What is Singularities: Definition and 178 Discussions

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 this was proved in Hironaka (1964), while for varieties over fields of characteristic p it is an open problem in dimensions at least 4.

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  1. S

    I Does Kerr's argument against singularities apply to all black holes?

    Roy Kerr has recently written a preprint (https://arxiv.org/abs/2312.00841) in which he strongly argues against the possible existence of singularities inside Black Holes. I've read that his arguments are really powerful and that he is most likely right. But, does it mean that Kerr has...
  2. fresh_42

    A Do Black Holes have Singularities?

    Do Black Holes have Singularities? "There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL's). Penrose and Stephen Hawking...
  3. L

    A Has anyone read this new paper on extending the BGV?

    I was wondering if anyone has read this new paper (link provided) one of the authors Will Kinney, seems very sure it forecloses on any cosmological model with no singularities. Can anyone speak about the limitations of the paper or if it does definitively prove a singular beginning in space...
  4. I

    I Exploring Field Strength & Singularities

    Why doesn't this work if the field is strong? Or does it work as long as there are no singularities? Mentor's Note: Original thread title was, "Calculating rest mass by integrating T_{00} over a 3 volume for static metric"
  5. S

    I Are there non-smooth metrics for spacetime (without singularities)?

    Are there non-smooth metrics for spacetime (that don't involve singularities)? I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics: Lorentz invariance holds locally in GR, but you're right that it no longer applies globally when gravity...
  6. penroseandpaper

    Classifying singularities of a function

    I came across this question on chegg for practice as I'm self learning complex analysis, but became stumped on it and without access to the solution am unable to check. Let $$ f(z)=\frac{cos(z)} {(z-π/2)^7} $$. Then the singularity is at π/2. And on first appearance, it looks like a pole of...
  7. G

    A What assumptions underlie the proof that singularities are inevitable?

    Poking around on the internet has not helped me. Penrose references Hawking and his 1996 book and I have ordered that, but I suspect my progress through that book will be slow. I have read that the assumptions include an energy condition, which I assume is expressed as a restriction on the...
  8. S

    C/C++ How can phase singularities be implemented in C++?

    hello i would like to ask how to implement phase singularities in C++. thanks very much.
  9. LCSphysicist

    Singularities when applying Stokes' theorem

    It is more or less a generic problem of stokes theorem: ##\int_{\gamma} F dr##, where ##F = (-y/(x²+y²) + z,x/(x²+y²),ln(2+z^10))## and gamma is the intersection of ##z=y^2, x^2 + y^2 = 9## oriented in such way that its projection in xy is traveled clockwise. So, i decided to apply stokes...
  10. Arman777

    A Kerr Metric: Removing Singularity via Coordinate Transformation

    We know that, the singularity of the Schwarzschild metric at ##r = 2M## can be removable via coordinate transformation to Kruskal-Szekers . Can we apply a similar argument to the Kerr metric? If so, what's the name of this coordinate system?
  11. I

    B Black Hole singularities in Quantum Gravity

    If singularities don't exist in QG then what prevents particles from just collapsing falling further until they collapse into a singularity? Is there a repulsive force in QG ? Is time infinitely stretched near a singularities? What else could be happening?
  12. T

    I Question about spacetime singularities

    Hello there.We know that spacetime may have singularities and the current theories can not describe it very much.I want to start reading about quantum gravity but what is the progress done so far for the resolution of questions about the singularity?Could a different approach perhaps a...
  13. tworitdash

    A Spectral domain double integral with singularities

    The integral looks like Y_{mut, mn} = -j^{m+n}nm \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \frac{2 ab (k^2 - k_x^2) \sin^2(\frac{k_yb}{2}) \cos^2(\frac{k_xa}{2})}{\omega \mu k_z (\frac{k_yb}{2})^2 [(n\pi)^2 - (k_xa)^2][(m\pi)^2 - (k_xa)^2]} dk_x dk_y Here, k_z = -1j \sqrt{(-(k_0^2 -...
  14. DarkMattrHole

    I Mass distribution behavior of the singularities during black hole mergers

    When two BHs collide the resulting single BH bulges and contorts until it settles down to a stable state. 1) Does this mean that during this 'settling' period the mass internal to the merged BH is not (yet) a singularity, but instead two 'singularities' spinning down around each other in...
  15. starstruck_

    Determine the singularity type of the given function (Theo. Phys)

    NOTE: Was not sure where to post this as it is a math question, but a part of my "Theoretical Physics" course. I have no idea where to start this and am probably doing this mathematically incorrect. given the function f(z) = cos(z+1/z) there should exist a singular point at z=0 as at z = 0...
  16. Cerenkov

    B The singularities of gravitational collapse and cosmology

    Hello. I'd just like to check a some points concerning the two kinds of singularities that Penrose and Hawking describe in this paper. https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1970.0021 The Singularities of Gravitational Collapse and Cosmology. 1. According to the Cosmic...
  17. Mlesnita Daniel

    B Could singularities be just rips in the space-time fabric?

