What is Singularity: Definition and 429 Discussions

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. A

    Big Bang Singularity: What Prevents Universe from Becoming Black Hole?

    Hi We know that a black hole is a dense object so dense that it gravitational makes it vanish from the universe. Now at the moment of the big bang creation event the ultimate in density and gravity was experienced, so what prevented the universe from going the way of black holes. Is it a...
  2. Cincinnatus

    What is the potential impact of the singularity on humanity?

    The new issue of IEEE Spectrum is all about "The singularity" the hypothesized time in the next 50 years when computers will become smarter than we are and usher in an era of technological accomplishment "to dwarf the industrial revolution". Singularity people like Ray Kurzweil think we'll...
  3. L

    What is the Nature of Singularity Semantics?

    It has been claimed that, "The singularity of a black hole is not a point in space it is not even a point in spacetime, in fact it is not even in spacetime. The singularity is not a point on the spacetime manifold. If it were it would obviously not be a singularity." The source is...
  4. J

    If no singularity, what’s inside a big black hole?

    Both string theory and loop quantum gravity claim possible elimination of the black hole singularities. If that is true, what do they predict the inside of a stellar size black hole contains? Is it some new ultra dense state of matter, or something else? I will try to ask various...
  5. M

    Singularity approaching towards pi

    Homework Statement Locate & name the singularity of the function Sinz /z- ∏ Homework Equations The Attempt at a Solution The function has singularity at z= ∏ but am not able to figure out what type of singularity it is , at z=∏ it gives 0/0 form which is indeterminate form...
  6. E

    Proving the Essential Singularity of e^{1/z} at z=0

    Homework Statement http://en.wikipedia.org/wiki/Essential_singularity What is the best way to prove that e^{1/z} has an essential singularity at z=0? I have tried showing that \lim_{z\to 0} z^k e^{1/z} does not exist for any natural number k, but I couldn't get it.Homework Equations The...
  7. N

    Investigating Logarithmic Singularity in 2D Tight Binding Approximation

    Homework Statement Given some dispersion relation for the tight binding approximation in 2D: e(k_x,k_y) = -2t_1[cos(k_x*a)+cos(k_y*a)]-4t_2[cos(k_x*a)cos(k_y*a)] Show that the density of states has a logarithmic singularity for some choice of parameters t_i. Homework Equations g(e)de=g...
  8. M

    What Type of Singularity Does f(z) = (1-e^z)/(1+e^z) Have at Infinity?

    Homework Statement Identify the singularity of f(z)= 1-e^z/1+e^z at z= infinity Homework Equations The Attempt at a Solution How shud i start
  9. D

    What is an integrable singularity and how is it determined?

    Hello. What is an integrable singularity? Is it a certain order of the singularity? \int_0^1\frac{1}{x}=\infty (not integrable) \int_0^1\log{x}=-1 (integrable)
  10. B

    Help with showing the existance of the Schwarzschild singularity at r=0.

    According to Wikipedia, if the metric was vacuum, spherically symmetric and static the Schwarzschild metric may be written in the form: ds^2=((1-2GM/(c^2r))^-1)*dr^2+r^2*(dtheta^2+sin(theta)^2*dphi^2)-c^2*(1-2GM/(c^2r))*dt^2 I need someone to help me to derive an expression from the...
  11. H

    Solving the Singularity Problem: Uncovering the Smallest Particles

    I'm trying to figure out how scientists concluded that all matter in the universe was compressed to the size of something smaller than an atom. If that's true than I think the there has to be undiscovered particles several folds smaller that the smallest known particle today. Particles so small...
  12. P

    Singularity and residue

    Homework Statement Do residues exist only for holomorphic function? Classify the singularity and calculate the residue of tanh(z) and tan(z) The Attempt at a Solution For both Essential isolated singularity because the numerator has an infinite number of terms. Residue = 0.
  13. S

    Isolated singularity (complex analysis)

    Homework Statement 1) \frac{e^{z}-1}{z} Locate the isolated singularity of the function and tell what kind of singularity it is. 2) \frac{1}{1 - cos(z)} z_0 = 0 find the laurant series for the given function about the indicated point. Also, give the residue of the function at the...
  14. marcus

    Singularity (Wikipedia and Mathworld definitions)

    This post is just concerned with definition of terms, for them as wants it. If you are NOT confused about what is meant by a singularity in math/physics, please ignore this. Sometimes a good online source, if you want the meaning of math and physics terms, is Wolfram Mathworld. Wolfram also has...
  15. M

    What is the alternative to the concept of a singularity in cosmology?

    What is a "singularity"? I'm not sure I understand this concept? Isn't it just a "mathematical" concept, like "infinity" or "zero"? Couldn't it be equated with a similarly non-sensical concept as "God"? I know Hawking tries to eliminate the concept of a "singularity". But I'm not sure of what...
  16. Loren Booda

    Exploring the Similarities between Geometrodynamic and Quantum Singularities

    What, if any, are the similarities between a geometrodynamic singularity and that of a collapsed quantum?
  17. P

    Is a Singularity One-Dimensional?

