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. A

    Does f(z) have a singularity at infinity and how can its residue be obtained?

    does f(z)=\frac{ze^{iz}}{z^2+a^2} have a singularity at infinity? if so, how do i get the residue there?
  2. S

    Exploring FTL Transport Using Singularities

    i don't know where to put this so feel free to move it: I wolud like to discuss ways of Faster than light transport using singularity based forms. (not in reality, only good ways of doing it) thers always the basic one of: ship> }-----------worm hole----------{ but what about...
  3. T

    Heaviside function or singularities function

    Does anybody knows heaviside function or singularities function such as <x-a>^n ;n=1,2,3... for mechanics i wish to know what does this mean and how to draw the shears stress and moments diagramusing this function.any recommended websites for this is appreaciable too thanx
  4. W

    Determine the nature of the singularities

    I am very confused by the wording of this question, it reads: Determine the nature of the singularities of each of the following functions and evaluate the residues (a>0) a) 1/(z^2 + a^2) b) 1/ (z^2+a^2)^2 Hint. fr the point at infinity use the transfor,ation w = 1/z for |z| -> 0...
  5. A

    Schwarzchild and Reissner-Nordstrom singularities

    The Schwarzschild metric has a spacelike singularity, while the R-N metric has a timelike one. The difference between the two physical systems is charge. Obviously you've a very slightly charged black hole, the SC metric is a good approximation because Q/M is too small to really be worried...
  6. A

    Singularities at end point in integration

    singularities at end point in integration... Hi, I Need to perform an integration with poles and zeros in the integrand. Please let me know if there a MATLAB routine/program that can handle the definite integral sqrt((x-a)*(x-b)/((x-c)*(x-d))) between the limits (c,d)...
  7. U

    Exploring Infinity Singularities: Why Don't They Suck in Everything?

    I have an interest in physics, I have not studied it at any high levels (as u will soon find out :smile: ), i just like to read and think about it, but I have a question, please don't blind me with maths! If a singularity at a black hole has infinity density, I'm guessing this means it has...
  8. E

    How can we expand a function near a singularity x=0?

    let,s suppose we have a function f so the limit when \epsilon\rightarrow{0} is infinite..now i would like to know how could i make an expansion of the function f near the singularity x=0 so we have.. f(x)=\frac{a0(x)}{(x-\epsilon)}+\frac{a1(x)}{(x-\epsilon)^{2}... i say a series that is valid...
  9. wolram

    Do scientists think black holes have singularities

    Do scientists think black holes have singularities and event horizons or think they are as described, why think they are nothing more than a dark massive body?
  10. A

    Exploring the Mysteries of Black Hole Singularities

    If black holes suck all matter into a singularity, where does it go and what does it do from there?
  11. I

    Quantum Mechanics & Singularities of Black Holes

    Hi. Can Quantum Mechanics explain what happens at the singularity of a black hole? If so, how?
  12. L

    Quantum Singularities - What Is It?

    Well as you guys may know, I watch a lot of Star Trek. In the shows, it often referres a Black Hole as a Quantum Singularity. Are these phenomenons actually true and exist or did the Star Trek proudcers use that terminology to make an extra "nerdy" feeling into the show? Well, I so far know...
  13. U

    Atoms, Black Holes and Singularities: A Historian's Questions

    I have a question ... if atoms cannot be compacted, beyond a certain minute level, how could they exist inside a black hole, and particularly at the 'singularity' point? Does the fact, that atoms cannot be compressed beyond a certain point, suggest falsification of the hypothetical singularity...
  14. B

    Singularities in Conservative Vector Fields: Understanding the Integral Around C

    Suppose we have a conservative vector field on a plane. Suppose also that we have a closed curve C on that plane. Then we have: \int_C \mathbf{F}\cdot d\mathbf{r} = 0 The line integral around C is zero because F is conservative. Here is what I don't understand: If you have one or more...
  15. G

    Why singularities and not exclusion?

    Hi, everybody always talks about black holes being singularities, but why does everyone always take GR's side and neglect Pauli's exclusion principle? Why do people assume gravity is stronger? Suppose I decide that gravity can't make mass infinitely dense because particles can't have the...
  16. K

    Can Particle Accelerators Create Viable Singularity Weapons?

    I came across a theory that said it's possible to create miniature black holes in particle accelerators. And that these would disappear quickly because they are so small. I thought for a singularity to form, there would have to be plenty of mass in one place. How do the velocities of the...
  17. T

    Zero-point volume singularities

    i have found no solid proof of black holes having zero point volume and is widly accepted but I've found no proof? could someone give me some?
  18. B

    How Does Nonlocality Impact Macroscopic Systems Like Human Consciousness?

    Hello Physics Geniuses, Can any of you explain the physics of nonlocality as it applies to macroscopic systems - such as a human being and human consciousness? We have an increasingly apparent anomaly in psychology/psychiatry which is an apparent singularity: realtime networks of real people...
  19. N

    What if dimensions have different sizes and expand at different rates?

    I may look at it wrong, but when I think of a Black Hole, I think of the 3 spatial dimensions we know of compacting to a point, rather than space folding back on itself (I guess it could be just semantics though). And when you think of a singularity, I think it is inherent in that process you...
  20. T

    Exploring Naked Singularities: How Could They Exist?

    Ok, just HOW could they exist, when the event horizon is just gravity, singularity is supposed to be infinitely contracted mass, and mass is supposed to have gravity? Any insights at all appreciated...
  21. M

    Quantum fluctations and singularities.

    Can one say that it is the same factors (whatever they may be, I don't know) in M-theory/String theory that puts away the effects of quantum fluctations, and also puts away the need/possibility of a singularity in a black hole? I see a connection since M-theory sets a limit of size (planck-...
  22. P

    Exploring the Mystery of Black Holes and Singularities

    Why is it said that a black hole is a literally bottemless pit in space-time? If it weren't bottemless, then the singularity inside would not have to be of infinite density. I'm not sure if I have missed anything important, so PLEASE help!
  23. Loren Booda

    Can Singularities Be Modeled as a Conventional Field?

    Is it possible to have a field f([pard](x)) - fractal or otherwise - where [pard](x) are discrete Dirac delta functions, and f interrelates the various magnitudes of those singularities as a conventional field would for points over a continuum?
  24. CJames

    Understanding Naked Singularities & Traversable Wormholes

    It has been a while since I have posted a question, and I realize that has been stifiling me a little. Instead of learning, I've been getting involved in little quarles and I almost let it drive me away from PF as it did before. So instead of falling back into that trap, I'm trying to gain...
  25. Labguy

    What prevents black hole singularities from being reached?

    Just checking current thought.
  26. B

    Is There Hope for Safe Passage Through Cauchy Horizon Singularities?

    Did anyone else hear about this new development? Apparently if a black hole has a steady influx of matter/energy, it may not develop a singularity which brings about infinite tidal distortion, but it could bring about a 'gentler' cauchy horizon singularity that could be possible to traverse...
  27. P

    Are singularities an infinitely large amount of matter

    Are singularities an infinately large amount of matter within an infinately small amount of space or are they on a Planck scale? :smile:
  28. D

    Is the Curvature of Spacetime the Cause of Singularities in Black Holes?

    Continuing on the PF2 thread about singularities... I had a thought that might give a sort of intuitive explanation of the singularity theorems -- eg the proofs that singularities exist at the center of black holes: Remember how photons emitted just exactly at the edge of black hole are...
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