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A problem with blackholes? Help me understand.

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qibbish

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Hello - I'm an undergrad studying physics and today, while tutoring a student on gravitational issues, I stumbled out of my depth. <br /><br />The student I was assisting asked if the earth would become a blackhole if compressed to the size of a ping pong ball and at first I entertained the possibiliy. After a moment, however, I corrected that view under the reasoning density = mass/vol, and gravitational attraction is based on mass and (inverse square) of radial distance. <br />In other words, no matter how much you alter the volume of an object its gravitational strength *per unit distance* stays the same, right?<br /><br />To say this again, the ping pong ball version of earth and the uncompressed version will exert the same gravitational effect at the same distance from the center - so if I stood 120,000 miles above the center of either they would exert the same pull, right? I say it like this because, due to the reduction in vol of the ping pong ball, the surface gravity would be more than our earth due to that surface being closer to the center. <br /><br />Anyhow, if this is right - and I assume it is not - then how can a star ever become a black-hole? If compression doesn't effect mass, and mass is all gravity is based upon, then where does the extra mass come from that tips the scale and warps space to such a degree that light can't escape? If that mass was present before the star went nova then shouldn't the pre-nova star have had the same gravitational field (or a greater one, as the nova ejects matter into space) ? <br /><br /><br /><br />
 
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thespeculator

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I would like to hear what the experts say as well.<br /><br />To my understanding you are correct. If you were to compress earth to that size and stand on it, you would feel more of a gravitational pull than you would if you could be inside of the earth that close to the center because then you would have matter surrounding you, pulling on you in all directions. So in concentrating all of those gravitational feilds to just below you, you would feel more force from them. <br /><br />Then again, the compression might induce fuson and cause it to ignite. Then if you were to somehow compress it to the size of the ball on a ballpoint pen, you might have sufficient gravitational density to make a black hole the size of a bb.<br /><br />I don't know though. I am but an undergrad myself, and not even one majoring in astronomy or physics. Engineering is my major.
 
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nexium

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I think the speculator gave a good answer. When you are below the surface of a planet, you get a close approximation of the gravity by subtracting the mass farther from the center than your location.<br />Earth likely has enough mass to make a bb size black hole, and the surface gravity would be something like a trillion g. Neil.
 
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derekmcd

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It has more to do with density and escape velocity than total mass. Even an atom can be crushed to create a blackhole. <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>
 
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yevaud

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As I recollect, there is no limit as to the mass of a Black Hole. Any amount of mass at all can form a black hole, as long as it's compressed to a suffiently high enough density. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>
 
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chriscdc

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Well the gravitational force between two objects is inversely proportional to te radius squared. <br /><br />The radius of the earth is on the order or 10^6 metres.<br />Let the earth mass blackhole have a radius of 10^-2 metres.<br />Therefore the force due to gravity will be approx (insert favorite joke about accuracy in cosmology) 10^16 times greater on the surface of the hole than on the surface or earth.
 
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qibbish

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So, what - according to newton or einstein - brings density into the equation of gravity? Isn't it based mainly on mass alone?<br /><br />Density = Mass/Volume.<br /><br />Gravitational attraction between two bodies depends on :<br /><br />the gravitational constant * (mass1 - mass2 / radial distance squared)<br /><br />Obviously deeper system exist, but what is it. What accounts for the gravity of a body to be proportional to the density of its mass and not merely its mass alone?<br /><br />I agree with what you're saying about the pull of matter surrounding you negating some of the downward pull that adds to weight, but escape velocities shouldn't have anything to do with it. A photon isn't effected by gravity directly due to being massless, right? Isn't it's effected by the warping of space- time itself (i.e. it travels on a straight path, but to us that path appears kinked due to space itself being warped). <br /><br />I hear where you're coming from - what with early last century "frozen star" theories and all, but I figured modern research had been moved by more recent theories.
 
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qibbish

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Thank you all for the enlightening discussion on my pupil's concepts, but the earth turning to a blackhole isn't really the crux of my question:<br /><br />My question is merely this - According to what I know of newtonian physics and relativity how can one argue that black holes exist if it's impossible for a star to gain mass through supernova. How does a star go from nova to blackhole without gaining mass? <br /><br />Now, it appears the answer involves density of matter - not just the mass of said matter, but I've never read anything in my textbooks that would account for that. <br /><br />So, if density of matter is crucial for the definition of the gravitational field then what is the equation for computing the gravitational force of a body? All that I've seen involve only the mass of an object.
 
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alokmohan

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When a star having more than three solar masses implode it turns to black hole.I find no cofusion.
 
