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. J

    Can Adding Spin to a Black Hole Create a Naked Singularity?

    "generic" naked singularity I don't understand the arguments/discussion against naked singularities. The reason is that it seems obvious to me that given a black hole, there is a generic procedure to form a naked singularity. This reasoning is probably flawed (otherwise there wouldn't be...
  2. Z

    Are black holes a point of singularity?

    Are black holes a point of singularity of infinite density, approaching that point as a limit, or just really massive and really dense? Is light really being "sucked in" by the gravity and actually being attracted to the object, or is it really just following the really really steep bend in...
  3. W

    More Complex Analysis-Removable Singularity

    Homework Statement Let f be analytic in the region (z:0<|z-a|<r) and isn't defined at z=a. Prove that if there is a neighborhood of z=a where Re f(z)>0 then z=a is a removable singularity of f. Hope you'll be able to help me Thanks in advance Homework Equations The Attempt...
  4. D

    Residues of an essential singularity and a simple pole

    Homework Statement Classify the isolated singularities and find the residues \frac {\sin(\frac {1}{z})}{1-z} Homework Equations I know the Taylor series expansion for 1/(1-z) when |z|<1 and I think I know the Taylor series for sin(1/z). The reciprocal of each term of the Taylor series of...
  5. T

    Simple description of a Singularity

    I am writing a paper and need to know if the following statement provides a simple yet accurate description of a Singularity. If not, please submit suggestions for improvement. (thank you in advance for any help): In scientific theory a Singularity is a zone of infinite density that is...
  6. A

    Finding the residue of a singularity

    Homework Statement The following function has a singularity at z=0 (e^z)/(1 - (e^z)) decide if its removable/a pole/essential, and determine the residue The Attempt at a Solution I played with the function and saw it can be re-written as: -1 /(z + z^2/2! + z^3/3! +...) In this...
  7. M

    QCD Coulomb Singularity: Quarkonium w/ 2 Gluons

    Hi all, I am just new to work on NLO in QCD. I need to know how a Coulomb singularity in QCD is defined? What is the form/expression of this singularity term? Can anyone explain with an example of any Feynman diagram? I am interested in the case of a quarkonium with two gluons in final state...
  8. T

    Singularity and Anti singularity

    What would happen if a singularity collapsed from normal matter collided with one collapsed from antimatter? Or if the collapse into a singularity negated the line between anti/normal matter, what would happen if a stellar sized mass of antimatter collided with a black hole?
  9. P

    Determining the density of a singularity

    I have a question about singularities. Determining the density of a singularity involves the mathematically absurd and undefined function of dividing by zero. What I don't get is this : How can a mathematically absurd entity exist in reality ? Also, if you multiply the density of a...
  10. G

    What Are the Singularities and Residues of the Function z^-n(e^z-1)^-1?

    Homework Statement z^-n(e^z-1)^-1 , z not equal to zero locate the singularities and evaluate the residue. Homework Equations The Attempt at a Solution i don't have an idea about when z is not equal to zero because i think that only singularity point is z=0 hence if there...
  11. T

    Can the big bang occur without time?

    If time and space did not exist before the big bang then how could the change from a singularity to the big bang occur? Since change needs time as a prerequisite.
  12. T

    Exploring the Possibility of Curled Dimensions in Gravitational Singularities

    This is a "Theoretical Question" so go easy on me. Since an atom is mostly empty space is a Neutron also mostly empty space or just space? In other words, in the case of a Neutron star we start with a Star with a diameter of 1,000,000 miles and since the distance ratio between the electron and...
  13. T

    Singularity Functions for Beam Bending

    There is a beam of width 10cm, and vertical reaction loads on each end (x1 = 0cm, x2 = 10cm). Starting from the left end of the beam, we have a vertical distributed load of 2,000 N/m spanning from 0cm to 5cm. Finally, we have a 1,000 N point load located 7.5cm from the left end of the beam...
  14. J

    Steepest descent contour includes singularity (asymptotic expansions)

    Homework Statement We require an asymptotic expansion of (t in general complex): \int _{-1} ^\infty \frac{e^{i \lambda t^2} }{\sqrt{1+t}} dt in the limit (lambda) tends to infinity. Hint given is to sketch the path of Im(it^2)=const through t=0 and t=-1 in the complex t-plane. The Attempt at...
  15. P

    Does Hawking deserve a Nobel prize for his singularity theorem?

