JohnFerkany Posted January 20, 2012 Report Posted January 20, 2012 I'm a pharmacologist not a physicist but I've always had a popular level curiosity about QM and cosmology. Question - Black holes are defined as a singularity surrounded by an EH. They can have different masses and this will effect their "size." However, the word "size" applies to the EH and not the BH itself which is a singularity. Given a singularity is a point, and points have no associated dimensions, can 2 BHs really "collide?" Consider the question from the perspective of having 2 naked singularities (if these in fact exist). Could 2 naked singularities actually "collide?" Cheers Quote
maddog Posted January 21, 2012 Report Posted January 21, 2012 I'm a pharmacologist not a physicist but I've always had a popular level curiosity about QM and cosmology. Question - Black holes are defined as a singularity surrounded by an EH. They can have different masses and this will effect their "size." However, the word "size" applies to the EH and not the BH itself which is a singularity. Given a singularity is a point, and points have no associated dimensions, can 2 BHs really "collide?" Consider the question from the perspective of having 2 naked singularities (if these in fact exist). Could 2 naked singularities actually "collide?"As I understand it - the current conventional wisdom is that "naked singularities" "should not" exist, as it would be bad for the universe if they did.What I have italicized of your post is "not quite" correct. A Black Hole would even itself not be a "single point". Instead it would a judiciously "small" radius -- kind of like the small epsilon value in Calculus (in case you took that) just small enough to be good enough and not be zero. The reason/justification for this being valid is because of angular momentum because the Black Hole is rotating (it is not thought that all Black Holes rotate). So even though the singularity is within the Event Horizon would still have nonzero radius just greater than zero. This allows density to be a finite value and the universe is saved from oblivion. As for your other comment about Black Holes colliding, it is thought they do. Since now it is conventional to think all Galaxies have BH at their centers, that when Galaxies collide the larger will acquire the smaller. Eventually likely that their respective center will also collide. Best example I can think of is M87. Great question. B) maddog Quote
CraigD Posted January 21, 2012 Report Posted January 21, 2012 Welcome to hypography, John! :) For selfish reasons, I and I imagine many others hope you spend some good time here in the future – pharmacology is a very cool scientific professions and frequent topic of discussion, which having input from a pro would almost surely improve. Black holes are defined as a singularity surrounded by an EH. They can have different masses and this will effect their "size." However, the word "size" applies to the EH and not the BH itself which is a singularity. Given a singularity is a point, and points have no associated dimensions, can 2 BHs really "collide?"First, be careful with this definition. According to classical physics, extended in the modern fashion by relativity, and using a semi-classical model of sub-atomic matter, all the mass in a black hole must be contained in a singularity – a spherical volume with zero radius – but I don’t think hardly any physicist believes this to be physically real. Best speculation is, at sufficiently great density, the gravitational interaction ceases to behave in the classical approximation or according to general relativity, so what’s in the center of a black hole is best described as “a quantum weirdness of non-zero volume”, called by some “quantum foam”. Since information about the inside of a black hole can’t, with some possible, limited exceptions, leak out past its event horizon, directly observing this weird not-a-singularity would seem to be impossible. Consider the question from the perspective of having 2 naked singularities (if these in fact exist). Could 2 naked singularities actually "collide?" With the previous caution about belief in literal physical singularities in mind, replacing “singularity” with “center of mass”, this question can be inverted to ask “can the masses of 2 black holes orbit one another, or in some other way remains spatially separate, within a single event horizon?” Surprisingly, the answer to this question is a resounding “maybe”. Various calculations suggest, tentatively, that orbits within the event horizon of a black hole are possible. One of several papers on the subject, a recent one, is Is there life inside black holes? by Vyacheslav I. Dokuchaev. If this speculation is wrong, or for failed orbits if it is right, collisions of matter within a black hole are, I suspect, weird, quantum physics-dominated phenomena. Moontanman 1 Quote
johnferk Posted January 23, 2012 Report Posted January 23, 2012 Thanks folks. If I understand the responses correctly, it boils down to the idea that it is a singularity with a non-zero radius. That leads into a further question - are all BHs the same size (note - I am not referring to the Schwarzschild radius which varies according to the mass of the B). I am referring to the entity that exists at the center of the BH which is the BH itself. One commonly reads that a BH has "infinite" density. My understanding (non sequitur) of "infinite" is that one "infinite" is identical to any other "infinite." If that is true, a micro BH generated in the LH Collider would have the same "infinite" density as a super massive BH at the center of a quasar notwithstanding the observation that the absolute mass of the two entities are radically different. That leads to the logical endpoints that the two DHs a)have different non zero and measurable radii thus allowing for a super dense but finite density, or B) there exists "large" and "small" infinite densities (which begs the question of the meaning of "infinite." Is that question clear as mud? Quote
sigurdV Posted January 23, 2012 Report Posted January 23, 2012 Thanks folks. If I understand the responses correctly, it boils down to the idea that it is a singularity with a non-zero radius. That leads into a further question - are all BHs the same size (note - I am not referring to the Schwarzschild radius which varies according to the mass of the B). I am referring to the entity that exists at the center of the BH which is the BH itself. One commonly reads that a BH has "infinite" density. My understanding (non sequitur) of "infinite" is that one "infinite" is identical to any other "infinite." If that is true, a micro BH generated in the LH Collider would have the same "infinite" density as a super massive BH at the center of a quasar notwithstanding the observation that the absolute mass of the two entities are radically different. That leads to the logical endpoints that the two DHs a)have different non zero and measurable radii thus allowing for a super dense but finite density, or B) there exists "large" and "small" infinite densities (which begs the question of the meaning of "infinite." Is that question clear as mud? Looking at set theory there are infinites of different size in the sense that their elements cant be paired... but I doubt infinitudes has any physical significance. Quote
