Singularity Definition and 433 Threads

A gravitational singularity, spacetime singularity or simply singularity is a location in spacetime where the density and gravitational field of a celestial body is predicted to become infinite by general relativity in a way that does not depend on the coordinate system. The quantities used to measure gravitational field strength are the scalar invariant curvatures of spacetime, which includes a measure of the density of matter. Since such quantities become infinite at the singularity point, the laws of normal spacetime break down.Gravitational singularities are mainly considered in the context of general relativity, where density apparently becomes infinite at the center of a black hole, and within astrophysics and cosmology as the earliest state of the universe during the Big Bang/White Hole. Physicists are undecided whether the prediction of singularities means that they actually exist (or existed at the start of the Big Bang), or that current knowledge is insufficient to describe what happens at such extreme densities.General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed. The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner. The termination of such a geodesic is considered to be the singularity.
The initial state of the universe, at the beginning of the Big Bang, is also predicted by modern theories to have been a singularity. In this case, the universe did not collapse into a black hole, because currently-known calculations and density limits for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not necessarily apply in the same way to rapidly expanding space such as the Big Bang. Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.

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  1. C

    History Technological Singularity vs Zoological History

    Fellow nerds will probably find the following blog post of great interest. EDIT: Removed link It is an alternative analysis with respect to Kurzweil's technological singularity proposal. Essentially anyone interested in topics like history in general and futuristic predictions will not...
  2. J

    Do We Really Understand the Singularity?

    How much do we know about the singularity? It's properties, size, weight? I understand it contained all the matter in the universe but do we know how much matter that amounts to in numerical terms? I understand it was incredibly unstable so how could it exist in the first place?
  3. M

    Singularity in Astrophysics: Meaning & Etymology

    Hi there, I need to know why a singularity in astrophysics is called a singularity. I have a general idea about what a singularity is but I am yet to find out which of the more commonplace meanings of the word the originator of this term had in mind when s/he used it in the context of...
  4. I

    Can a Black Hole Have Angular Momentum?

    A black hole is a singularity at which the curvature of spacetime becomes infinite. I understand that when a star collapses it can have a net angular momentum, but when it collapses down to a 0-dimensional singularity, what does it mean for that to have angular momentum? Thanks
  5. M

    Proving z0 is an Essential Singularity of ef(z) | Singularity Homework

    Homework Statement Show that if z0 is an isolated singularity of f(z) that is not removable, then z0 is an essential singularity for ef(z).Homework Equations z0 is a pole of f(z) of order N iff f(z) = g(z)/(z-z0)^N, where g is analytic at z0 and g(z0) is not 0, iff 1/f(z) is analytic at z0 and...
  6. F

    Partial fractions and singularity point

    Hi, I have a question regarding partial fractions. One of my Math lecturers said that to find partial fraction, we are actually finding the singularity points. I don't understand what happens at a singularity point that allows us to decompose a function into the sum of two other functions...
  7. E

    Radius of Ring Singularity in Kerr Black Hole

    I researched this some, but could not find a method to calculate the radius of the ring singularity in a Kerr black hole. I would think it is a function only of black hole mass and angular velocity. Please let me know if there is some reports or papers on this.
  8. E

    Singularity or just a very small, massive shell?

    The nature of a black hole is that gravity attracts objects at a speed faster than light making it impossible for them to be able to escape but if the object is accelerating towards the black hole it would slow down and become more massive the close it got because it is approaching the speed of...
  9. M

    Can the Casimir Effect prevent the formation of singularities in black holes?

    *Disclaimer: I do not claim to be knowledgeable quantum mechanics past amateurism. I'm just interested in the topic.* I had a thought during Classical Mechanics Physics class two days ago on the nature of singularities in black holes. I realized-at least in my speculation-that singularities...
  10. G

    Would artificial intelligence and singularity mean the end of humanity?

    If you haven't seen the TIME article: http://www.time.com/time/magazine/article/0,9171,2048299,00.html So what exactly would happen if AI became more intelligent than any human that could ever exist? What would stop such a machine from creating another machine more intelligent than itself ad...
  11. A

    A Singularity: Finite Function, Infinite Derivatives

    Hi, Do you know the name of this kind of singularity at A ? The function is finite but the left derivative is +\infty and the right derivative is -\infty. http://shareimage.org/viewer.php?file=mt79897bbpxxse1v8pzb.jpg Thanks
  12. J

    Eliminating the Euler Angle singularity without quaternions?

    Hi all, I've formulated using Lagrangian formalism the equations of motion for a spinning top. I know about the gimbal lock/singularity that occurs at theta=0 and I was wondering if there was any other way to do it without dwelving into quaternions. Yogi published a paper "A Motion of Top...
  13. C

    Could black holes form without a singularity?

    This is not a question - more a topic of discussion; as I am not expecting definitive answers. At the center of black holes we stipulate singularities, now I understand that mathematically a singularity does not make sense; infinite density and zero spatial volume being irreconcilable and an...
  14. bcrowell

    Empirical verification of conditions for Hawking singularity theorem when Λ≠0?

