated,since 4 Solar masses is what is needed for black hole formation ,then at the center of mass between 2 ordinary stars,each double the Sun in mass, there should always be a black hole.(There were also about five other consistent predictions)If we view a binary system of such stars 5 million kilometers apart,then the barycenter should be located at the point precisely 2.5 kilometers between the pair.This point should act as if there were a body of 4 Solar masses concentrated at it,and the stars orbit it.

Or Newton's theory has to be reviewed.So where are those 'ordinary' black holes out there?No mention I have seen of any yet

**Note** ;On submitting the paper to informal peer-review,most of the objections were about singularities depending crucially on density rather than just mass.Also,they said if this were the case,objects on earth would be attracted towards the Sun-Earth center-of-mass rather than to the Earth's center.The authors countered by saying

\*The density requirement actually favours a barycenter.Between say, two ordinary stars of mass 2 Solar-Masses each(where a Solar Mass is the mass of the Sun),the barycenter of it simply is a point in space which acts as if 4 solar masses are concentrated there.Since points have no extension,there should result a situation of such density a singularity would appear.

\*Objects on Earth should appear to be attracted to the Sun-Earth barycenter and fall towards/into it,but do not for the same reason the Earth doesn't;the objects together,with the Earth, are in orbit around it,so this vitiates the attraction of the barycenter .

Edit;The question is why these 'virtual' black holes are unobserved.If a gravitational system acts as if its entire mass(sum of the masses of its members) is concentrated at the barycenter,then what prevents a barycenter of sufficient mass from having the characteristics of a black hole/neutron star(event-horizon, et cetera)?To put it another way,is a barycenter of sufficient 'mass' distinguishable from a black hole of equal mass ?Are these barycentric/virtual singularities unobserved by noneexistence or simply by nobody looking out for them,since they are unexpected?

Note,as the authors wrote in their synopsis(and in the paper title,their paper is heuristic;they insist they are proposing something which should occur,and in its absence,a revision to conventional (Newtonian?)theory may be needed.Both authors,though physicists,have no actual physical experience at an observatory.

**Tags:** star, black-hole
> **Comments:**
> **username_1**: Re *then at the center of mass between 2 ordinary stars,each double the Sun in mass, there should always be a black hole*: This is completely bogus and displays an ignorance of Newtonian mechanics.  
> **username_2**: Why $would$ a black hole form in between two stars that are widely separated?  
> **username_3**: Mixing relativity and Newtonian physics with black holes.  Any "result" of thinking like that will be useless.  
> **username_4**: I’m voting to close this question because it doesn't look like it is about science, but about a crackpot theory. Another possibility is that the article mentioned is indeed a valid article, but has been misinterpreted by the OP. In this case, the question would be about the misconception and would be valid on this site. Please, provide a reference for the cited article and/or the author's names. If it turns out it is a valid paper I will retract my vote.  
> **username_0**: @prallax,Hi the paper,we were told, has been sent to a peer-reviewed journal(which in its editorial policy allows informal group discussions of papers in consideration)Am I misinterpreting it?I don't think so,though I am from math faculty rather than physics.No reply from journal editors yet on review results.However,it is your prerogative to view the concept in the paper what you wish.I don't get what your objection is,perhaps you could itemise it.Most of the informal review disputed it,but they also said what they objected to ,as shown in my clarification.  
> **username_5**: @AnnexRemotelearn do you have a link to a pre-print of the paper? Or the names of the authors? Perhaps they published it on [arXiv](https://arxiv.org/)? +1 from me. Even if it's ultimately wrong, it's still an interesting question.  

---

## 2 answers

### Answer by username_6 on 2021-08-16. Score: 7

*Two* stars are not "a sphere". So their combined gravitation field is not that of a single black hole at their barycentre.

To give an idea of just *how* wrong this is, below is the Newtonian gravitational potential for two uniform spheres (in purple) and a single point mass at their barycentre (in green). Note that at the gravitational potential of the point mass ("a black hole") is not the same as the gravitation potential of the two uniform spheres. This is particularly apparent at the barycentre, in the middle.