joekgamer Posted January 24, 2012 Report Posted January 24, 2012 My understanding (non sequitur) of "infinite" is that one "infinite" is identical to any other "infinite." There are an infinite number of both integers and real numbers, yet aren't there more real numbers than integers? In fact, each integer has an infinite number of real numbers that can be created from it by adding more places to the right of the decimal point. Thus, for each of the infinite number of integers there is an infinite number of real numbers that share its digits to the left of the decimal point. From this, it can be concluded that there are indeed more real numbers than integers. This contradicts your above claim that each "infinite is identical to any other infinite." Hope this helped. Quote
CraigD Posted January 25, 2012 Report Posted January 25, 2012 Thanks folks. If I understand the responses correctly, it boils down to the idea that it is a singularity with a non-zero radius.“A singularity with a non-zero radius” is a contradiction in terms. What we’re discussing, I think, are the mutually exclusive predictions that the mass that produces a black hole is contained within space of zero volume – a singularity, and the prediction that it is contained within a space of non-zero volume – not a singularity. That leads into a further question - are all BHs the same size (note - I am not referring to the Schwarzschild radius which varies according to the mass of the B). I am referring to the entity that exists at the center of the BH which is the BH itself.If we assume that the mass of a black hole is a singularity, then yes, as all singularities are spheres of radius 0, all are the same size. If we assume otherwise, then no. One commonly reads that a BH has "infinite" density.It’s common to write that a non-zero mass singularity has infinite density – this NASA website for students 14 and over, for example, flatly states that sufficiently massive stars collapse into infinite density singularities surrounded by event horizons and called black holes. I would say that site oversimplifies to the point of most likely being wrong – not necessarily a bad thing, pedagogically, as when teaching, it’s often more important to nurture thinking and avoid bewildering the student than to avoid technical falsehood. It’s interesting, especially in light of calculations such as Dokuchaev’s, to consider the average density of a black hole, that is, its mass divided by the volume within its event horizon. I find this table, which I made years ago, helpful:Body M (kg) r (m) F (N) D (kg/m^3) Proton 1.66e-27 2.46e-54 9.14e71 2.66e133 About 3 gold atoms Planet 1e25 1.48e-2 1.52e20 7.33e29 Star 1e31 1.48e4 4.10e10 7.33e17 3 M SM 6e34 8.89e7 1.14e3 2.04e10 Survivable spagetification 1e36 1.48e9 4.10e0 7.33e7 Milky way's SMBH 8e36 1.19e10 6.40e-2 1.15e6 Globular Cluster (5M SM) 1e37 1.48e10 4.10e-2 7.33e5 40 M SM 8e37 1.19e11 6.40e-4 1.15e4 50 M SM 1e38 1.48e11 4.10e-4 7.33e3 130M SM 2.6e38 3.85e11 6.06e-5 1.08e3 About water density, about mass of Andromeda's SMBH 8e39 1.19e13 6.40e-8 1.15e0 About density of air at sea level 1e9 SM 1e40 1.48e13 4.10e-8 7.33e-1 Largest observed supermassive black hole Galaxy 1e42 1.48e15 4.10e-12 7.33e-5 3e52 4.45e25 0.00e0 8.15e-26 Universe 1e53 1.48e26 0.00e0 7.33e-27 (4.4e26) (6e-27) Critical density of open/closed Friedmanm universeNotice that the average density of some known black holes is less than that of the air, and that, intriguingly to me, the average density of the visible universe, that of a very hard vacuum, is about that of a black hole with an event horizon (Schwarzschild) radius about the same as the radius of the visible universe, suggesting that our entire universe may actually be a black hole. My understanding (non sequitur) of "infinite" is that one "infinite" is identical to any other "infinite." If that is true, a micro BH generated in the LH Collider would have the same "infinite" density as a super massive BH at the center of a quasar notwithstanding the observation that the absolute mass of the two entities are radically different. That leads to the logical endpoints that the two DHs a)have different non zero and measurable radii thus allowing for a super dense but finite density, or B) there exists "large" and "small" infinite densities (which begs the question of the meaning of "infinite."I wouldn’t worry too much about the importance of calculated densities for various black holes and models of them. What is good to contemplate when considering such ideas as tiny black holes created by artificial means such as particle accelerators, or natural ones such as cosmic rays, is why we don’t find such little black holes, and why they don’t grow into big ones. The most accepted explanation is because of Hawking radiation, which calculates that all black holes actual radiate, but that unlike ordinary light sources like stars, whose luminosities are roughly proportional to their square of their radii, their luminosity is inversely proportional to the square of the Schwarzschild radii. Thus, very small black holes are very luminous, so much so that they radiate all of their mass energy, “evaporating” so quickly that their being black holes is more a intermediate stage of whatever event briefly produces them than a lasting state. All observed black holes, which are at least on the order of the mass of a star, have such low hawking radiation luminosity that they lose mass from radiating more slowly than they gain it from absorbing infalling cosmic background radiation, so will effectively never evaporate. Somewhere between micro-black holes that exist for only tiny instants and star and greater-mass ones that will exist practically forever, there could be “Goldilocks” (not too large, not too small) black holes, formed early in the history of the universe, with masses on the order of the Moon’s, that will evaporate about now. Some astronomers believe that events such as gamma ray bursts may be such black holes reaching the final, brightest seconds of their lifetimes, though these hypothesis are very speculative. Quote
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