Singularity Definition and 423 Threads

Homework Statement Show that if z0 is an isolated singularity of f(z) that is not removable, then z0 is an essential singularity for ef(z).Homework Equations z0 is a pole of f(z) of order N iff f(z) = g(z)/(z-z0)^N, where g is analytic at z0 and g(z0) is not 0, iff 1/f(z) is analytic at z0 and...

Hi, I have a question regarding partial fractions. One of my Math lecturers said that to find partial fraction, we are actually finding the singularity points. I don't understand what happens at a singularity point that allows us to decompose a function into the sum of two other functions...

I researched this some, but could not find a method to calculate the radius of the ring singularity in a Kerr black hole. I would think it is a function only of black hole mass and angular velocity. Please let me know if there is some reports or papers on this.

The nature of a black hole is that gravity attracts objects at a speed faster than light making it impossible for them to be able to escape but if the object is accelerating towards the black hole it would slow down and become more massive the close it got because it is approaching the speed of...

*Disclaimer: I do not claim to be knowledgeable quantum mechanics past amateurism. I'm just interested in the topic.* I had a thought during Classical Mechanics Physics class two days ago on the nature of singularities in black holes. I realized-at least in my speculation-that singularities...

If you haven't seen the TIME article: http://www.time.com/time/magazine/article/0,9171,2048299,00.html So what exactly would happen if AI became more intelligent than any human that could ever exist? What would stop such a machine from creating another machine more intelligent than itself ad...

Hi, Do you know the name of this kind of singularity at A ? The function is finite but the left derivative is +\infty and the right derivative is -\infty. http://shareimage.org/viewer.php?file=mt79897bbpxxse1v8pzb.jpg Thanks

Hi all, I've formulated using Lagrangian formalism the equations of motion for a spinning top. I know about the gimbal lock/singularity that occurs at theta=0 and I was wondering if there was any other way to do it without dwelving into quaternions. Yogi published a paper "A Motion of Top...

This is not a question - more a topic of discussion; as I am not expecting definitive answers. At the center of black holes we stipulate singularities, now I understand that mathematically a singularity does not make sense; infinite density and zero spatial volume being irreconcilable and an...

As far as I know, the classic paper applying the Hawking singularity theorem to our universe is this one: Hawking and Ellis, "The Cosmic Black-Body Radiation and the Existence of Singularities in Our Universe," Astrophysical Journal, vol. 152, p. 25, 1968...

Homework Statement Hello friends, I'm a student of mechanical engineering and I have a problem with computing residues of a complex function. I've read some useful comments. Now I ve got some ideas about essential singularity and series expansion in computing the residue. However, I still...

Can somebody please explain to me the idea of zero mass and infinite density, my mind just is not comprehending it, it seems almost illogical to me. Please help my brain make sense of this. Non-mathemetical please as I am not part of the scientific community. If the answer is just a simple...

In general, how do you define the dimension of a singularity? E.g., we think of a Schwarzschild singularity as pointlike, so that its world-line is one-dimensional, and on a conformal diagram we represent it as a spacelike line, which seems to make sense. In point-set topology, we have...

We are told that at the centre of a black hole lies a singularity; very small and very heavy. We here a lot about the mass but not the size (diameter) of this object,I asume this is not zero So, incredibly tiny though it may be , it would still bel greater than 0. Questions;- What then is the...

In the current mainstream theory of black holes, there exists a singularity of infinite density. However, it seems to me that matter actually could not compress tightly enough to reach this point. As matter coalesces in a black hole, space-time would increasingly curve. As the density...

I am trying to solve this integral equation numerically. The kernel has a singularity at the endpoint 1. Any suggestions?? f(s) = \int_0^1 \frac{1+st}{(1-st)^3} f(t) dt

Please teach me this: What is the difference between singularity and infinity points.Because we often encounter with infinity counterterms in QTF theory,but trying to avoid the singularity counterterms. Thank you very much in advanced.

Find any singularities in the following,say whether they are removable or not f(x) = (x2 + 2)/x Attempt at a solution when f(0) = ((0)2 + 2)/0 =2/0 which isn't defined So 0 is a singularity

I have read that inside a black hole there is a point called "singularity", where all the laws of physics break down. But exactly what does that mean?

Hello, Can anyone help me with that? It's a problem taken from Wald book on General Relativity,in the section of Schwarzschild solution Thanks Show that any particle (not necessarily in geodesic motion) in region II (r < 2M ) of the extended Schwarzschild spacetime, Figure 6.9, must...

What exactly is singularity? I was working with a friend earlier today discussing a possible resolution to the black hole mystery. His theory having to do with singularities was very interesting, but I left the conversation clueless of what a singularity actually is. I can't believe I have...

Hi all, I'm doing some analysis of a bicycle mechanics problem and at one point the approximations I'm making mean that the problem reduces to the classic inverted pendulum. I'm very confused, as the equations I've worked out appear to have an unphysical singularity in them, and I can't see...

Please correct me if I'm wrong in any sense. And please forgive me if I'm posting this in the wrong forum. I guess my general question is, presuming the big bang model is correct (one that includes a singularity), does that prove actual infinites exist? In other words, we know infinites exist...

Hi everyone, I'm brushing up on some complex analysis and I came across the following example, which is driving me crazy: I learned that z_0 is a pole of order k of f(z) if f(z)=\frac{g(z)}{(z-z_0)^k} where g(z) is analytic on some open disk around z_0. And an essential...