[![enter image description here](https://i.sstatic.net/aMnr9.png)](https://i.sstatic.net/aMnr9.png)

> **Comments:**
> **username_6**: To be honest I'd wonder if this was some kind of joke.  I can't imagine anyone seriously proposing it.  
> **username_0**: The question is why these 'virtual ' black holes are unobserved.If a gravitational system acts as if its entire mass(sum of the masses of its members) is concentrated at the barycenter,then what prevents a barycenter of sufficient mass from having the characteristics of a black hole/neutron star(event-horizon et cetera)?To put it another way,is a barycenter of sufficient 'mass' distinguishable from a black hole of equal mass ?Are these barycentric/virtual singularities nonobserved by noneexistence or simply by nobody  looking out for them,since they are unexpected?  
> **username_6**: "If a gravitational system acts as if its entire mass is concentrated at the barycenter,"..... **It doesn't**.   The gravitational potential surrounding and between two stars is ***very*** different from the potential surrounding a single black hole.  Barycentres don't have "mass".  And yes, two stars is distinguishable from one black hole.  They are "nonobserved" by "nonexistence."  
> **username_7**: @AnnexRemotelearn "The question is why these 'virtual ' black holes are unobserved.", did you even read this answer? It is not that something is missing from our observations, but your understanding of physics that is flawed. You just can't combine two point masses and pretend they are one different point mass. That only works for a spherical distribution of point masses.  
> **username_0**: You said you can't combine two point masses,and their barycenter doesn't act as if the mass of the system is concentrated there.Could you give me some of your citations/reference to support this?Though I was from the math faculty,rather than physics,high school physics said so.And our textbooks came from reputable publishers in/from Europe and America.  
> **username_6**: **See picture**.  I'm getting rather bored of this nonsense now. This is gravitational equivalent of "Elephants are actually plants". or "Substances can't mix if they are made of atoms".  What is this "Institution?"  Where can we see this "paper".  Who are the authors?  This is deep crackpot material, if it is as you describe.  
> **username_2**: @AnnexRemotelearn the gravitational potential for a binary system is known as the Roche potential https://en.wikipedia.org/wiki/Roche_lobe  

---

### Answer by username_8 on 2021-08-16. Score: -1

If a sphere acts as if its entire mass is at it's center, then you have to form a sphere to have a black hole.

If there are two stars, there are two spheres, separated from each other by miles, or by AUs, or by light years. Not one sphere of matter.

I note that a black hole with a radius of ten solar masses would have an event horizon radius of about 30 kilometers and thus a diameter of about 60 kilometers. To be a black hole all of its mass would have to be within that diameter of about 60 kilometers.

So a line connecting the centers of the two stars would go from the outer surface of star A, through the center of star A, to the inner surface (facing star B) of Atar A, through empty space, through the barycenter of the two stars, through empty space, through the inner surface of star B, thorugh the center of star B, and to the other surface of star B, in 60 kilometers or less.

And a black hole with 4 solar masses would have a smaller radius and diameter than 60 kilometers.

according to a table in an answer by user177107 to the question: [https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe/40758#40758[1]](https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe/40758#40758%5B1%5D)

A star with a mass of 2.05 solar masses would be spectral type A2V with a radius 1.97 times that of the Sun. The Sun has an equitorial radius of about 695,000 kilometers and thus a diameter of 1,390,000 kilometers. So two spectral class A2V stars would each have diameters of about 2,738,300 kilometers. So even if the two stars were touching each other, there would be about 5,476,600 kilometers from the outer surface of star A to the outer surface of star B, which is about 9,127 times as large as the radius of a black hole of 10 solar masses.

So it is impossible for two stars each with two solar masses to get close enough to each other to form a black hole.

What if the two stars are white dwarfs? The smallest white dwarf star known was discovered in 2021 with a radius of 2,100 kilometers (1,305 miles) and a diameter of 4,200 kilometers.

[https://www.sciencenewsforstudents.org/article/white-dwarf-star-smallest-ever-found-moon-size-most-massive[2]](https://www.sciencenewsforstudents.org/article/white-dwarf-star-smallest-ever-found-moon-size-most-massive%5B2%5D)

Thus two such white dwarfs would have a total diameter of 8,400 klometers even if they were touching each other, which is 140 times the diameter of a 10-slar-mass black hole.

The more massive a white dwarf is, the smaller it will be. In fact, calculations show that a white dwarf about with 1.2 solar masses would be infintely small. Thus it is impossible to have two white dwart stars with a total mass above 2.4 solar masses, let alone 4 solar masses.

Neutron stars are believed to have masses in the range of 1.4 solar masses to 2.14 solar masses. Thus it is possible for two neutron stars to have a total mass of 4 solar masses.

In 2020 a study calculated that neutron stars should have diameters between 13 and 15 miles, or 21 to 24 kilometers.

[https://astronomy.com/news/2020/03/how-big-are-neutron-stars[3]](https://astronomy.com/news/2020/03/how-big-are-neutron-stars%5B3%5D)

Thus two neutral stars which would touching each other would have a total diameter of 42 to 48 kilometers. It may be possible that two neutron stars each with 2 solar masses could orbit each other closely enough to form an event horizon around the pair of neutraon stars.

But even though calculatins suggest a mass above 2.16 solar masses would enough to form a black hole - thus indicating that two neutron stars each with 1.1 solar mass would be enough to forma black hole if they orbited closely enough, there are no known black holes with only 2.17 solar masses.

