Singularities Definition and 178 Threads

http://arxiv.org/abs/1008.2768 "To pursue our analysis further, we must determine more carefully the relationship between the renormalization scale µ and the density ρ. One appealing choice, advocated by Weinberg in his analysis of inflation in asymptotically safe gravity [3], is to take the...

Every mass has a Shwarzchild's radius. Once the mass is compressed down to its Shwarzchild's radius, does it necessarily turn into a gravitational singularity, or does it just trap light from leaving? In other words, do all black holes have a gravitational singularity? and do all black holes...

Do we know the magnitude of gravitational force needed to violate the Pauli exclusion principle? Also, I my research has told me that violating the principle still isn't enough to turn the fallen star into a black hole. It could still become a neutrons star, so if that is the case, what...

Homework Statement Let f be analytic at the complex plane excapt for z= -1 and z=3 which are simple poles of f. Let \Sigma_{-\infty}^{-1} a_{n}(z-2)^{n} be the Laurent series of f. In part A I've found that the series converges at 1<|z-2|<3 . B is: Find the coeefficients a_{n} of the...

First off, let me say that while I am an avid astronomer, I know very little about the mathematics of astrophysics. My specialty falls more under mechanical engineering. While initially they may not seem all that related, history shows that the mixing of varying disciplines often sparks...

Homework Statement Find all Laurent expansion of the function f(z) = 1/(z(8(z^3)-1)) with centre z = 0. The Attempt at a Solution I tried to find all the singularities and came up with z = 0, z = 1/2, z = (1/2)exp((n*pi*i)/3) where n = +-2,+-4,+-6... . But according to the solution n can only...

When two black holes collide, do their singularities merge the instant their event horizons touch? Or is there a lag between the event horizons touching and the singularities merging when there are actually two singularities inside a single black hole?

Homework Statement Find two analytic functions f and g with common essential singularity at z=0, but the product function f(z)g(z) has a pole of order 5 at z=0. Homework Equations Not an equation per say, but I'm thinking of the desired functions in terms of their respective Laurent...

Singularities in GR are often associated with geodesic incompleteness. My question is what does it actually mean for a geodesic to be incomplete?

Homework Statement Evaluate the Integral \int dx/((a^2+x^2)*sqrt(1-x^2)) from -1 to 1 Using contour integration Homework Equations Residue theorem/Cauchy integral forumulaThe Attempt at a Solution So I know that at the end-points of the interval (abs(z) = 1) that a singularity exists, so a...

Hello I've read that there are two kinds of singularities : temporals and spatial ones. How can we know the kind of a singularity ? What are the differences between spatial and temporal singularities ? Thanks, Jeff

OK, this is a long one. Black holes are a singularity, right? As is, their dimensions are 0mX0mX0m? That is why their gravity is so strong, because objects can get much closer and thus make the distance between them 0 and force of gravity infinite. In order for this to be possible, there...

Homework Statement Find all the singularities of f(z) = \frac{{{e^{\frac{1}{{z - 1}}}}}}{{{e^{\frac{1}{z}}} - 1}} in the extended complex field, classify them and find Res(f, 0) and Res(f, infinity) Homework Equations Res(f, z0) = a-1 in the Laurent series around that z0 {e^z} =...

Homework Statement (1/s)Ln(s^2+1) Find and classify all singularities in the "extended" complex plane. Draw but do not evaluate the contour you would use to find the inverse laplace transform. Homework Equations (1/s)Ln(s^2+1) The Attempt at a Solution...

Homework Statement Determine the location and nature of singularities in the finite z plane of the follow function and apply Cauchy Integral Formula Homework Equations g(z) = sin 2z ------- z^15 The Attempt at a Solution I know there is a pole of order 14 at z = o...

I posted it in SR/GR but probably it really belongs here: I can explain my motivation. Non red-shifted Hawking radiation is very intense. So when observer approaches the singularity, singularity is always hidden behind the apparent horizon. However, the horizon it covered with a cloud of...

The Marcel Grossmann meeting is a major international conference held every three years--on "recent developments in theoretical and experimental general relativity, astrophysics and relativistic field theories." The twelfth in the series--MG12--was in Paris last month. Abhay Ashtekar chaired...