    First off, this is just an assumption. My knowledge of the field is extremely limited and I beg you to come and correct my mistakes, so I can learn. So, I guess we all know how that space-time fabric is bended by gravity. When a star dies, all of the atoms are brought extremely close...
  18. G

    Analyzing the Singularity of f(z) = z cos(1/z) Using Solutions to f(z) = 0

    Hey, I have been asked to show that z = 0 is not a removable singularity of: f(z) = z cos(1/z) The catch is, I have to show this by first finding all the solutions to the equation (f(z) = 0) then use them to show that the singularity is not removable. The only relevant theorem I can find is...
  19. Islam Hassan

    I Big Bang Singularity vs Black Hole Singularities

    Is there a fundamental difference between the (speculative) understanding of a singularity arising from the creation of a black hole and the singularity which we think may have been at the origin of the Big Bang? Noteably, would there be two basic theoretical types of singularities...
  20. A

    I Radial Acceleration of Rotating Singularities: Planck Length & Beyond

    And if so, how much? Should the radius be thought of as zero, an infinitesimal, or as the Planck length? v2/r = ω2r If its zero, then you immediately run into a problem when trying to calculate it with linear velocity. v2/r = ar v2/0 = undefined OR ω2r = ar ω20 = 0 Which would mean that...
  21. Space_Girl

    B Black Holes Must Have Singularities Says Einstein Relativity

  22. D

    I Is it possible to stretch a singularity?

    Hi everyone When a smaller black hole gets sucked into a larger one, is it theoretically possible for the gravity of the larger black hole to stretch the smaller black hole so that it no longer has an infinitely dense centre? I guess it won't matter once they are completely merged, but in...
  23. Cerenkov

    B Can somebody help me understand singularities better please?

    Hello. :) This is my first post. I'm an amateur astronomer with a interest in cosmology. My understanding of cosmology is entirely derived from reading Hawking's 'A Brief History of Time', Guth's 'The Inflationary Universe' and relevant articles in Scientific American, Sky & Telescope and...
  24. T

    I Singularities in General Relativity

    There are two kind of singularities which are familiar in General Relativity. One of them is the singularity of Black Holes and the other is at the beggining of the universe. I'm confortable with the former singularity --it seems to make sense. But as with the latter, I'm not so confortable...
  25. U

    MHB Green's Theorem with Singularities

    So here's the question: You are given that F is a conservative vector field, except for singularities at the points (0,1), (2,0), (3,0), and (0,4). You are given the following information about line integrals around the following closed paths: 1) Around the curve C1 given by x^2 + y^2 = 2...
  26. S

    I Understanding Isolated Singularities in the Residue Theorem

    Hello! Why do the singularities in the Residue Theorem must be isolated? If we have let's say a disk around ##z_0##, ##D_{[z_0,R]}## where all the points are singularities for a function ##f:G \to C## with the disk in region G, but f is holomorphic in ##G-D_{[z_0,R]}##, we can still write f as a...
  27. A

    B Difference betwen space-like and time-like singularities

    See the Wikipedia article on Penrose-Hawking singularity theorems: https://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems. It says that A singularity in solutions of the Einstein field equations is one of two things: 1. a situation where matter is forced to be compressed to a...
  28. SothSogi

    I I need a list of all singularities in physics

    Hi there everyone :smile: I'd like to have a list of all the instances where a singularity appears in physics, e.g., in relativity, causing the black hole thing. Specific cases where \frac{x}{0} appears. For instance, I heard that there is another case in quantum mechanics, or quantum...
  29. W

    I Observing Naked Singularities: Implications for Quantum Gravity

    A number of press outlets are reporting a new work that appears in Physical Review D that it might be possible to observe naked singularities. See the story here: http://www.spacedaily.com/reports/Can_we_see_a_singularity_the_most_extreme_object_in_the_universe_999.html It got me thinking about...
  30. Mr Davis 97

    I Evaluating improper integrals with singularities

    For two improper integrals, my textbook claims that ##\displaystyle \int_0^3 \frac{dx}{(x-1)^{2/3}} = 3(1+2^{\frac{1}{3}})## and that ##\displaystyle \int_0^8 \frac{dx}{x-2} = \log 3##. However, when I put these through Wolfram Alpha, the former exists but the latter does not, and it says that...
  31. T

    B Singularities forming universes?

    The whole universe started off with a Big Bang, before this all matter was contained inside a singularity. Since other singularities are formed when a star forms a black hole hypothetically could this cause the creation of other universes?
  32. P

    B How do we study space-time singularities?