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newtonian

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gibbish - When a star collapses into a black hole it is not gaining mass - that is the crux of your question and answer both.<br /><br />It is not the mass, but the small volume of the mass, that causes a black hole.<br /><br /><br />If a black hole had earth's mass, roughly, it would be exceedingly tiny (as an above poster calculated).<br /><br />The event horizon would also be a tiny radius.<br /><br />No where near our distance from earth's center of gravity.<br /><br />And, remember, as above posters noted, there is much mass on earth that would be outside the event horizon of an earth-mass black hole.<br /><br />For a black hole to exist, all the rquired black hole mass must be WITHIN the event horizon.<br /><br />To briefly answer your question - the star becomes a black hole even though some mass is lost because sufficient mass is comprssed to within the event horizon of said mass - i.e. within Schwartzchild (sp?) radius.<br /><br />BTW - I don't think we have confirmed earth-mass black holes. It would not be nearly enough mass to convert a neutron star to a black hole. Unless, of course, we are talking about the origin of our universe where density was sufficient for any variant fractions of small masses due to small volumes to become tiny black holes of earth-mass or even much less mass.<br />
 
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willpittenger

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I suspect the original poster is confused becuase you are only talking 3 solar masses. I believe that the 3 solar masses part comes into play AFTER the supernova happens. If the mass is still more than that, you get a black hole. <div class="Discussion_UserSignature"> <hr style="margin-top:0.5em;margin-bottom:0.5em" />Will Pittenger<hr style="margin-top:0.5em;margin-bottom:0.5em" />Add this user box to your Wikipedia User Page to show your support for the SDC forums: <div style="margin-left:1em">{{User:Will Pittenger/User Boxes/Space.com Account}}</div> </div>
 
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el_naso

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Hi, I´m not very fond in phisics (nor in english, I´m a student so please forgive the little mistakes).<br /><br />Ok, as far as I understand this matter it´s all a problem of how density affects gravity.<br /><br />So imagne it like Einstein did: imagine a 3d universe as a 2d universe. You´ll get something like an elastic gauze (be imaginative). Now put something heavy on that gauze, say, a bowling ball. Such heavy object should leave a notch (forgive the dictionary language).<br /><br />What we do next is put another objet over the gauze, this time, somthing much more dense, but with the same mass, this would be our bh. Let´s say this object is a the tiny ball of a pen, only this time, as heavy as the bowling ball.<br /><br />So, (correct my if I´m wrong, again, all this is what I know, not what I understand, but enough of philosophy) the "notch" left should be the same radius than the one left by the bowling ball but a lot deeper.<br /><br />Also, if u stand orbiting the bh at the same distance the earth´s surface previously was you should feel the same gravity, but get a little closer and...
 
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qibbish

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Thank you for all the detailed posts written thus far, but one question still remains for me. I understand that density is the key to understanding this situation, but what confuses me is that density is NO WHERE near newtonian takes on gravity, just mass.<br /><br />Let me put this in a clearer context. I'm a physics student. As a physics student I'd like to understand where the density argument comes in. Newton's laws of universal gravitation don't make mention of volumes or densities, so was it through general relativity? If so, can somebody point me to that aspect of it. <br /><br />I grew up with the universal law of gravity explained as G * (m1 -m2 / d^2) where G is the constant, m1 is mass one and d^2 is radial distance squared. <br /><br />This does not take density into effect, so must be wrong - right?<br /><br />Again, my problem is that I'm refusing to accept "common knowledge" but rather am attempting to frame everything in physical properties and equations. Further more, I realize an application of newtonian physics is quite dated, but my post is really based on suprise that newtonian physics can't explain blackholes and a wish to uncover what (specifically) does. <br /><br />I really don't care about earth black holes at all, and only brought that up to explain what brought me to re-examine something I felt I understood.
 
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dragon04

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The gravity of a 5 solar mass BH is very close to the same mass as the original 5 solar mass star that created it.<br /><br />The key to the issue is what happens on both sides of the event horizon.<br /><br />Think about this. Take a 10KG bowling ball and put it in the middle of a 100 m^2 sheet of latex. I will warp the surface of that latex in a certain way.<br /><br />Now. Take that same 10KG bowling ball and make it the size of a pea. It will deform the latex in a different way. The inward curvature will be a smaller diameter, but much deeper.<br /><br />Its mass has not changed. But its expression relative to the latex sheet has. We took a mass and simply made it more dense.<br /><br />In either case, if we roll a ball at a specific velocity across the latex sheet, there is a defined distance at whic the ball will not be able to roll past and will fall to the center of the depression.<br /><br />And in either case, we define an "event horizon". The density of the object merely defines the size of the curvature of space around it and the relative proximity we can be before we can't roll past. <div class="Discussion_UserSignature"> <em>"2012.. Year of the Dragon!! Get on the Dragon Wagon!".</em> </div>
 
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dougum3882

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Qibbish, remember that blackholes were predicted as a consequence of Einstein's theory of gravity, not Newton's theory of gravity. Newton's theory simply gives you a way of calculating the gravitational force between bodies of given mass at a certain distance from each other, but it doesn't say anything about what each mass does to the space around it. A blackhole is a blackhole, not because of its gravitational effect on the objects around it, but because of its effect on the space around it. Newton's theory doesn't include density which is why blackholes weren't theorized by physicists using Newton's theory of gravity. Einstein's theory say that mass curves space and that if space is curved enough then you will have a blackhole. But what makes mass curve space enough to have a blackhole is when that mass is compressed into a small enough space (large mass in a small volume gives large density).
 