Lets say anti-matter is less sparse than it currently is. What would happen if two singularities one of matter and one of anti-matter were to merge? Anything special, or the same thing that happens every time matter and anti-matter merge?

Hi! I've been trying to find explanations about the theoretical formation of naked singularities, and all I could come up with was Wikipedia, and frankly, the explanation didn't "set" in my mind, I couldn't really visualize it. It reads: "From concepts drawn of rotating black holes, it is...

I've found a fairly concise review of the Kerr metric at http://www.physics.mcmaster.ca/phys3a03/The%20Kerr%20Metric.ppt The Kerr Metric for Rotating, Electrically Neutral Black Holes: The Most Common Case of Black Hole Geometry. Ben Criger and Chad Daley. On slide 6 they give the usual...

Homework Statement Hi all. According to my book, a pole z_0 of a function f(z) is defined as \mathop {\lim }\limits_{z \to z_0 } f(z) = \infty. Now let's look at e.g. f(z) = exp(z). Thus we have a singularity for z = infinity, since the limit in this case is infinity. This is what I don't...

Do any singularities (including the big bang singularity) have: 1. Infinite density 2. Infinite mass 3. Volume Also, based on the questions above, are naked singularities different to black hole singularities?

Hi, everyone : I am reading about "Nodal singularities" ,and I have not been able to find a clear def. of what they are. Neither of the standard sources: Wiki, Google, or some of the books I have checked, has a clear explanation. Here is the context: We are trying...

At first, I don't see any value in the cosmic censorship hypotesis. If ring singularity (RS) is directly observable (interesting how it looks like. Any simulations?) inside the second horizon, why outside we should be afraid to look at that beast? So I started to thing about RS and Jets...

I've read that Hawking believes the Universe somehow prevents naked singularities, and made a bet about it with Kip Thorne. But it seems to me that if you take a static black hole and continually inject material into it with high angular momentum, eventually you would have a naked singularity...

I wasn't sure where to put this, so astrophysics seems like a good bet? I'm only fourteen, but I'm incredibly interested in astrophysics, quantum mechanics, black holes and the like. I've read about naked singularities, that they can occur the black hole's charge is great enough and the...

If a large (>1.5 SM) conventional star collapses to become a black hole, textbooks say that a singularity will form in the BH. A singularity is characterized by a gravitational field of infinite potential. (Or infinite spacetime curvature if you prefer that terminology). 1. As I understand...

Hi There! Being direct to the point: Does normalization removes singularities? Such as infinite. I came up with this question because, while I was working with a not normalized function, I reached a very strange result. There are two points where the probability tends to infininte...

I am a little bit confused about dealing with integrals around singularities because my professor seems to treat some situations more rigorously than others. We talked this integral and said \int_{-\infty}^{\infty}\frac{1}{x^3} dx = undefined This seems a little bit unintuitive to me...

Singularities are places where time ends for anything in them. In other words, if Bob falls into a black hole at 2:00, time will end for the matter in his body and he won't exist time-wise past 2:00. But according to the Big Bang theory, the universe began in the form of a singularity. Obviously...

Homework Statement Identify the zeroes, poles and essential singularities of f(z) = z^{2/3} Homework Equations f(z) = e^{\frac{2}{3}\log{z}} Which I'm not sure will be useful... The Attempt at a Solution I know that f is 0 at z=0, but what is the order of this zero? Is there such a...

I have to solve the following coupled differential equations d^2f(r)/dr^2+1/r*df(r)/dr+(2-2*f(r)^2-2*a*g(r)^2-l_1^2/r^2)*f(r)=0 d^2g(r)/dr^2+1/r*dg(r)/dr+(2-2*g(r)^2-2*a*f(r)^2-l_2^2/r^2)*g(r)=0, where a is the coupling. I think that it is not possible to solve it analytically (even in...

I have a few questions about these. My main question concerns the "theory" that all fundamental particles are actually black holes. If this were the case, at least for an electron, they would be naked singularities because q+a > m. 1) What are the effects of a naked singularity that make...