Homework Statement Determine whether the set, together with the indicated operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails. "The set of all 2 x 2 singular matrices with the standard operations." Homework Equations...

could a particle of antimatter be the singularity inside a black hole?

From what I can discover it seems that a naked singularity is a singularity without an event horizon. It also seems that this may be a black hole in the making, as it is a product of continued gravitational collapse. This seems to raise three questions: 1. If a singularity is a point at...

Let's say you start outside the event horizon r>2m, how long does it take according to your own wristwatch to hit the singularity at r=0 (ignoring the fact the tidal forces rip you apart...), assuming you just free fall and plunge in radially? I'm thinking you need to consider the timelike...

Hi, I was just pondering the moment of the Big Bang, and have been doing some reading on the subject, in which there exists problems consolidating the mathematics of relativity and quantum mechanics. To my understanding the theory of realtivity predicts the universe started from the Big Bang...

Since atoms above a certain atomic number are unstable and have an extremely short lifespan, then the atoms of the unknown element that comprises the mass of a collapsing star in the process of becoming a black hole just before the stage where a singularity is achieved should by all accounts...

if a matrix is invertable can it be singular ?

Is there any merit to the idea that all black hole singularities are in essence one and the same singularity?

I've been reading up a bit on black holes but I don't quite grasp why there should be a singularity at the center. As far as I understand a singularity forms when all the mass of an object collapses to withing the schwarzschild radius, according to wikipedia...

Homework Statement I = \int^{2}_{0} (1-e^{-x})/\sqrt{x} I=\int^{2}_{0.1}x/sin^2(x) Homework Equations The Attempt at a Solution I tried to integrate by part, but I approached to trivial solution. I know that the answer is involved with Error function, but I don't know how I could reach the...

Since the black hole has infinite brightness near the singularity just below the photon sphere, would the big bang singularity also possesses such characteristic?

Since the big bang singularity has infinite density, gravity, and heat, am I correct to think that it has infinite energy? Since the black hole singularity also has infinite density, gravity, but has finite heat, does it have infinite energy as well? With regards to the black hole...

This may seem like a foolish question, but I can't seem to find the answer anywhere. Also, please forgive the question if it is ambiguous but the context in which it arises is not clear to me: There is a mapping H(x,p,\cdot): \mathbb R \to \mathbb R with x,p fixed, which attains its maxima...

When can true singularity take place? Was the big bang the only chance for this condition? Do black holes represent a singularity? I would doubt this because a black hole only exists because there is a contrasting environment with which to compare and identify the event.

Photons "live" in a singularity? I did some searches, but couldn't find an answer to this on this forum. Since a photon can travel 1 km, 1 lightyear, 1 million lightyears in ZERO time from its own perspective, and if we did a though experiment from the point of view of a photon, does that...

Was re-reading 'A Brief History of Time' the other night and came across this ::: "Two black holes collide to create an event horizon greater than the sum of the areas of the originals." There are no attempts to explain this phenomenon throughout the reading; though I believe there may be an...

If during star collapse the mass not blown away is large enough to form a black hole, shouldn’t the resulting extraordinary high temperature essentially convert all the mass into contained radiation? The basic pressure formula for this intense radiation would likely be P = pc*2 (where p is the...

Hawking singularity theorem -- what if not all geodesics incomplete? The Penrose singularity theorem tells us that once you get a trapped surface, at least one geodesic is guaranteed to be incomplete, going forward in time. But this doesn't mean that 100% of the mass of a collapsing star has to...

Since r is time-coordinate below the horizon, how can you interpret that the r=0 singularity is an event at fixed time?

Okay one more question for you guys I'm having trouble figuring out, probably because the search function on here is difficult to use successfully if you're unfamiliar with the terminology involved. One of the popular physics books I've read is called "The Conscious Universe" by Kafatos and...

If all galaxies originated from big-bang, and if currently galaxies are still moving away one from the other, shouldn't it be possible to determine also where they are moving away from? i.e.where the big-bang-singularity was?

"generic" naked singularity I don't understand the arguments/discussion against naked singularities. The reason is that it seems obvious to me that given a black hole, there is a generic procedure to form a naked singularity. This reasoning is probably flawed (otherwise there wouldn't be...

Are black holes a point of singularity of infinite density, approaching that point as a limit, or just really massive and really dense? Is light really being "sucked in" by the gravity and actually being attracted to the object, or is it really just following the really really steep bend in...

Homework Statement Let f be analytic in the region (z:0<|z-a|<r) and isn't defined at z=a. Prove that if there is a neighborhood of z=a where Re f(z)>0 then z=a is a removable singularity of f. Hope you'll be able to help me Thanks in advance Homework Equations The Attempt...

Homework Statement Classify the isolated singularities and find the residues \frac {\sin(\frac {1}{z})}{1-z} Homework Equations I know the Taylor series expansion for 1/(1-z) when |z|<1 and I think I know the Taylor series for sin(1/z). The reciprocal of each term of the Taylor series of...

I am writing a paper and need to know if the following statement provides a simple yet accurate description of a Singularity. If not, please submit suggestions for improvement. (thank you in advance for any help): In scientific theory a Singularity is a zone of infinite density that is...