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. T

    Black Hole Singularity of a Universe

    In a recent lecture by Stephen Hawking he mentions that our universe started as a singularity. Can this singularity be caused by energy from a Black hole in another space and time? This in turn would mean that an infinite number of universes can be and are created.
  2. L

    Why wouldn't black hole singularity evaporate before it can form?

    I assume people much more knowledgeable then me must have already thought this through, but the following line of thought has me very curious. I'm making a lot of intuitive leaps here though, so I am sure there is a lot of places I could have gone drastically wrong. Hawking radiation is...
  3. J

    Singularity Paradoxes: Nothing or Something?

    The singularity paradox Maybe this has been dealt with, but it seems that cosmologists can't seem to decide if the cosmic singularity is a "nothing" or a "something". If it's a "nothing" then accounting for a universe somehow emerging from nothing is becomes very difficult to explain. It may...
  4. ShayanJ

    Series solutions near an irregular singularity

    Consider a linear differential equation of the form y''+p(x)y'+q(x)y=0 with an irregular singularity at x_0. How can I found a series solution to it near x_0 ? Thanks
  5. J

    Inflation of singularity at moment of evaporation?

    I have had an idea kicking around in my head for some time now. It all started last summer when I was kayaking down a river and I had stopped in an eddy to relax for a moment. The rate of flow of the water was strong enough to make sizable vortices along the eddy fence around the boulder that...
  6. J

    Singular behavior of the density state called a van Hove singularity

    Homework Statement I was doing a condensed matter problem (3rd year) of a phonon dispersion relation for a monatomic linear chain. It asked told me to derive an expression for the density state per unit length and I obtained the following: g(\omega) = \frac{L}{a\p} \frac{1}{4C/M -...
  7. J

    What will be the point of humans after the technological singularity?

    ... I mean if it ever does happen
  8. P

    MHB Residue at essential singularity

    Consider the function $$f(z)=\frac{e^{\frac{1}{z-1}}}{e^z -1}$$ $z_0=1$ is an essential singularity, hence $$f(z)=\displaystyle\sum_{-\infty}^{+\infty}a_n(z-1)^n$$ near to $z_0=1$ and i want to find $a_{-1}$. I can write $$f(z)=\frac{\sum\frac{1}{n!(z-1)^n}}{e\cdot...
  9. P

    Questions on Big Bang Singularity

    I have a question that is probably un answerable. At the exact moment the Big Bang was sent into Motion, it is assumed that all the mass-energy was condensed into a very powerful singularity. At that moment, the mass and gravity should have been so instance that an explosion would be...
  10. Q

    Big Bang singularity vs Black hole singularity

    One speaks of the Big Bang initial condition as a singularity possessing an extremely low entropy (to explain the growth of entropy throughout time to our present stage of the universe). If that singularity truly possesses infinite density, that would make perfect sense, since what would become...
  11. R

    Integral from 0 to ∞ with singularity at x=0

    Here's an integral that is currently giving me grey hairs: \int_0^{\infty} \frac{1}{x} \exp(i \frac{k}{x}(a-c \cos(\theta + wx))) dx I've tried different approaches like contour integration around x=0 and replacing the exponential by its Taylor sum to have: \int_0^{\infty}...
  12. A

    Simultaneity of events inside a singularity

    Hello, I was wondering if the following idea had been proposed in one form or another within a scientific community. Provided that the space within the singularity is dimensionless, that being 0 in length on all the axes (is it?) the following is in order. From this follows that the Planck's...
  13. N

    Can torsion avoid the big bang singularity

    Interesting theory for consideration: Cosmology with torsion: An alternative to cosmic inflation http://arxiv.org/abs/1007.0587Nikodem J. Poplawski (Submitted on 4 Jul 2010 (v1), last revised 2 Nov 2010 (this version, v2)) In this work, we considered the ECKS theory of gravity which is the...
  14. N

    How has LQG resolved the Big Bang Singularity

    I get the impression from the following material that LQG models have 'resolved' the divergent big bang singularity into a finite big crunch... If so, what changed and is this a generally accepted 'new start' at the front end of the FLRW model which follows?? I may have missed some discussions...
  15. N

    Big Bang Singularity: What is it?