    Hello. I'm wondering if a singularity is one-dimensional. Thanks.
  18. M

    Solving for Non-Essential Singularity of f(z) at z=0

    Homework Statement f(z) = sin(z)/[cos(z^3)-1] Show that z=0 is a non-essential singularity with an ORD(f:0)=-5 and determine the co-eff. a_-1 Homework Equations The Attempt at a Solution So, after expanding the power series z^5f(z) I showed that h(0) = 2, ie removable and has...
  19. M

    Laurent Series and Singularity Proofs.

    Homework Statement Let D be a subset of C and D is open. Suppose a is in D and f:D\{a} -> C is analytic and injective. Prove the following statements: a) f has in a, a non-essential singularity. b) If f has a pole in a, then it is a pole of order 1. c) If f has a removable singularity...
  20. H

    Can naked singularity actually move the space craft in PAST?

    Can naked singularity actually move the spacecraft in PAST? A singularity is a place where the laws of physics break down. So if singularities can interact with the outside Universe, then anything is possible. For instance, it would be possible to send a spacecraft round such a naked...
  21. H

    Naked singularity can actually move the spacecraft in past?

    Naked singularity can actually move the spacecraft in past? A singularity is a place where the laws of physics break down. So if singularities can interact with the outside Universe, then anything is possible. For instance, it would be possible to send a spacecraft round such a naked...
  22. H

    Naked Singularity: Exploring Scalar Field, Dust & Gravitational Collapse

    Naked Singularity ... ? -------------------------------------------------------------------------------- How the Scaler Field collapse, Dust collapse and spherical gravitational collapse provide the possibility of existence of NAKED SINGULARITY? Also can anyone explain me about this...
  23. H

    NAKED SINGULARITY: Exploring Censorship Possibilities

    Problem is... How the Scaler Field collapse, Dust collapse and spherical gravitational collapse provide the possibility of existence of NAKED SINGULARITY? Also can anyone explain me about this... "In known examples of naked singularities for dust and perfect fluids, the...
  24. N

    Friendly discussion: How do you feel the singularity came to be?

    Hello. It seems from what I’ve gathered on these forums since I’ve read and posted on here, it seems there are only a few possibilities of how the original singularity came to be, which caused the big bang. Those are: 1.) Oscillating universe – The universe goes through a natural cycle of...
  25. W

    Singularity and movement question

    Hello all, This is a thought experiment I have been tangling with for quite some time now and still cannot find anything worthwhile on the net to determine its outcome. I'd like to know what happens if two singularities would collide head on. ( I know that singularites have no strict...
  26. T

    Is there a true singularity in nature?

    I am well aware that a number of physical models contain or predict singularities. My question is: Is there any experimental evidence that any singularity actually exists or are they all artifacts of the models? Lest someone jump right in with the singularity at the center of a black hole, let...
  27. A

    What Are the Chances of the Consciousness Singularity Being Plausible?

    I've read too much about this on the immortality forum and I can't buy the idea... so, I ask you guys, what do you think are the chances of any of that being plausible? To remind you: http://brainmeta.com/index.php?p=singularity "The '''Consciousness Singularity''' refers to a...
  28. B

    Mass of a Singularity: Hawking's Explanation

    In "Universe in a Nutshell" Stephen Hawking says that black holes have mass, and it is the mass of the original star + matter absorbed - hawking radiation in time, or something like it. Right, but: if a singularity has for definition an infinite density, this mean that it is the maximum...
  29. S

    What Are the 10 Signs of the Singularity?

    Here: http://www.deanesmay.com/posts/1152629462.shtml (Thanks to Instapundit for the link)
  30. A

    Exploring the Singularity Phenomenon: Understanding its Meaning and Impact

    What is singularity? How come of it?
  31. T

    Exploring Singularity Functions: Understanding f(x) with an Illustrated Diagram

    f(x) = <x-a>^1 - <x-2a>^1 - a<x-3a>^0 function y = f(x) by means of singularity functions this is a diagram of singularities function.Can anybody pls explain to me how to draw the diagram or any website regarding this materials so that i can get to learn plsss. thanx very much
  32. H

    Exploring the Concept of Singularity: What Does it Mean to Be One?

    What is singularity? Many people talking about the universe say that we're one, why is it? Are we really one in one? many in one? or one in many? How would you explain "being one"?
  33. H

    What is the current understanding of the origin of the universe?

    Did our Big Bang start from a singularity or with a Planck density? What does the standard model say? Under the Planck density I understand the Planck mass divided by the volume of a sphere wirh the Planck radius. If the standard model has no answer, what is(are) the opinion(s) of our...
  34. T

    Medical Making the Consciousness Singularity a Reality

    Ok, enough wishy-washy fluffy talk of the Consciousness Singularity, how do we do this thing? I want details. No crystalline, chakra, or third-eye nonsense. Just suggestions rooted in hard facts. Here are some concrete ideas for bringing about the Consciousness Singularity: FIRST STEP...
  35. S

    The view from a ring singularity?