    Hawking radiation is almost certainly not going to win him a Nobel prize, because experimental detection is beyond our technology. But how about the singularity theorem which he and Roger Penrose proved? This theorem convinced the physics community that black hole would indeed form in realistic...
  16. K

    Singularity in Rutherford cross section

    The Rutherford differential cross section \frac{d\sigma}{d\Omega} goes like cosec(\vartheta)^4 which means at \vartheta=0 the differential cross section is infinite, which is ok. My question is, given that the differential cross section is proportional to the probability per unit solid...
  17. C.Braestrup

    Question: what exactly is a singularity?

    hi!, just wondered what exactly is a singularity? yes i could google it, but i figured you guys were smarter. on forehand, thanks.
  18. E

    Relativistic gravity incomplete? Big Bang singularity

    I have a question regarding the conditions "prior" to the Big Bang. I realize tere is no empirical evidence for these conditions, only speculations. At the point of the Big Bang, all of matter and energy was "infinitely" densely concentrated at a single point, correct? Even though GR breaks...
  19. L

    Singularities in C* of f(z) = \frac{{\pi z - \pi {z^3}}}{{\sin (\pi z)}}

    Homework Statement Find and classify the singularities in C* of f(z) = \frac{{\pi z - \pi {z^3}}}{{\sin (\pi z)}}, and give information about Res(f, 0) and Res(f, infinity) The Attempt at a Solution I found that the singularities in C are z = n, with n \in Z, n\neq 0, n\neq 1. These...
  20. A

    Schwarzchild spacetime singularity

    Hi all! I'm studying black holes and there's a point that I cannot understand. The book I'm reading is Modeling black hole evaporation, by Fabbri and Navarro Salas. The path is the following. After introducing the Schwarzschild metric ds^2 = \left(1 - \frac{2M}{r} \right) \ dt^2 - \left(1 -...
  21. Y

    How is singularity formed inside a black hole?

    Wikipedia and some other web sites mention that: At the center of a black hole lies the singularity, where matter is crushed to infinite density, the pull of gravity is infinitely strong, and spacetime has infinite curvature. This means that a black hole's mass becomes entirely compressed into a...
  22. A

    The Singularity: Closer Than We Think?

    ... or is it far?
  23. S

    The singularity moment at the beginning of the universe

    Being no more than a pop-sci reader in this subject, I'd like to ask the experts a naive question: At that instant where the entire universe was concentrated at a single point, it seems to me all matter had a definite position and momentum. Isn't this a spectacular fall of the uncertainty...
  24. S

    Contour integral around essential singularity

    Is there a way to perform a contour integral around zero of something like f(z)/z e^(1/z), where f is holomorphic at 0? If you expand you get something like: \frac{1}{z} \left( f(0) + z f'(0) + \frac{1}{2!} z^2 f''(0) + ... \right) \left( 1 + \frac{1}{z} + \frac{1}{2!} \frac{1}{z^2} + ...
  25. R

    A^k matrix singularity and (A^k)^-1 = (A^-1)^k

    Homework Statement Let A be nonsingular. Prove That for any positive integer k , A^k is nonsingular, And (A^k)^-1 = (A^-1)^k. Homework Equations The Attempt at a Solution
  26. R

    String Theory, the singularity and photons

    Hey all, first post here. I had the opportunity recently to ask Steven Weinberg a question that the physics professors at my university didn't have an answer to. In short, Weinberg said he couldn't understand where I was going with my question. My heart broke as I obviously wasn't able to convey...
  27. J

    What is an Algebraic Singularity in Complex Analytic Functions?

    What does an algebraic singularity of a complex analytic function mean?
  28. T

    Double Slit Experiment Near The Singularity of a black hole

    I've been wondering for a long time whether or not the theory that one electron can be in two places at the same time holds near the singularity of a black hole?
  29. K

    Is z=0 a Non-Isolated Singularity in \(\frac{1}{\sin(\frac{\pi}{z})}\)?

    Hi, The function \frac{1}{\sin(\frac{\pi}{z})} has isolated singularities at z=+-1, +-1/2, ... However, it is said that it has an non-isolated singularity at z=0. A non-isolated singularity has to be a point where its neigborhood too is also singular. But, for some \epsilon > 0 ,\...
  30. I

    Complex Analysis - Removing A Singularity

    Ok, so I'm suppose to be able to remove the singularity to find the residue of the function (z)cos{\frac{1}{z} I tried to see how "bad" the singularity was by taking the limit, but I can't figure out if \lim_{ z \to 0 } (z)cos{\frac{1}{z} goes to 0 or if it is...
  31. G

    Branch-cut singularity and the multiparticle contribution to the full propagator

    I have been reading Chapter 7 of Peskin & Schroeder about full propagator, the Kallen Lehman spectral representation, and got stuck at the branch cut singularities and at the complex logarithm of negative numbers. I have posted in the Analysis forum (but have not received any answer) the...
  32. G

    Branch-cut singularity of a complex logarithm

    Hi! Does anyone know what a branch-cut singularity is? I have been trying to understand its importance in physics, but I got lost. I would guess that a singularity in physical context should mean that the value of a function should become very big near that singularity. But if we take complex...
  33. D