    As far as I know, the classic paper applying the Hawking singularity theorem to our universe is this one: Hawking and Ellis, "The Cosmic Black-Body Radiation and the Existence of Singularities in Our Universe," Astrophysical Journal, vol. 152, p. 25, 1968...
  15. B

    Residue of a complex function with essential singularity

    Homework Statement Hello friends, I'm a student of mechanical engineering and I have a problem with computing residues of a complex function. I've read some useful comments. Now I ve got some ideas about essential singularity and series expansion in computing the residue. However, I still...
  16. Y

    Understanding Singularity: Zero Mass, Infinite Density

    Can somebody please explain to me the idea of zero mass and infinite density, my mind just is not comprehending it, it seems almost illogical to me. Please help my brain make sense of this. Non-mathemetical please as I am not part of the scientific community. If the answer is just a simple...
  17. bcrowell

    Defining the dimension of a singularity?

    In general, how do you define the dimension of a singularity? E.g., we think of a Schwarzschild singularity as pointlike, so that its world-line is one-dimensional, and on a conformal diagram we represent it as a spacelike line, which seems to make sense. In point-set topology, we have...
  18. D

    Size of a Singularity: Exploring Mass & Diameter

    We are told that at the centre of a black hole lies a singularity; very small and very heavy. We here a lot about the mass but not the size (diameter) of this object,I asume this is not zero So, incredibly tiny though it may be , it would still bel greater than 0. Questions;- What then is the...
  19. B

    Would gravitational time dilation prevent Singularity in a black hole?

    In the current mainstream theory of black holes, there exists a singularity of infinite density. However, it seems to me that matter actually could not compress tightly enough to reach this point. As matter coalesces in a black hole, space-time would increasingly curve. As the density...
  20. R

    Integral equation with endpoint singularity

    I am trying to solve this integral equation numerically. The kernel has a singularity at the endpoint 1. Any suggestions?? f(s) = \int_0^1 \frac{1+st}{(1-st)^3} f(t) dt
  21. N

    What is the difference between singularity and infinity in QTF theo?

    Please teach me this: What is the difference between singularity and infinity points.Because we often encounter with infinity counterterms in QTF theory,but trying to avoid the singularity counterterms. Thank you very much in advanced.
  22. A

    Is f(x) = (x2 + 2)/x a removable singularity?

    Find any singularities in the following,say whether they are removable or not f(x) = (x2 + 2)/x Attempt at a solution when f(0) = ((0)2 + 2)/0 =2/0 which isn't defined So 0 is a singularity
  23. M

    What Happens at a Black Hole Singularity?

    I have read that inside a black hole there is a point called "singularity", where all the laws of physics break down. But exactly what does that mean?
  24. camipol89

    Particle falling into a black hole singularity within a finite proper time

    Hello, Can anyone help me with that? It's a problem taken from Wald book on General Relativity,in the section of Schwarzschild solution Thanks Show that any particle (not necessarily in geodesic motion) in region II (r < 2M ) of the extended Schwarzschild spacetime, Figure 6.9, must...
  25. R

    What exactly is singularity? I was working with a friend earlier

    What exactly is singularity? I was working with a friend earlier today discussing a possible resolution to the black hole mystery. His theory having to do with singularities was very interesting, but I left the conversation clueless of what a singularity actually is. I can't believe I have...
  26. E

    Lagrangian: singularity in inverted pendulum EoMs?

    Hi all, I'm doing some analysis of a bicycle mechanics problem and at one point the approximations I'm making mean that the problem reduces to the classic inverted pendulum. I'm very confused, as the equations I've worked out appear to have an unphysical singularity in them, and I can't see...
  27. M

    Do Singularities Prove Actual Infinities Exist?

    Please correct me if I'm wrong in any sense. And please forgive me if I'm posting this in the wrong forum. I guess my general question is, presuming the big bang model is correct (one that includes a singularity), does that prove actual infinites exist? In other words, we know infinites exist...
  28. C

    Confusion about Essential Singularity in 1/(1-z)

    Hi everyone, I'm brushing up on some complex analysis and I came across the following example, which is driving me crazy: I learned that z_0 is a pole of order k of f(z) if f(z)=\frac{g(z)}{(z-z_0)^k} where g(z) is analytic on some open disk around z_0. And an essential...
  29. D

    What does singularity have to do with whether or not it is a Vector Space?

    Homework Statement Determine whether the set, together with the indicated operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails. "The set of all 2 x 2 singular matrices with the standard operations." Homework Equations...
  30. P

    Black hole with antimatter particle singularity

    could a particle of antimatter be the singularity inside a black hole?
  31. E

    Can a Naked Singularity Become a Black Hole?

    From what I can discover it seems that a naked singularity is a singularity without an event horizon. It also seems that this may be a black hole in the making, as it is a product of continued gravitational collapse. This seems to raise three questions: 1. If a singularity is a point at...
  32. L

    How long does it take to reach the singularity in a free fall at r=0?