    I have been doing some thinking about the collapse process inside a rotating black hole. (I think that the probability of creating a non rotating black hole with its point singularity and awkward infinities is so unlikely as to be not worth bothering about). Note this analysis requires no new...
  36. J

    Question about the singularity

    I have a quick question about the singularity, is it infinitly small and dense and if so why? Why do we know it to be so as infinitely dense and small? Any help with this will be much appreciated.
  37. Loren Booda

    Upon the initial cosmological singularity

    What perspective can one take concerning the origin of the universe in the big bang model? Can a collapsed observer occupy the singularity itself, or is there a higher dimensional "superspace" (John Archibald Wheeler) one shares apart from it? Might an observer possesses properties beyond...
  38. S

    Quantum Geometry and Schwarzschild Singularity?

    In a recent paper Ashtekar and Bojowald:http://www.arxiv.org/abs/gr-qc/0509075 gave details (page's 25-26) of the backwards quantum evolution of a specific process of Space-time "leaping". Quote from page 25: " For our quantum Einstein’s equation (55), this coefficient is given by p|τ − 2δ|...
  39. marcus

    Quantum evaporation of a naked singularity

    this seems to be an interesting paper, though I can't tell for sure (don't understand the idea of naked singularity well enough, how you can have one) http://arxiv.org/abs/gr-qc/0506129 Quantum evaporation of a naked singularity Rituparno Goswami, Pankaj S. Joshi, Parampreet Singh 4...
  40. P

    Exploring the Singularity of Black Holes: Time Travel and Evaporation Explained

    I read that the singularity at the centre of a black hole is always in the future since time slows down to zero the nearer you approach it . So when a black hole evaporates ,at the moment when its mass falls below where gravity overcomes the exclusion principle does the matter in the singularity...
  41. P

    Need help with Impulse function and unit step function at singularity

    I have some trouble wrapping my head around singularity One of assignment question is to show that the unit function is not defined at 0. To do that, I need to show \lim_{\Delta\to0}[u_{\Delta}(t)\delta(t)]=0 \lim_{\Delta\to0}[u_{\Delta}(t)\delta_{\Delta}(t)]=\frac{1}{2}\delta(t)...
  42. O

    Is renormalization in quantum field theory a valid approach?

    I had a dream this morning about a Stargate type device, and i remembered that a singularity is infinity. And i got to thinking that a black hole is supposed to be a singularity. So is a black hole a physics representation of infinity? and what does that mean?
  43. wolram

    Detecting Initial Singularity with Cosmological Tests - Szydlowski et al.

    http://rainman.astro.uiuc.edu/coffeepap_Friday.html astro-ph/0504464 Title: Can the initial singularity be detected by cosmological tests? Authors: Marek Szydlowski, Wlodzimierz Godlowski, Adam Krawiec, Jacek Golbiak Comments: 30 pages, 7 figures In the present paper...
  44. X

    What is a stress singularity and why does it disappear at certain angles?

    Hello! I've found in my FE Analyses (For an 'L' shaped model) that for each value of Poisson's Ratio there exists a certain substanded angle above which the elastic solution has no stress singularity. Can somebody tell me what really a stress singularity means mathematically? and that why does...
  45. G

    Understanding the Degree of Singularity in Matrix Operations

    I understand that the "singular values" used to form the diagonal matrix D in a singular value decomposition of a matrix A are the square roots of the eigenvalues of A^TA. But I'm having trouble getting a grip on the concept of "singularity" in the context of a matrix. Previously I've only...
  46. bayan

    Exploring Singularity for Oral Presentation

    Oral Ideas:( Hello. I will be doing an oral presentation for my English SAC. I origionaly wanted to talk about space-time then I changed it to Singularity because I only have about 10 mins to talk and I don't believe that I can scratch the surface in 10 mins. About singularity I know only a...
  47. wolram

    What Is the Significance of a Naked Singularity in General Relativity?

    From Wikipidia In general relativity, a naked singularity is a gravitational singularity without an event horizon. The singularities inside black holes are always surrounded by an area which does not allow light to escape, and therefore cannot be directly observed. A naked singularity, by...
  48. bayan

    Can Mass Exist in a Singularity?

    Hi all. I was interested to know if any mass can exist in singularity? Personaly I think I cannot because there are no dimentions or anything, but a friend of mine says that mass can exist(he is not really a physisit and hasn't got much of a knowledge)? Who is right?
  49. D

    Mathematica Black Holes-mathematical singularity or physical reality?

    Black Holes-mathematical singularity or physical reality? Hi, I posted maybe a week ago and got some excellent feedback on experimental eveidence for GR. this post is intended to start debate, not as a question demanding an answer... after reading around for some time and speaking to my...
  50. T

    Quantum singularity reactor: theoretically possible?

    I’ve seen quantum singularity reactors on Star Trek and Babylon 5, and I’ve got a few questions. First of course, are they theoretically possible? How would they work exactly? And how much power could they generate? (One such reactor on a starship in Babylon 5 generates 330 exawatts, for...
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