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taylordnz
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if a black hole has infinite density wouldn't that mean it has infinite mass because its equation is
volume x mass = density
whats your opnion
volume x mass = density
whats your opnion
if a black hole has infinite density wouldn't that mean it has infinite mass
taylordnz said:if a black hole has infinite density wouldn't that mean it has infinite mass because its equation is
volume x mass = density
whats your opnion
Integral said:We have no concrete knowledge of what happens inside the event horizon of a black hole. Any comments on the physical dimensions of the mass inside the event horizon are pure speculation. We can only know the total mass from exterior measurements not the configuration of the mass, only that it is contained within the radius of the event horizon.
No so. The only thing we can say today is exactly what Integral posted. There is no solution in either GR or QM that we can be certain of that yet "stands the test".jcsd said:Ah yes, but the Scwarzchild solution can be extended into the event horizon right up to the singularity, so if we assume general relativity is correct we have a resoanble idea what's going on in there.
Yu can be certain that GRvstands the except when microscale physics become important. The problem is if you reject GR then there's not much point in talking about black holes anyway. It is reasonable to assume that GR holds within certain parameters.Labguy said:No so. The only thing we can say today is exactly what Integral posted. There is no solution in either GR or QM that we can be certain of that yet "stands the test".
The "test" to which I was referring is at the "microscale" you mention. There is no way I would reject GR. In fact, I have all my money on the bet that all the "other experiments" about to be conducted (LIGO, etc.) will all confirm GR to the point where any doubters will have to concede. Since 1919 there have been too many confirmations on so many areas (predictions) of GR that I don't believe it is possible for it to fail, in as far as it went.jcsd said:Yu can be certain that GRvstands the except when microscale physics become important. The problem is if you reject GR then there's not much point in talking about black holes anyway. It is reasonable to assume that GR holds within certain parameters.
Orion1 said:
The BH density is determined from its photosphere, not its event horizon.
Although there is a radial Schwarzschild Solution in classical GR, BH density cannot be determined from this radial solution, because non-rotating event horizons do not exist.
The mass of a Chandresekhar BH is:
[tex]M_c = 1.457 M_o[/tex]
The radial solution for a spherically symmetric Chandresekhar BH photosphere is:
[tex]r_c = \sqrt[3]{ \frac{3 M_c}{4 \pi \rho_c}}[/tex]
The radial solution for a spherically symmetric gravitational BH photosphere is:
[tex]r_g = \frac{G M_c}{c^2}[/tex]
QM/GR shutdown:
[tex]r_c = r_g[/tex]
[tex]\sqrt[3]{ \frac{3 M_c}{4 \pi \rho_c}} = \frac{G M_c}{c^2}[/tex]
Density solution for spherically symmetric gravitational Chandresekhar BH:
[tex]\rho_c = \left( \frac{3c^6}{4 \pi G^3 M_c^2} \right)[/tex]
This density formula does not violate QM or GR and exists at QM and GR 'quantum shutdown'.
For densities at [tex]r_c < r_g[/tex] a formula must be demonstrated that does not violate QM or GR.
College Physics 101 - Entrance Examination:
Based upon the Orion1 Equations:
What is the mass of a Chandresekhar BH?
What is the radius of a Chandresekhar BH photosphere?
What is the density of a Chandresekhar BH?
Sorry, but you failed to qualify for this course.
The "density" of a BH isn't measured from its event horizon. We can't see or measure an event horizon radius. The only way we can arrive at an Rs is to know the BH mass. From the mass we use the classical [tex]\frac{2GM}{c^2}[/tex] to get the Rs, and, as you stated, [tex]\frac{3GM}{c^2}[/tex] for the photon sphere. As an aside, the "Oppenheimer" limit (there are several other names too) is 3.2 Ms instead of the 4 mentioned in an earlier post.jcsd said:I don't see the relevnace tho' to the topic, the 'density' of a balck hole is usually measured from it's event horizon, out of interest the radius of a Scwarzchild black holes photon sphere is simply:
[tex]\frac{3GM}{c^2}[/tex]
I'm not sure you can say that the black hole has any kind of photosphere as that is to do with the optical properties of a star, I suppose the venet horizon would be the nearest analogy to a photosphere.
Labguy said:The "density" of a BH isn't measured from its event horizon. We can't see or measure an event horizon radius. The only way we can arrive at an Rs is to know the BH mass. From the mass we use the classical [tex]\frac{2GM}{c^2}[/tex] to get the Rs, and, as you stated, [tex]\frac{3GM}{c^2}[/tex] for the photon sphere. As an aside, the "Oppenheimer" limit (there are several other names too) is 3.2 Ms instead of the 4 mentioned in an earlier post.
And, knowing the mass, therefore the EH and photon sphere radius, still tells us nothing at all about density of or in a BH since the EH is simply an "area of influence" defined by the math above. Density is and would be where there is a measurable quantity of matter (the mass) and a defined volume, Planck size or larger. As Integral mentioned in an earlier post, no sense guessing because we don't have the means to peer inside any Event Horizon for any information at all other than that it exists.