    I am a bit confused about big bang. Is the big bang referred to as the expansion of universe from singularity or not. Sorry if i have posted it in wrong section
  16. B

    Singularity and size of universe

    Hello all . what's size of universe before the big bang ? We consider big bang after Planck time or before Planck time ? There was no singularity in big bang is that true ? loop quantum cosmology says that
  17. bcrowell

    Penrose's argument that q.g. can't remove the Big Bang singularity

    I came across this argument in the book The Nature of Space and Time, which is based on a series of lectures given by Hawking and Penrose. Although it relates to Penrose's Weyl curvature hypothesis (WCH), it does not depend on it, and that, to me, makes it a lot more interesting, since I...
  18. F

    Conditions for curvature singularity

    Hi All, I was wondering if it is correct to say that a vanishing metric determinant is a necessary (but probably not sufficient) condition for a curvature singularity to exist at some point(s), or is one forced to construct the full Kretschmann scalar? Cheers! FD
  19. D

    Removing a Singularity for a Second Order ODE

    I was given the following equation to solve: x^2*y'' + x*y' + k^2*x^2*y = 0 B.C. y'(0)=0, y(1)=0 where k is just some constant. I am having a hard time removing the singularity created by the boundary condition at y' and not aware of a method how. Any advice would be greatly appreciated.
  20. K

    Seeking Help with Electromagnetism: Understanding 'Cancelling the Singularity

    I am currently reading a book about the electromegnetism. When I went through the introductory chapter, there is a small part that I do not understand clearly. Therefore, I hope that I can seek help here. Quote: --- --- --- --- ---...
  21. C

    Limits and integrating over a singularity

    Suppose one needs to evaluate a definite integral over a singularity, like: -\int_{-1}^3 \frac{1}{x^2} dx The textbook way to do so is to split the integral into two parts around the singularity and take the limit, like so: \lim_{b\rightarrow 0} -\int_{-1}^b \frac{1}{x^2} dx and...
  22. C

    Complex analysis: Integration About Singularity

    Homework Statement Evaluate the integral ∫sin(z)/(z^2-4) dz about the contour C such that it is a circle of radius 2 centered at z = 2. Homework Equations All theorems of complex analysis except residue theorem. The Attempt at a Solution There is a singularity at z = 2, so we...
  23. N

    Complex Integration with a removable singularity

    Hi, I'm trying to make headway on the following ghastly integral: \int_0^{\infty} x^{\frac{3}{2}}e^{-xd} J_o(rx) \frac{\sin (\gamma \sqrt{x}\sqrt{x^2+\alpha^2}t)}{\sqrt{x^2+\alpha^2}}\ dx where d,r, \alpha, \gamma ,t \in \mathbb{R}^+ and J_o is the zeroth order Bessel function of...
  24. L

    Why doesn't hawking radiation prevent a space-like singularity

    As I understand it, as a particle is observed approaching an event horizon, will would never be observed to cross the horizon, and it's red shift would tend towards infinity. I've read conflicting things about this, A, that that red shift WOULD NOT reach infinity in a finite time, and B, that...
  25. grav-universe

    Shrinking event horizon to point singularity

    Varying coordinate systems in GR has given me a new perspective that may help to resolve a problem that has been nagging at me ever since I began working with GR. In every problem I've ever dealt with, a complex mathematical result describes an impossible scenario, something that cannot occur...
  26. M

    Singularity in Laplacian operator

    I am trying to understand the following basic problem, \partial_{xx} f^\alpha (x) = \alpha (\alpha-1) \frac{1}{f^{2-\alpha}} \partial_x f + \alpha \frac{1}{f^{1-\alpha}} \partial_{xx} f So it is not hard to see that if f tends to zero the laplacian becomes undefined (im not sure if i...
  27. K

    Infinite being removable singularity

    Homework Statement I am confused about the concept of removable singularity, when it comes to the infinite. Here are two examples in which infinite is claimed to be the removable singularity: 1, f(z)=\frac{1+z^4}{z(1+z^2)^3}; 2, f(z)=sin\frac{1}{z-1} Actually, I don't even know why the infinite...
  28. K

    Singularity in infinite space-time

    in an empty infinite space time, there lies the possibility that something came from nothing, since infinity encompasses everything. yes? no? i assume that the matter that appear out of thin air, without any external intervention in my belief. was Hydrogen. the simplest element in the table...
  29. genphis

    Is the Multiverse Hypothesis Losing Steam in Scientific Circles?

