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

    Coordinate singularity in Schwarzschild solution

    Hi! I have the following problem I don't really know how to approach. Could someone give me a hand? The line element of a black hole is given by: ds^2=\Bigg(1-\frac{2m}{r}\Bigg)d\tau ^2+\Bigg(1-\frac{2m}{r}\Bigg)^{-1} dr^2+r^2\Big(d\theta ^2+\sin^2(\theta)d\phi ^2\Big) It has an apparent...
  2. 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...
  3. Cerenkov

    B A Singularity in Semi-Classical physics too?

    Hello. My question is based upon my (mis?)understanding of these two premises. 1. General Relativity breaks down when trying to describe the extreme conditions that are inferred to have existed in the very early universe. 2. According to this link...
  4. LYCON

    Black hole vs mathematical singularity

    What is the difference between mathematical singularity and black hole singularity[emoji780]
  5. avischiffman

    B Real-Life Demonstrations of Black Holes for Video

    Hi, I am working on a video, and I was wondering if any of you knew of some real-life demonstrations I can do about black holes? So far I have the gravity well, and the balloon covered by foil that you crush to show same mass but denser. My video is about the anatomy of a black hole, so I cover...
  6. R

    I Big Bang Singularity: Was It As "Infinitely Dense" As We Think?

    The big bang supposedly originated from an infinitely dense singularity of space/time. The concept of infinitely dense is an artifact from our current perception of how immense our universe is today and how spread-out space/time is. However, if I were present in the reference frame of that...
  7. binbagsss

    GR Cone Singularity Homework: Q1 & Q2 on Setting B(r=0)=0

    Homework Statement question attached- I am stuck on some of the reasoning as to why we set ##B(r=0)=0## please not as described in the attempt I am interested in the concepts and have not posted my solution to A, nor any solutions not relevant to the concepts I am trying to understand...
  8. C

    I Did the big bang singularity not have a history?

    Hello! Hawking has written, that the physical mechanics and the time before the big bang singularity cannot be measured, as time in this big bang singularity has been bent indefinitly and therefore has just started with the big bang. Questions: 1. Does Hawking mean, there has not been any time...
  9. M

    I Black hole event horizon confusion

    Leonard Susskind said "everything that ever fell in, to make the black hole, [..] [is] all contained in [...] progressively thinner and thinner shells that approach the horizon asymptotically, never quite getting there" and from the perspective of someone outside the black hole "a shell, called...
  10. binbagsss

    A Why Scalar Quantities Matter in Singularity Tests

    Apologies if this is a stupid question, so for e.g, in a Schwarzschild space-time we look at ##R^{abcd}R_{abcd} ## (we seek some scalar quantity that blows-up and can not use ##R##as we are looking at vacuum solutions so we know this is zero) The reason we seek a scalar is because it is the...
  11. J

    What is the singularity of e^(-1/z^2)?

    Homework Statement Homework Equations Singularity is where function is not analytic means we can't differentiate denominator. It tends to 0. The Attempt at a Solution expanding e^-1/z^2 = 1 - 1/z^2 + 1/z^4 - ... This has essential singularity at z = 0 as that's where the denominator goes to...
  12. D

    B Temperature of a black hole....observed from the singularity

    I'm just a layman here, who enjoys science and astronomy. I was reading about the temperatures of the cores of black holes being extremely cold, and how time at the singularity...progresses super, super slowly. But this is only as measured from an outside observer's perspective (such as from a...
  13. 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...
  14. L

    MHB [Complex Analysis] Singularity in product of analytic functions

    Suppose f,g:ℂ→ℂ are analytic with singularities at z=0. I was wondering whether f(z)^2 or f(z)g(z) will have a singularity at z=0? For each, can you give me a proof or a counterexample?
  15. A

    Laurent series of z^2sin(1/(z-1))

    Homework Statement Find Laurent series of $$z^2sin(\frac{1}{1-z})$$ at $$0<\lvert z-1 \rvert<\infty$$ Homework Equations sine series expansion. The Attempt at a Solution At first, it seems pretty elementary since you can set w=\frac{1}{z-1} and expand at infinity in z, which is 0 in w...
  16. alex4lp

    A Why is all the mass of a BH in the singularity?

    Hi everybody, and thanks in advance. My doubt is: why should the mass go in the singularity? I'm thinking about this situation: imagine a sphere with radius R<2M; then that sphere generates a BH. Schwarzschild tensor metric is valid only in the exterior region of the mass and for this reason i...
  17. zonde

    I Coordinate singularity at Schwarzschild radius

    I would like to ask how rigorous is the statement that Schwarzschild metric has coordinate singularity at Schwarzschild radius. The argument is that singularity at Schwarzschild radius appears because of bad choice of coordinates and can be removed by different choice of coordinates. However...
  18. W

    B Could time move inside a black hole?

    At the event horizon for a black hole is R=2GM/C^2 This means that, as a star collapses, it gets more dense until this limit is reached. Assuming a consistent density (just an approximation as I know this will not really be the case), the Mass will reduce proportionally to the cube of R, but...
  19. S

    I Difference between oscillatory/cyclic model and big bounce?