    Let's say you start outside the event horizon r>2m, how long does it take according to your own wristwatch to hit the singularity at r=0 (ignoring the fact the tidal forces rip you apart...), assuming you just free fall and plunge in radially? I'm thinking you need to consider the timelike...
  33. P

    How Can We Analyze the Singularity at the Big Bang?

    Hi, I was just pondering the moment of the Big Bang, and have been doing some reading on the subject, in which there exists problems consolidating the mathematics of relativity and quantum mechanics. To my understanding the theory of realtivity predicts the universe started from the Big Bang...
  34. T

    How Do Atoms in Collapsing Stars Remain Stable Before Becoming Singularities?

    Since atoms above a certain atomic number are unstable and have an extremely short lifespan, then the atoms of the unknown element that comprises the mass of a collapsing star in the process of becoming a black hole just before the stage where a singularity is achieved should by all accounts...
  35. P

    Matrix Invertability & Singularity: Explained

    if a matrix is invertable can it be singular ?
  36. B

    Exploring the Possibility of a Single Black Hole Singularity

    Is there any merit to the idea that all black hole singularities are in essence one and the same singularity?
  37. D

    Understanding Black Hole Singularity

    I've been reading up a bit on black holes but I don't quite grasp why there should be a singularity at the center. As far as I understand a singularity forms when all the mass of an object collapses to withing the schwarzschild radius, according to wikipedia...
  38. F

    How can I fix up the singularity?

    Homework Statement I = \int^{2}_{0} (1-e^{-x})/\sqrt{x} I=\int^{2}_{0.1}x/sin^2(x) Homework Equations The Attempt at a Solution I tried to integrate by part, but I approached to trivial solution. I know that the answer is involved with Error function, but I don't know how I could reach the...
  39. D

    Infinite brightness in the singularity?

    Since the black hole has infinite brightness near the singularity just below the photon sphere, would the big bang singularity also possesses such characteristic?
  40. D

    The Big Bang singularity - does it have infinite energy?

    Since the big bang singularity has infinite density, gravity, and heat, am I correct to think that it has infinite energy? Since the black hole singularity also has infinite density, gravity, but has finite heat, does it have infinite energy as well? With regards to the black hole...
  41. K

    The Codimension of a singularity

    This may seem like a foolish question, but I can't seem to find the answer anywhere. Also, please forgive the question if it is ambiguous but the context in which it arises is not clear to me: There is a mapping H(x,p,\cdot): \mathbb R \to \mathbb R with x,p fixed, which attains its maxima...
  42. baywax

    When can true singularity take place? Was the big bang the only chance

    When can true singularity take place? Was the big bang the only chance for this condition? Do black holes represent a singularity? I would doubt this because a black hole only exists because there is a contrasting environment with which to compare and identify the event.
  43. W

    Photons live in a singularity?

    Photons "live" in a singularity? I did some searches, but couldn't find an answer to this on this forum. Since a photon can travel 1 km, 1 lightyear, 1 million lightyears in ZERO time from its own perspective, and if we did a though experiment from the point of view of a photon, does that...
  44. 6

    Exploring Singularity Behaviors When Black Holes Collide

    Was re-reading 'A Brief History of Time' the other night and came across this ::: "Two black holes collide to create an event horizon greater than the sum of the areas of the originals." There are no attempts to explain this phenomenon throughout the reading; though I believe there may be an...
  45. B

    Must a black hole be a point singularity?

    If during star collapse the mass not blown away is large enough to form a black hole, shouldn’t the resulting extraordinary high temperature essentially convert all the mass into contained radiation? The basic pressure formula for this intense radiation would likely be P = pc*2 (where p is the...
  46. bcrowell

    Hawking singularity theorem - what if not all geodesics incomplete?

    Hawking singularity theorem -- what if not all geodesics incomplete? The Penrose singularity theorem tells us that once you get a trapped surface, at least one geodesic is guaranteed to be incomplete, going forward in time. But this doesn't mean that 100% of the mass of a collapsing star has to...
  47. 2

    Solve Reactions R1 & R2: Singularity Functions

    Homework Statement The beam in the picture is 16 inches long and support a is in the middle. I have to find the reactions R1 and R2 useig singularity functions. Unfortunatly i have no way on this computer to draw my FBD.The Attempt at a Solution q =...
  48. M

    Exploring the r=0 Singularity at Fixed Time

    Since r is time-coordinate below the horizon, how can you interpret that the r=0 singularity is an event at fixed time?
  49. E

    Philosophical/quantum implications of Big-Bang singularity

    Okay one more question for you guys I'm having trouble figuring out, probably because the search function on here is difficult to use successfully if you're unfamiliar with the terminology involved. One of the popular physics books I've read is called "The Conscious Universe" by Kafatos and...
  50. J

    Where was the big bang singularity?

    If all galaxies originated from big-bang, and if currently galaxies are still moving away one from the other, shouldn't it be possible to determine also where they are moving away from? i.e.where the big-bang-singularity was?
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