    Possibility of a technological singularity

    Some of you may be familiar with the concept of a supposed 'singularity' http://en.wikipedia.org/wiki/Technological_singularity that some people think will happen in the coming hundred years or so. The idea was popularized by Ray Kurzweil, and some of you may have read his book 'The...
  34. B

    Isolated singularity in complex plane

    Homework Statement Locate each of the isolated singularities and tell whether it is a removable singularity, a pole, or an essential singularity. If removable, give the value of the function at the point. If a pole, give the order of the pole. f(z) = \pi Cot(z\pi) Homework Equations...
  35. stevebd1

    Collapse to a ring singularity

    One thing I’ve always found a bit of a curiosity is how a rapidly rotating star might collapse to a ring singularity relative to the speed of light and what the final parameters of the ring singularity might be (i.e. reduced circumference considering r=0 at the ring edge). Due to the...
  36. A

    Proving Essential Singularity at z=0: Using Taylor Series Method

    Homework Statement Hey guys. I need to show that this function has an essential singularity at z=0. I used Taylor series to get what I got, which is a series inside a series...:confused: And I can't see how am I suppose to show it from here. Any ideas guys? Thanks. Homework...
  37. Ivan Seeking

    Google & NASA Back Futurists: Singularity University

    http://www.ft.com/cms/s/0/8b162dfc-f168-11dd-8790-0000779fd2ac.html?nclick_check=1
  38. N

    Removable Singularity of L_a^2(G): Proof of Limit at z=0

    Homework Statement If G = { z in C: 0<|Z|<1} show that every f in L_{a}^{2}(G) has a removable singularity at z = 0 Proof: We must show that lim z->0 z*f(z) = 0 for all f in L_{a}^{2}(G) By a corollary 1.12, if f in L_{a}^{2}(G), a in G and 0<r<dist(a,bdr G), thne |f(a)| <=...
  39. D

    Explaining Weak & Null Singularities in Black Holes

    I understand the concept of a spacetime (future) singularity in a BH I understand what is a ring singularity in Kerr'sblack hole Could anyone explain (for dummies) what is meant by "weak" and "null" singularity?
  40. M

    Singularity - Black Hole or Naked

    In all descriptions of black holes or naked sigularities (latest issue of Scientific American) that I've seen, the assertion is made that because gravity is so strong the collapsing star ends up as a point of infinity density. However, it may be possible that internal pressure is so strong that...
  41. T

    Singularity of function of complex variable

    Homework Statement I have to proof that this equation: x_r(\omega)=\frac{1}{\pi}*PV \int_{-\infty}^{\infty}\frac{x_i(\omega')}{(\omega'-\omega)}d\omega' (where P denotes Principal Value Integration of Cauchy, r and i denotes rispectively real and imaginary part of x function) is equivalent to...
  42. DrGreg

    Removing the Schwarzschild coordinate singularity

    I'm creating this thread to discuss some issues raised by kev in the Understanding maximally extended Schwarzschild solution thread, to avoid diverting that thread from its original question. As any fule kno, the problem with Schwarzschild coordinates is their coordinate singularity at the...
  43. S

    Can any one explain me about the bigbang singularity

    can anyone explain me about the bigbang singularity
  44. C

    Universe started from a cosmic singularity

    It is a widely accepted theory that the universe started from a cosmic singularity and eventually through many years and processes gave us what we have today. But here's one question I ponder: how did the singularity get there in the first place? We know what the singularity caused, but what...
  45. D

    Colapse to singularity and Pauli principle.

    If a star is sufficiently massive, neither electron or neutron degeneracy pressure will stop it from forming a black hole. How is Pauli exclusion principle reconciled with collapse to a singularity ? Since no two neutrons can occupy the same quantum state at the same time, how comes a...
  46. N

    How can we be sure of a singularity?

    I have often been told that at the start of our "universe" (I prefer "self-contained energy system" - SCES, myself) all energy was contained in a singularity. What is the evidence for this all-containing singularity being the initiation of the big bang? Is it not reasonable that the extremely...
  47. M

    Why Does lnZ Not Represent an Isolated Singularity?

    why lnZ is not isolated singularity?
  48. F

    Singularity in reference to blackholes and right before the big bang?

    Now correct me if I'm wrong. Gravitational singularity is when It has a defined mass but no volume and the equation for density is d=m/v. If a black hole's mass is say 10^40 yottagrams and its a singularity so it has no volume = 0. How can it have infinite density if the equation is (10^40...
  49. J

    Singularity Theorem Proof on IanBay's Site

    At http://members.lycos.co.uk/ianbay/ I'm attempting to write up the proof of the singularity theorem, but its not uite finished for various reasons... In The large scales structure of spacetime on page 98 the following statement is made "Further if any component of \left( dA_{\alpha...
  50. Phrak

    Does a Schwartzchild blackhole have a singularity?

    Does a Schwartzchild black hole have a singularity at its center?
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