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chriscdc

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(Gm1m2)/r^2 models both masses as point sources therefore density is not factored in.<br /><br />With a non point source then density would describe the amount of mass per unit volume, thus allows you to calculate gravitational potential per unit volume. Then you can then work out the total force on a particle at a certain point.<br /><br />A star thus can stay a star as the density is lower, thus the force on the particles are lower as they are further away. As the force is inversely proportional to r^2 then such a change in distance has a large effect on the force between them.
 
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newtonian

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dougum3882 - That's part of it - but you skipped "c." Newton did not factor in "c," if I remember correctly. <br /><br />As in E=mc^2<br /><br />When gravity is strong enough it slows light and bends it back into the black hole - please correct me if I am wrong.
 
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newtonian

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gibbish - Your post stimulated my sense of humor:<br /><br />I grew up with the universal law of gravity explained as G * (m1 -m2 / d^2) where G is the constant, m1 is mass one and d^2 is radial distance squared. <br /><br />This does not take density into effect, so must be wrong - right? <br /><br />OK, I'll try to answer:<br /><br />Wrong!<br /><br />Right?<br /><br />I believe the formula is right, which is why I answered wrong right in contrast to your right which is wrong!<br /><br />Er - I mean I answered right not wrong even though my answer was wrong which is why it was right.<br /><br />Now that I have appeased my sense of humor, I will stop using right and wrong:<br /><br />The formula is correct - as another poster noted this is simplifying by using the masses as point sources - which would be the center of gravity.<br /><br />Black holes still have the same gravity as a star of the same mass - right? <br /><br />Unless, of course, you come too close!<br /><br />The effect changes for a star vs a black hole of the same mass once one reaches the radius of the star. After that, Newton's formula oversimplifies as it does not take into account the variant directions of different portions of the star's total mass - that difference is newtonian and does not need relativity to explain - though relativity will give more precise numbers.
 
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yevaud

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Everyone has been dancing around this.<br /><br />The key to the problem is the dichotomy of Internal Electron Degeneracy Pressure and Neutron Degeneracy. By sheer amount of mass being "packed" into such a small region, these are both overcome, resulting in an Earth mass black hole, despite the fact that this violates the routine standard of the Chandrasekhar Limit.<br /><br />This is where density is key, and violates what we have observed. There are no known Earth Mass Singularities (that we know of), but it's not prohibited. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>
 
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dragon04

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<font color="yellow"> This is where density is key, and violates what we have observed. There are no known Earth Mass Singularities (that we know of), but it's not prohibited. </font><br /><br />Great point. And to that point, what <b>natural</b> forces or energies known at this time could create an Earth mass BH?<br /><br />We know that gravity is a Weak Force. And we also know how much mass is required in order for gravity to be a player in the creation of a BH. <br /><br />It would appear to me that barring some incredible leap in quantum knowledge that Earth mass BH's are theoretically impossible as a result of any <b>natural</b> process.<br /><br /><br /> <div class="Discussion_UserSignature"> <em>"2012.. Year of the Dragon!! Get on the Dragon Wagon!".</em> </div>
 
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Saiph

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2 main questions: how does a star get enough mass to form a bh, and how does density fit in (since it isn't mentioned in the equations).<br /><br />1) When a massive star dies (~8 solar masses and up) it undergoes a supernovae explosion. This explosion sheds a lot of the stars mass, but not all. If whats left near the core is ~3 solar masses or less...the core will collapse into a neutron star. It will collapse until neutron degeneracy pressure is enough to counter the gravity of the dead core. No other mechanism between this neutron degeneracy, and the state the core was in before the explosion, will suffice (since fusion doesn't work anymore).<br /><br />If the remnant core is />3 solar masses...not even this degeneracy pressure suffices, and it continues to collapse until another force arises to stop it. To date, there is no known mechanism to supply such a force...so it collapses completely, to form a BH.<br /><br />2) Density comes into gravitation "implicitly". I have two equal masses, each less than 1 meter in radius. One is more dense than the other. At one meter...which one has a greater gravity? Ans: neither, they have the same (same m's same r in F=GMm/r^2).<br /><br />But, which one has a greater gravity on the surface of the object? Ans: the denser one. At the surface, they both have the same mass (as all the mass for each object is still "below" the test particle). However, the denser object has a smaller radius to it's surface, so R is smaller, giving a higher "surface" gravity.<br /><br />This applies to BH's, because once the "surface gravity" is strong enough, it bends light back on itself, and you get a BH. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>
 
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newtonian

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Yevaud and Dragon04 - I suspect that natural forces may have existed at the origin of the universe that would have allowed the creation of earth-mass black holes. [Also supernatural forces, btw.]<br /><br />Is there a lower limit for mass of a mini-black hole assuming a radius of less than Planck length is possible?<br /><br />The density for a very brief time after the big bang, especially if not uniform, perhaps could have allowed this.<br /><br />However, wouldn't these more dense masses have been propelled FTL (faster than light) to beyond our visibility horizon so that we would not see them - at least for the most part? [Before general FTL inflation]<br /><br />Alternately, could mini-black-holes make up a part of dark matter???
 
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