    After watching a program featuring stephen hawkings, which discussed the beginning of the universe and the big bang. I am troubled by the concept of accepting that there was nothing before the big bang. if indeed it was spurned from a singularity which is infinitely dense with energy/matter...
  30. S

    Upper limit on the characteristics of Singularity

    "Upper limit" on the characteristics of "Singularity" I know GR fails in "singularities". Is there an upper limit on characteristics of the singularity like a maximum value for the density of matter after which GR fails? I came across a number of threads which discuss what happens after...
  31. K

    Infinite universe and big bang singularity

    Hello. Cosmologists leave open the possibility that the universe as a whole may be infinitely big. My question is, does that mean that the entire infinite universe was compressed into the initial singularity? And how can a universe go from a singularity to being infinitely big in a finite time?
  32. T

    How can I handle the singularity in my integrand equation?

    I have an equation that relates two variables: k(\mathbf{x},\mathbf{x}') =exp(-(\mathbf{x}-\mathbf{x}')^2) If I want to determine the value of this equation where x' is kept constant and x is actually the set of every real number then I can express the function as the integral where the...
  33. R

    Log(z) : singularity, series and pole

    Firstly does log(z) have any singularity other than z=0? Secondly, z=0 is a pole of what order for log(z)? What is the Laurent series expansion for log(z) at z=0?
  34. P

    Penrose Singularity Theorem

    Can anyone help me with this? Homework Statement Explain why Penrose's singularity theorem does not apply to each of the following geodesi- cally complete Lorentzian manifolds: (a) Minkowski's spacetime; (b) Einstein's universe; (c) de Sitter's universe; (d) Anti-de Sitter spacetime.2...
  35. J

    Singularity theorms and perturbation from exact symmetry

    The singularity theorems apply to situations away from exact symmetry ... away from Schwarzschild solution or Friedmann solutions for example. There are a number of accounts of the singularity theorems but none addressing the problem of proving a 'trapped set' still persists after slight...
  36. E

    The Singularity: A Fundamental State of Energy Before the Big Bang?

    If at the beginning of the universe there was no matter, would this mean that the singularity before the "Big-Bang" was a pure/fundamental state of energy? If so, would the "god particle" be a flawed concept?; would it not be a theoretical form of energy rather than a particle?
  37. M

    Black Hole Singularity Blue Shift

    Theoretically, would everything be REALLY REALLY blue at the singularity of a black hole because of the blue shift caused by all the light racing to it (the singularity)? Arigato, -llama
  38. A

    How comes the big bang singularity didn't need space and time?

    Obviously before the big bang there was no space and no time, so how comes the big bang singularity itself existed without space and time? do black holes' singularities not need space and time to exist too? or at least in order for them to come and exist there has to be space and time at first place
  39. J

    Why isnt a bh singularity a reference point?

    is the question
  40. J

    Is your information destroyed when you reach the singularity

    from my understanding from an observer in the universe, your information is plastered on the event horizon, and ultimately retrieved when the event horizon shrinks to the schwartschild radius and the singularity explodes. please coreect me if I am wrong on that. if the singularity does not...
  41. F

    MHB Singularity of Positive Semi Definite Matrices

    Hello,I'm given a sparse symmetric positive semi definite matrix and I want to check whether it is singular or not.What's a quick way to do that? (I can't do any kind of factorization because the matrix can be huge)I know the following:- if any of the diagonal entries is zero, then the matrix is...
  42. U

    Whats the difference between t=0 singularity and the singularity in a black hole ?

    I just don't see how they can be the same, if singulariity t=0 eventually went all berserk (due to quantum repulsive force perhaps) or whatever other reason like it actually did why is it not happening inside of black holes?
  43. F

    Singularity, Infinity, Edge, Expansion

    First post in the Physic forum, the thread title are the words that really get on my nerves. I have the following questions. a) Cosmologists say the universe started at a singularity, there for there is a point where the universe started to expand from, if you could look at the singularity...
  44. H

    Integral variable substitution for removing singularity

    Homework Statement Hi! In an assignment I have reached an integral that has the form: \int\frac{A+Bx+Cx^2}{Dx+Ex^2} where A-E are constants, the integration variable is x and the limits are 0 to 1. I'm supposed to remove the singularity at x=0 by substitution. A-E have values but they're...
  45. tom.stoer

    Singularity theorems (Hawkign & Penrose)

    Does anybody kow about a good summary (online) of the singularity theorems?
  46. C

    Is There a Ground Zero for the Big Bang?

    If we could find the point in space where the singularity happened would you expect to find abnormalities in space time? Is there a ground zero, where there is no relative motion where everything is rushing away?
  47. 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...
  48. J

    Questions about 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?
  49. 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...
  50. 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
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