I guess that is why the question specifies 4 solar masses as the minimum mass of a black hole.

But actually the least massive known black holes have masses of about 5 solar masses.

> It is thought that beyond 2.16 M☉ the stellar remnant will overcome the strong force repulsion and neutron degeneracy pressure so that gravitational collapse will occur to produce a black hole, but the smallest observed mass of a stellar black hole is about 5 M☉.[b] Between 2.16 M☉ and 5 M☉, hypothetical intermediate-mass stars such as quark stars and electroweak stars have been proposed, but none have been shown to exist.[b]

[https://en.wikipedia.org/wiki/Neutron\_star#Mass\_and\_temperature[4]](https://en.wikipedia.org/wiki/Neutron_star#Mass_and_temperature%5B4%5D)

So possibly two hypothetical quark stars or electroweak stars could be close enough to each other that an event horizon forms around them, making them a black hole.

So it may be theoretically possible for two neutron stars or quark stars or electroweak stars to be close enough to each other for an event horizon be around the two objects, making them a black hole. But they would have to be very close, separated by just a few kilometers at most, to have sufficient matter density for a black hole.

Added 08-17-2021

It seems inuitively very doubtful that two objects that are not dense enough to have event horizons could get close enough to form an event horizon around the pair of them. So if someone wanted to convince physicists that was possible they would have to do more complex math to find out whether it was possible.

The only two ways I can think of for two ultra dense and ultra compact stars to get so close together would be:

One) They were on a collision course. So soon after getting close enough to hypothetically form an event horizon around the pair, they could collide and their mass would probably combine to form a single singlelarity.

Two) They were originally a binary star with the two normal stars separated by millions or billions of kilometers. Over ages, as the two normal stars gradually developed into neutron stars or other compact stars, some force caused their orbit around their barycenter to decay. And eventually, after they both became compact stars, their obit decayed enough for them to get close enough to form an event horizon around the pair. And then either that force would cause their orbits to continue shrining until they eventually merged into one object, or else the event horizon would prevent the interactions causing orbital decay, and the orbits would stabilize.

End of addition 08-17-2021

I note that the more massive a black hole is the wider its event horizon will be, and the less dense it has to be to still be dense enough to be a black hole.

So it might possibly be possible that the entire universe is within the event horizon of a gigantic black hole formed by the gravity of all the stars and other objects within it combined.

Here is a link to an article mentioning a suggestion that the entire universe could be within a black hole.

[https://matrixdisclosure.com/black-holes-entire-universe-inside/#:~:text=Moreover%2C%20says%20a%20physicist%2C%20even%20our%20universe%20is,Hole%2C%20our%20particles%20would%20reach%20a%20parallel%20universe.[5]](https://matrixdisclosure.com/black-holes-entire-universe-inside/#:%7E:text=Moreover%2C%20says%20a%20physicist%2C%20even%20our%20universe%20is,Hole%2C%20our%20particles%20would%20reach%20a%20parallel%20universe.%5B5%5D)

> **Comments:**
> **username_0**: Golding,I greatly appreciate the comprehensiveness of your reply,backed with URL citations.As somebody from a country where the intellectual tradition is sparse,it is encouraging.I was also amazed you cited the notion the Universe could be part of a singularity created by the mass-energy in it;this concept was mooted in a previous colloquim in physics,but was laughed out of court.I'll get back to you shortly with som clarification.  
> **username_8**: @AnnexRemotelearn  I read abuut an idea the whole universe cold be a black hole as a rather far out idea long ago.  And here is a link to an article discussing whether the whole universe could be within a black hole.  https://matrixdisclosure.com/black-holes-entire-universe-inside/#:~:text=Moreover%2C%20says%20a%20physicist%2C%20even%20our%20universe%20is,Hole%2C%20our%20particles%20would%20reach%20a%20parallel%20universe.     I expect that the more scientific discussions of that idea would involve a lot of math.  
> **username_2**: " It may be possible that two neutron stars each with 2 solar masses could orbit each other closely enough to form an event horizon around the pair of neutraon stars." Can you provide a source or at least some reasoning for this? Just simply stating that it happens, as you did in your "Edit", is not sufficient...  
> **username_2**: Also, when you say that " And eventually, after they both became compact stars, their obit decayed enough for them to get close enough to form an event horizon around the pair.".... this is generally due to common envelope evolution which is observationally unavoidable, not due to some magical gravitational collapse scenario....  
> **username_8**: @Daddy Kropotkin  I wrote that "It may be possible".  I didn't write that it happens.  There is a big difference between writing that something might possibly or cceivably be possible and writing that it actually has happened, which requires that it is certainly possible.  
> **username_2**: And I'm simply asking you to justify why you think that is possible.  

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