    I hope I am posting this in the correct forum, I am trying to better understand space-time singularities. I can find easily the basic, and advanced information on what it is and the different theories. My main question is how do scientists study these space-time singularities? Thank you for...
  33. T

    Classifying singularities of a complex function

    Homework Statement [/B] Find and classify the isolated singularities of the following: $$ f(z) = \frac {1}{e^z - 1}$$ Homework EquationsThe Attempt at a Solution I have the solution for the positions of the singularities, which is: ## z = 2n\pi i## (for ##n = 0, \pm 1, \pm 2, ...##) and this...
  34. P

    Singularities and Laurent series

    Homework Statement Classify the singularities of ##\frac{1}{z^{1/4}(1+z)}## Find the Laurent series for ##\frac{1}{z^2-1}## around z=1 and z=-1 Homework EquationsThe Attempt at a Solution So for the first bit there exists a singularity at ##z=0##, but I'm confused about the order of this...
  35. P

    Classifying Singularities and the Laurent Series

    Homework Statement Classify the singularities of ##\frac{1}{z^2sinh(z)}## and describe the behaviour as z goes to infinity Find the Laurent series of the above and find the region of convergence Homework Equations N/A The Attempt at a Solution I thought these two were essentially the same...
  36. Will Langas

    B Are Larger Black Holes Less Dense Than Smaller Ones?

    What has a higher density? Black Holes or Singularities? I looked online and all I saw was that they both have infinite densities.
  37. H

    Question on Phenomena beyond General Relativity

    Hello, I'm Harry. I'm new here, hope not breaking any posting rules in any ways :) I have a question and would like to ask for some suggestions and information. The question is about general relativity or gravity and structure of the Universe in general; I know there are definitely quite a...
  38. M

    Singularities of a complex function

    Homework Statement [/B] Find and classify all singularities for (e-z) / [(z3) ((z2) + 1)] Homework EquationsThe Attempt at a Solution [/B] This is my first attempt at these questions and have only been given very basic examples, but here's my best go: I see we have singularities at 0 and i...
  39. J

    Singularity Theorems: An Accessible Reference

    I've read Hawking's introduction: http://arxiv.org/abs/hep-th/9409195v1, which are nice. I would like something that explains the other singularity theorems and how they are related to Big Bang. I've tried reading Hawking & Ellis but I can't understand most of the definitions.
  40. RUber

    Differentiating Integral with Green's function

    Hello, I am having trouble finding the proper justification for being able to pass the derivative through the integral in the following: ## u(x,y) = \frac{\partial}{\partial y} \int_0^\infty\int_{-\infty}^\infty f(x') K_0( \sqrt{ (x - x')^2 + (y-y')^2 } \, dx' dy' ## ##K_0## is the Modified...
  41. bcrowell

    Do non-black hole singularities have observable properties?

    I hope the topic of this post is not too philosophical to be appropriate here. Some recent discussions on PF have helped to crystallize my view of how classical GR treats singularities, and black hole singularities in particular. However, I'm not sure to what extent these ideas generalize to...
  42. T

    Kelvin-Stokes' theorem in the presence of singularities

    My concern regards solving a class of somewhat ill-defined surface integrals occurring in Mathematical Physics and EMF Theory. I'll be using a simplified, representative example. Consider the surface S given by (x/2)^2 + (y/2)^2 + (z/3)^2 = 1 0 <= z. And the integral ∫F⋅ds where we have in...
  43. D

    Gravity around a near maximal black hole

    It's been a long time since I posted here, but I've read on the forum from time to time. And I have a curiosity and some questions about these objects, namely the naked singularities. From what I understand, a naked singularity is a singularity without an event horizon, so they are visible...
  44. bcrowell

    Boundary Construction for B.H. & B.B. Singularities

    There is a general topic of boundary constructions, which means how to adjoin idealized points in a sensible way to a given spacetime. There is a menagerie of these methods, including the g-boundary (Geroch), b-boundary (Schmidt), c-boundary (Geroch, Kronheimer, and Penrose) and a-boundary...
  45. edguy99

    Insights Animating Black holes and Singularities - Comments

    edguy99 submitted a new PF Insights post https://www.physicsforums.com/insights/animating-black-holes-singularities-infinite-force-gravity/ https://www.physicsforums.com/insights/wp-content/uploads/2015/05/graviytanimation-80x80.png...
  46. C

    Why must singularities create an entire universe?

    I've been studying sciences since I was a child, and I'm fairly certain every mention of a singularity leads to the big bang and the creation of the universe. I don't understand why though? There is a black hole and potential singularity at the heart of every galaxy. So why have I never heard...
  47. Q

    What are the equations explaining the mass of singularities?

    What exactly are the equations explaining why a singularity's mass is the way it is?
  48. T

    Singularities of a Complex Function

    Homework Statement What are the region of validity of the following? 1/[z2(z3+2)] = 1/z3 - 1/(6z) +4/z10 Homework EquationsThe Attempt at a Solution Knowing that this is the expansion around z=0, I am trying to find the singularities of the complex function. Which is when z2(z3+2) = 0 I...
  49. Darth Frodo

    Singularities Complex Analysis

    Homework Statement Determine the location and type of singularity of f(z) = 1/sin^2(z) Homework EquationsThe Attempt at a Solution I'm not really sure how to calculate this. At this point, we don't have explicit formulae for the coefficients of a Laurent series so I really don't know what to...
  50. O

    I don't believe in singularities

    It seems to me that singularities are taken for granted as existing, otherwise there couldn't be a big bang. Is that so? To me, to believe in singularities is in no way different to believing in a God. Is there any reason you can think of that precludes all other scenarios from explaining...