Lastly, since there can be no "static" (non-rotating) black holes, why do the excercises in static math, unless it is a fun or practice thing?
But, Weinberg put forth that the pressure (P) must also be taken into account when trying to estimate a BH "density". I see no value for P anywhere above. Also, as pointed out in a past PF post, the "mass divided by volume" version doesn't work for a BH when you are just considering V to be the (Rs)3 because the "volume" in a BH is not just governed by our 3 dimensional spatial conditions, and a BH therefore has no meaningful volume! Your "any region of space" comment would not apply to a BH as the "region" is unknown. Exactly where is the GR "breakdown" that Integral mentioned? I don't know, do you?jcsd said:If you ever read in a textbook about the denisty of a black hole it means it's mass over the volume of the sphere formed by the event horizon. It is a term that is used. Yes I am awrae that 4 is just an approximation of the acutal limit which is nearer 3, but the absolute limit is affected by svereal factors
I don't think you uunderstand, the density, or average density if you prefer of any region of space is merely it's mass divided by it's volume. Talking about the density of a black hole does not imply anything about it's 'structure' or the distribution of mass in the region. As I said earlier you can be sure if someone is talking about it's black hole they are talking about the density of the region bounded by it's event horizon.
Agreed, there are no "theoretical barriers to Schwarzschild black holes", just practical barriers since they don't exist, as you just acknowledged. Have you ever heard of any case where a star had no angular momentum?jcsd said:I really don't get your point, are you saying thaty the Schwarzschild solution has no practical applications? This is not the case as it can provide a good approximation in many cases where the angular momnetum is low. There's ceratinly no thepretica barrier to Schwarzschild black holes, it's just that we should expect to see Kerr black holes form as stars in just about all cases have angular momentum.
Labguy said:But, Weinberg put forth that the pressure (P) must also be taken into account when trying to estimate a BH "density". I see no value for P anywhere above. Also, as pointed out in a past PF post, the "mass divided by volume" version doesn't work for a BH when you are just considering V to be the (Rs)3 because the "volume" in a BH is not just governed by our 3 dimensional spatial conditions, and a BH therefore has no meaningful volume! Your "any region of space" comment would not apply to a BH as the "region" is unknown. Exactly where is the GR "breakdown" that Integral mentioned? I don't know, do you?
there are no "theoretical barriers to Schwarzschild black holes", just practical barriers since they don't exist, as you just acknowledged. Have you ever heard of any case where a star had no angular momentum?
My questions above are rhetorical and I wouldn't actually expect an answer. If you did answer I probably really wouldn't understand, any more than Orion1 really understands... :surprise:
It is a vacuum fluctuation pressure, not the "gas law" type. I'm sure there is a link somewhere but I wouldn't know. Sometime, I actually post things from memory without relying on the internet. I used to read a few books and have a "near" photographic memory. Just haven't read enough books to be an expert on anything...What kind of pressure i.e. some sort of link?
To what little I know, what practical applications when applied to only a static BH?No, but it doesn't stop the Scwarzchild solution from having practical applications.
You have no way of knowing what I (or Orion1) do or do not understand. Are you suggesting that on this subject you are the only one who does understand? If so, collect your Nobel prize.But that is beacuse you don't understand, I'm not introducing any new concepts...
Yes, when generalities are thrown out as gospel I will tend to nit-pick. Stellar evolution is much more specific and complicated than the generalities you will find in almost any single book or website; they are simplified by necessity. Past examples are when I nit-picked on the statement that "accreting white dwarf stars will become a Type Ia supernova when the mass exceeds 1.44 solar masses". That isn't even close to accurate. Another was that "a BH can only emit one virtual particle from a pair since the other particle must fall back into the EH to return the borrowed energy". That isn't correct either. The (my) posts on these and other nit-picks can be found somewhere in past PF posts by a search, I assume. Ask Marcus and a few others if my nit-picking explanations were correct or not. They were.... and I really don't see the point to any of your posts as they're just based on nit-picks that are irrelevant to the my posts.
No, there isn't. Especially when one party totally relies on just one point of view (theory as yet) out of several plausable theories that will all have merit for consideration until more research and information bolsters one and/or rejects others. I try to stay open-minded for now until we know more, much more, than today.I mean is there really any point to this?
A black hole is a region in space where the gravitational pull is so strong that it prevents anything, including light, from escaping. This creates a dark, empty space with a high concentration of mass.
Scientists use a variety of techniques to explore the density and mass of black holes, including observing the effects of their gravitational pull on nearby objects, analyzing the radiation emitted from the black hole, and using mathematical equations to calculate their properties.
Scientists use a variety of tools and technology to study black holes, including telescopes, x-ray detectors, and computer simulations. They also use advanced mathematical and scientific theories, such as general relativity, to understand the behavior of black holes.
Studying black holes allows scientists to gain a better understanding of the fundamental laws of physics and the behavior of matter in extreme conditions. It also helps us to understand the formation and evolution of galaxies and the universe.
No, it is currently not possible for humans to physically explore a black hole due to the extreme conditions and immense gravitational pull. However, scientists continue to develop new technologies and theories to further our understanding of these mysterious objects.