Timeline for What is the definition of a timelike and spacelike singularity?
Current License: CC BY-SA 3.0
19 events
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Jan 27, 2020 at 10:57 | comment | added | tparker | This answer defines what a timeline singularity is, but not a spacelike singularity. | |
Nov 5, 2019 at 15:15 | comment | added | safesphere | Finally, a singularity may not be revealed by an affine parameter for some geodesics. As an illustration, consider $\rho=1/\varphi^n$ in polar coordinates. Here $\rho=0$ is a singularity, even if the affine parameter is unbound. | |
Nov 5, 2019 at 14:40 | comment | added | safesphere | Also, while a singularity is not a part of the same metric manifold, @LubošMotl is right that a singularity can be viewed as a manifold in a more general sense, such as a point set in some coordinate space, although indeed not a point set of events in spacetime. For example, the Schwarzschild singularity is a coordinate point set of $(r=0, -\infty<t<+\infty)$, which is a spacelike straight line in the Schwarzschild coordinates removed from the Schwarzschild spacetime. Defining the Big Bang as a point set or point in some (e.g. embedding affine) coordinates depends on the cosmological model. | |
Nov 5, 2019 at 13:32 | comment | added | safesphere | Any transformation "replacing" the Schwarzschild coordinates with those "well behaved" is necessarily singular at the horizon and thus mathematically forbidden. A point at the horizon in any "well behaved" coordinates does not map to any event in the physical spacetime and thus is missing from the manifold. Therefore geodesics are interrupted and incomplete at the horizon making it a physical singularity by definition. By using a singular transformation you can create or remove singularities anywhere at will. It is not a valid mathematical procedure and its results are unphysical as explained. | |
Sep 1, 2018 at 22:05 | comment | added | tparker | When you say "In 2+1-dimensional GR, curvature vanishes identically," don't you mean it vanishes identically in vacuum? You can certainly have nonzero Ricci tensor and therefore curvature in 2+1D in the presence of matter fields. | |
Apr 14, 2013 at 19:43 | history | edited | user4552 | CC BY-SA 3.0 |
fix a mistake in the definition
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Apr 14, 2013 at 18:25 | history | edited | user4552 | CC BY-SA 3.0 |
better reference
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Apr 14, 2013 at 18:16 | history | edited | user4552 | CC BY-SA 3.0 |
add more discussion about technical definition of singularity, and reference to Carroll
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Apr 14, 2013 at 17:36 | comment | added | user4552 | [...] Re your second comment, you gave an incorrect definition. I gave the correct one provided in the Penrose paper. The sentence where I explained the Penrose definition was this one: "A timelike singularity is one that is in the past light cone of some points in spacetime but in the future light cone of others." The later material about putting it on a table, etc., was presented as interpretation, not as a definition. The material about naked singularities was likewise interpretation, and its purpose was to explain why we would care about the notion of a timelike singularity. | |
Apr 14, 2013 at 17:35 | comment | added | user4552 | @LubošMotl: Thanks for your comments, but I disagree with them. Re your first comment, the definition of singularity you gave in your answer was incorrect, since it didn't define a conical singularity as a singularity. The one I gave fixes that problem. | |
Apr 13, 2013 at 7:14 | comment | added | Luboš Motl | But the main reason why I downvoted this is that you pretended the curve-like definition of spacelikeness or timelikeness of singularities like manifolds (in the coordniate space) to be insufficiently rigorous and accurate - but what you actually replaced this self-evident definition by is pure handwaving about objects on the table and circular references to other phrases such as naked singularities. This explains and answers nothing. The OP and anyone else can't understand why you wouldn't place a big bang singularity or Schwarzschild singularity "on the table" or strip it naked. | |
Apr 13, 2013 at 7:12 | comment | added | Luboš Motl | The claims such as "there are two types of singularities, curvature and conical ones", are truly outdated and while your intent was admirable, such comments teach much more wrong things than correct things. Many singularities, e.g. in conifolds, importantly mix the singular curvature and the conical structure, the singular curvature is nearly omnipresent, while the conical character may be so unusual that the singularity isn't conical in a useful sense. | |
Apr 12, 2013 at 17:05 | comment | added | user23071 | That's excellent. Yes, my main question was what you explained in your last two paragraphs, not what singular spacetime was, but that's also nicely written. | |
Apr 12, 2013 at 17:03 | vote | accept | user23071 | ||
Apr 12, 2013 at 15:27 | history | edited | user4552 | CC BY-SA 3.0 |
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Apr 12, 2013 at 15:21 | history | edited | user4552 | CC BY-SA 3.0 |
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Apr 12, 2013 at 15:14 | history | edited | user4552 | CC BY-SA 3.0 |
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Apr 12, 2013 at 15:04 | history | edited | user4552 | CC BY-SA 3.0 |
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Apr 12, 2013 at 14:58 | history | answered | user4552 | CC BY-SA 3.0 |