    If a Big Bounce can occur "after a universal singularity is reached or a repulsive quantum force causes re-expansion" then what differentiates it from oscillatory/cyclic models if both of them defend that the universe will re-expand from a singularity or before that...
  20. wolram

    B Solving the singularity problem

    I admit i know little about this subject, but am interested in any thing that solves the singularity problem. May be some one will look at this paper to see if it makes sense arXiv:1709.09794 (cross-list from gr-qc) [pdf, other] Falsifying cosmological models based on a non-linear...
  21. T

    I Proper time to reach the singularity - rocket acceleration

    I was assuming that the proper time lapse between ##r=2M## and ##r=0## increases with increasing acceleration outwards. According to this paper https://arxiv.org/pdf/0705.1029v1.pdf Fig.2. it turns out however that the proper time to reach the singularity is longer with low acceleration but...
  22. wolram

    B Does the Singularity Really Exist Beyond the Standard Model?

    People keep saying that it is an artefact of the mass and the singularity does not exist, yet other theorists suggest they lead to worm holes, Do they exist or are they or are they (beyond the standard model)?
  23. C

    I Particle at event horizon as black hole evaporates

    If you are observing a particle enter a black hole, you watch its proper time go to zero at the event horizon as it is 'frozen' there from your frame of reference. What happens in your reference frame as the black hole evaporates? While you can't illuminate where the particle is from your frame...
  24. Zantra

    Technological singularity and artificial intelligence

    I didn't find this exact topic, so here we are! Let me begin by saying that the singularity is inevitable- Its not "if", it's how soon. Elsewhere on this board it was mentioned that we're far from autonomous driving. Assuming we mean level 5 autonomy, it means millions of hours of road...
  25. B

    B Do we exist within a singularity

    So there is a thought experiment about a monkey endless typing random words. Given a large enough amount of time, it is certain that the monkey will end up writing everything that has already been written from start to finish one after another. So this being applied to our current theory of the...
  26. F

    I Black Hole Formation Sequence: Time in the Equations?

    Hello all, To my knowledge, there are still a lot of questions regarding the specifics of black hole formation. My question is in regards to formation time. I've read that the actual formation takes "less than a second" according to the equations. Does anyone know where time shows up in the...
  27. A

    I Black hole - between horizon and singularity

    What occupies the space between a black hole's event horizon and the singularity? Stuff hurtling to the singularity? Vacuum?
  28. J

    Analytic Integration of Function Containing the Exponential of an Exponential

    Homework Statement Can this function be integrated analytically? ##f=\exp \left(-\frac{e^{-2 \theta } \left(a \left(b^2 \left(e^{2 \theta }-1\right)^2 L^2+16\right)-32 \sqrt{a} e^{\theta }+16 e^{2 \theta }\right)}{b L^4}\right),## where ##a##, ##b## and ##L## are some real positive...
  29. E

    B Is it possible to reach the singularity?

    The question is; After an object goes through the event horizon, is it possible for the object to reach the singularity? As far as i know, singularity, bends space down and actually space moves faster than light towards the singularity. But what tells us that the singularity's bending has a...
  30. vktsn0303

    A Understand Convolution, Singularity, Kernel, etc: Math Reading Guide

    I'm reading a book on vortex methods and I came across the above mentioned terms, however, I don't understand what they mean in mathematical terms. The book seems to be quite valuable with its content and therefore I would like to understand what the author is trying to say using the above...
  31. J

    2D Integrating With Quadratic Arg. of Delta Function

    Homework Statement I have a 2D integral that contains a delta function: ##\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\exp{-((x_2-x_1)^2)+(a x_2^2+b x_1^2-c x_2+d x_1+e))}\delta(p x_1^2-q x_2^2) dx_1 dx_2##, where ##x_1## and ##x_2## are variables, and a,b,c,d,e,p and q are some real...
  32. H

    How are singularity functions used in beam analysis?

    HI I am going through an example on signularity functions. I don't understand how the author went from the line which I highlighted in blue to the line which I highlighted in red.
  33. R

    I Are quark stars a realistic solution to the black hole singularity problem?

    Is this a realistic solution to the black hole singularity problem, Going beyond that, neutrino stars?
  34. F

    Find and classify the isolated singularity

    Homework Statement Find and classify the singularity. f(z) = sin(z) / z Homework Equations sin(z) = (z - z3 / 3! + z5 / 5! - z7 / 7! + z9 / 9! - ... The Attempt at a Solution so the singularity is at z = 0. f(z) = (1/z) * (z - z3 / 3! + z5 / 5! - z7 / 7! + z9 / 9! - ...) f(z) = 1 - z2 /...
  35. J

    A Analytical Integration of a Difficult Function

    Is it possible to integrate the following function analytically? ##\int_{0}^{\infty} \frac{\exp{-(\frac{A}{\tau}+B\tau+\frac{A}{\beta-\tau})}}{\sqrt{\tau(\beta-\tau)}}d\tau,## where ##A##, ##B## and ##\beta## are real numbers. What sort of coordinate transformation makes the integral bounded...
  36. ivant6900

    B Do we still live in a Big Bang Singularity?