One of the sessions at the April meeting of the American Physical Society (APS) will be on what replaces classic GR singularities (like bigbang or black hole) when you move to a quantized theory. Abhay Ashtekar will discuss this from the Loop side. Gary Horowitz will discuss the String side of...

Okay, I know there is observational evidence for spinning black holes, so therefore I must be confused about something, and I want you to tell me what. If you have a star that is spinning, therefore it has orbital angular momentum (mass revolving around a point), then as it is collapsing in...

Hi I'm not very clued up on the mathematics behind these things and I tried searching for relevant threads but everything I found was a bit over my head so sorry if this has come up loads of times before but I was hoping someone might be able to explain in simple terms the reasoning behind...

I have a question regarding conservative vectorfields and singularities. Suppose we have a vectorfield who is defined everywhere in R^2 except at the origin where it has a singularity, and suppose it's curl is zero. We then have that it is conservative in every open, simply connected subset in...

Let V be the variety of the ideal (f) a singular point is a point where all the partial derivatives of the f are zero. I know you can find singular points by writing down all these partial derivatives and also that the points are zeros of f (such as all points on the variety) and solve that...

consider the function \frac{1}{\epsilon^2 + z^2} So we know that there are two poles, one at z = i \epsilon, one at z = - i \epsilon. So when this function never hits 0 on the real line, how do the singularities affect its behavior on the line? Okay, so poles are a subclass of singularities...

In 2006, the mathematically rigorous proof of the Poincaré conjecture was completely excepted. The Poincaré conjecture was put forward by Henri Poincaré in the early 1900's. It is a theorem about the characterization of the 3D sphere amongst 3D manifolds. It was considered one of the most...

Hi I'm just working on an integral where I need to classify the singularities of the integrand \frac{{\sin \left( {\pi z} \right)}}{{z^4 - 1}}. There are singularities at z = \pm 1, \pm i but the ones I'm interested in are at z = \pm 1. \frac{{\sin \left( {\pi z} \right)}}{{z^4 -...

Homework Statement Determine if the following are removable, pole (with order), or essential singularities. a) f(z) = (z^3+3z-2i)/(z^2+1) a=i b) f(z) = z/(e^z - 1) a=0 c) e^e^(-1/z) a=0 2. The attempt at a solution Part a is pretty straightforward, just simplify it down to...

Homework Statement i have a problem about the naked singularities which are appeared in einstine' s solution and mathematically possible ... in that i have readed that for the weak conjecture states (by the penrose and hawking singularity theorems ) that all singularities in gravitational...

This just out: http://arxiv.org/abs/gr-qc/0702144 Singularities and Quantum Gravity Martin Bojowald 41 pages, lecture course at the XIIth Brazilian School on Cosmology and Gravitation, September 2006 IGPG-07/2-4, NSF-KITP-07-19 "Although there is general agreement that a removal of...

What of the possibility that dark energy prevents total gravitational collapse of black holes, and might also have helped avoid an actual singularity at the big bang?

Specifically what I`m referring to is the final discussion summing up the program in which the weakness of lqg was characterized explicitly as "the whole theory". Was this a constructive way to end the program? Perhaps some of you would rather ignore this.

How can a smooth deformation of a Lorentzian manifold possibly create one or more singularities?

Homework Statement Investigate the possible behaviour of the singularity as t \rightarrow 0 in the Kasner solution. Homework Equations The metric for the Kasner solution is given by ds^2 = c^2dt^2 - X_1^2(t)dx_1^2 - X_2^2(t)dx_2^2 - X_3^2(t)dx_3^2 The Attempt at a Solution I...

http://online.kitp.ucsb.edu/online/singular_m07/ go here for Ashtekar talk http://online.kitp.ucsb.edu/online/singular_m07/ashtekar/ I found it works best when I click on "download the whole movie", which takes 5 minutes or so and then I have it on desktop so i can listen to it again. the...

In "week182", back in 2002, I referred to this very nice thesis: Joris van Hoboken, Platonic solids, binary polyhedral groups, Kleinian singularities and Lie algebras of type A,D,E, Master's Thesis, University of Amsterdam, 2002, available at...