    My question is very simple but it is something I have been thinking about for some time. Every time a person needs to have the expansion of the Universe explained or the question "What does the Universe expand into?", people who know a bit about the topic answer that it expands into and onto...
  37. binbagsss

    Elliptic functions, removable singularity, limits,

    Homework Statement [/B] please see attached. b) The solution seems a bit vague is the idea here, what this comment is saying, that since this is a simple zero the form of ##lim_{z\to a} f_a(z) (z-a)=0## since, crudely, it is of the form ##\frac{0.0}{0}##. Compared to the point ##z=-a##...
  38. K

    I Size and shape of a black hole singularity?

    How and if singularity is related to Plank size (h) , are they be related ? If they are; can the singularity have squared shape (like pixel) , if it is h size so that is the "smallest" understand by "physics" and any curve (circle) would break the rule of h begin the smallest ? Does my question...
  39. FallenApple

    I Do Event Horizons always contain a singularity?

    So a black hole consists of an event horizon and a singularity in the center. What about the cosmological horizon( which is also an event horizon)? Is a cosmological horizon's geometric center a singularity? I can imagine that an electron has a cosmological horizon. Yet an electron is...
  40. TGVF

    A Singularity also with Euler-Rodrigues parametrisation?

    Hello, Trying to develop a multibody dynamics software of my own (just to understand the nitty-gritty details of such stuff), I chose the Lagrangian equations approach, with the Euler-Rodrigues parametrisation (quaternion) for 3D rotation as it is supposed to remove the gimbal locking...
  41. D

    B The Singularity and Hawking radiation

    Hello everyone! Im a newcomer, a teenager who has countless doubts with respect to relativity, quantum theory etc. But these two questions bother me the most: 1) Hawking radiation states that when the separation of a particle (eg. a photon) into charged particles happens in the event horizon...
  42. Noisy Rhysling

    How can a singularity be used to prevent the formation of the Moon?

    I have a race that is famous for going over the top with solutions to problems. Their garbage trucks dump the waste directly into their sun. Entire cities move around the globe to keep the sun at "high noon" ... so they don't have to light the streets at night. "Can openers" have self-contained...
  43. Elnur Hajiyev

    A Light from the singularity of a charged black hole

    According to Cosmic Sensorship Conjecture, naked singularities are prohibited in General Relativity. To my knowledge, naked singularity means light from the singularity can escape to infinity. In Reissner-Nordström metric, references say naked singularity appears only if ##GM^2<P^2+Q^2##...
  44. A

    A How to compute limit of removable singularity?

    I am given an implicit expression for an algebraic function, ##w(z)## as:##f(z,w)=(1-3 z+3 z^2-z^3)+(-4+8 z-4 z^2)w+(6-6 z)w^2+(-4)w^3+(1)w^4=0## with ##\displaystyle \frac{dw}{dz}=-\frac{\frac{df}{dz}}{\frac{df}{dw}}=\frac{6 w^2+8 w z-8 w+3 z^2-6 z+3}{4 w^3-12 w^2-12 w z+12 w-4 z^2+8 z-4}##...
  45. CaptDude

    I Question about "the big bang happened everywhere at once"

    Is it fair to think about the statement "the big bang happened everywhere at once." as meaning the singularity that spawned the "big bang" was very large by cosmic scales, even infinitely large? (I am aware that the word "singularity" refers to a place where the math breaks down and not a point...
  46. T

    B Exploring a Micro Singularity in Euclidean Space Time

    What if the LHC produced a mini black hole and as a result a micro singularity was produced. If you were using Euclidean space time what equations and factors do you think would be most relevant?
  47. wolram

    B What Do Scientists Think a Black Hole Is?

    AFAIK, scientists do not believe in the singularity, one way out of the singularity is quantum gravity, but as we have no testable theory of quantum gravity what do scientists think a black hole is?
  48. Q

    Identifying Types of Singularity in Differential Equations

    Homework Statement Identify the type of singularity at x=0 for these differential equations x*Sin[1/x]*y''[x]+y[x]==0 x^2*y''[x]+Sin[1/x]*y[x]==0 Homework Equations A Singular point is regular if f(x)(x-x_0)^n is defined as x approaches x_0 and is analytic in a near a neighborhood of that...
  49. Q

    Using Contour Integration with no singularity

    Homework Statement Using contour methods, evaluate the following integrals. In any case in which you wish to argue that some portion of a closed contour gives a negligible contribution, you should explain why that is so. Integral[E^I(k+delta*I)x^2 dx from negative Infinity to Infinity] as...
  50. strangerep

    A Physical Relevance of Singularity Theorems?

    I've been reading this recent review paper by Senovilla & Garfinkle on The 1965 Penrose singularity theorem. In sect 8.3 (p38): Their eqn(6) is on p8: ##R_{\rho\nu} u^\rho u^\nu ~\ge~ 0 ~.## The message I take away from this is that much of the theory about singularity theorems has turned out...
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