Questions tagged [singularities]

Use this tag for questions about singularities in physical quantities, i.e. cases where a quantity becomes or appears to become infinite or ill-defined. Consider the more specific tags [black-holes] and [wormholes] for certain kinds of singularities occurring in general relativity. For the procedure of "getting rid" of singularities, consider the [regularization] tag.

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1answer
284 views

Better derivation for the gravitational potential energy

I was shown this derivation for the gravitational potential energy, and I'm not very happy about it assuming that $\frac{1}{\infty} = 0$. Is there a better derivation, either using a completely ...
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5answers
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Work done in assembling a point charge is infinite [closed]

Griffiths says The energy of a point charge is infinite $$W=\frac{\epsilon_{0}}{2\left(4 \pi \epsilon_{0}\right)^{2}} \int_0^\infty\left(\frac{q^{2}}{r^{4}}\right)\left(r^{2} \sin \theta\; \mathrm{d}...
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0answers
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+50

Expansion in flat spacetime

I have been studying Raychaudhuri equation and focusing theorem related to it. Focusing theorem says that if the strong energy condition is satisfied and rotation tensor vanishes $\omega_{ab}$=0 then ...
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2answers
66 views

How do you actually use fields?

Note: I'm probably using the wrong letters/notation here. I apologize. I use $\omega$ to represent an object, and $\mathcal{U}$ is the universe. I'm not sure how else to do it. $m(\omega)$ and $x(\...
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1answer
60 views

Removable singularity of metric?

The metric of 2D plane is \begin{equation} ds^2=dr^2+r^2d\phi^2, \end{equation} which is singular at $r=0$ (is it because vanishing Jacobian?). It is said this singularity is removable if $0<\phi&...
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1answer
41 views

Is it possible that a black hole has a universe in itself? [duplicate]

Every black hole has a singularity. But the singularity is covered by a thing called 'Event horizon'or ' Schwarzchild Radius'. Our universe is originated from a naked singularity. By naked singularity,...
2
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1answer
60 views

Does electric charge $e$ become complex at some scale $\mu$?

\begin{equation} \mu \frac{\partial{e}}{\partial \mu }=\frac{{e}^3}{12\pi^2}=\beta({e})\end{equation} This is the equation for beta function in quantum electrodynamics, it tells us about how coupling ...
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0answers
77 views

What kind of causality would be broken if black hole singularities would be real?

In his article "The Universe as a Whole" 1, physicist Dennis Sciama said We therefore face a crisis in theoretical physics. Either classical general relativity breaks down, or effectively ...
2
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1answer
76 views

Infinite Coulomb force when charges contact

The Coulomb force between charged particles is inversely proportional to the square of the distance. Yet, why don't we observe the infinite force when the distance approaches zero? Say we can bring ...
0
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1answer
37 views

Distinction between different points at Big Bang Singularity

As per the Big Bang model of Cosmology roughly 13.8 billion years ago a singularity exploded exponentially to eventually become the present universe. At the present time (basically current time-slice) ...
14
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2answers
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Physically unacceptable solutions for the QM angular equation

I'm reading Griffiths's Introduction to Quantum Mechanics 3rd ed textbook [1]. On p.136, the author explains: But wait! Equation 4.25 (angular equation for the $\theta$-part) is a second-order ...
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2answers
47 views

What is the difference between coordinate- and curvature-singularities?

I recently came across the following question: The Schwarzschild metric in ingoing Eddington coordinates has the line element $$d s^{2}=-\left(1-\frac{2 M}{r}\right) d v^{2}+2 d v d r+r^{2}\left(d \...
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1answer
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Physical Size of a Naked Singularity [closed]

I have watched a few videos about naked singularities, and it is my understanding that one is a singularity without an event horizon. My question, is could you ever have that with anything larger ...
0
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1answer
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What is the physical shape of a rapidly spinning singularity?

Let's say I have a star 20x the mass of the sun. At the end of its life, it collapses into a black hole. Now correct me if I am wrong, but as it collapses it rotational speed dramatically increases ...
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2answers
97 views

Black Hole Formation

If you plot a space-time diagram of an object falling through the event horizon of a black hole, and draw the past and future "light cones" of the object at every point, wouldn't the point ...
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1answer
59 views

What happens when an expression for a physical quantity becomes undefined?

Now I am taking a quite a specific example here. Let's consider a circular race track banked at an angle of $\theta$. The coefficient of friction between the track and the tire is $\mu$. What's the ...
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1answer
53 views

What is a naked singularity?

What is a naked singularity? Would a naked singularity be one that that the event horizon is so small that it is the same size as the singularity? what could make one that small?
2
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1answer
70 views

Seeking intuitive explanations regarding $A_{n-1}$ singularities

I am studying Ben Craps' lecture notes Big Bang Models In String Theory for my undergraduate thesis. I am not well versed in topology, and would like intuitive explanations for certain ideas regarding ...
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0answers
58 views

Non-Vacuum Solutions for Black Hole Interiors

Everything I read about black holes—discussions using Penrose diagrams and Kruskal coordinates, etc.—seems to be based on vacuum solutions to EFE. Sometimes it’s said that all trajectories entering a ...
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0answers
39 views

Derivation of the Schwarzschild solution [duplicate]

For the Derivation of the Schwarzschild solution my Professor use: $R_{\mu\nu} = 0$ since we are in vacuum. I see that we are in vacuum, but we assume a mass at point $r = 0$. Thus, the curvature is ...
0
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1answer
32 views

What causes a singularity as opposed to something of a quantitatively extreme value?

Something that approaches infinity or is "essentially infinity" (an oxymoron) or is "near-zero" is the very opposite of the quality of infinity, and yet explanations tend to use ...
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1answer
55 views

Schwarzschild Naked Singularity Creation

In the Schwarzschild metrics (Plank units): $$ds^2=-\left(1-\frac{2m}{r}\right)dt^2+\left(1-\frac{2m}{r}\right)^{-1}dr^2+r^2\left(d\theta^2+\sin^{2}\theta d\phi^{2}\right),$$ we can have a Black Hole (...
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1answer
90 views

Gravitational attraction as distance approaches zero

Imagine a $x$-$y$ plane, which induces an acceleration field obeyed by the equation $ a= -\frac{C}{z^2} \vec{k}$ where $z$ is the perpendicular distance from the plane to the ball and $C$ is just ...
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0answers
26 views

Does tidal force continue to increase as a man falls into a black hole?

Small black holes have collosal tidal forces at their event horizons. But there are black holes large enough where a man can cross the event horizon without being ripped apart. But does the tidal ...
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1answer
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Is black hole supposed to oscillate in/out of singularity as matter falls on it?

So, as soon as star radius becomes smaller that Schwarzschild radius it becomes a black hole. But as matter continues to fall on it attracted by the gravitational pull its radius sooner or later will ...
3
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1answer
82 views

What is happening when a metric function changes sign?

I currently worked on a type of modified Tolman-Oppenheimer-Volkoff (TOV) equation. Usually people have this equation from a static spherically symmetric metric that has this form: $$ ds^2= -C(r) dt^2+...
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2answers
67 views

What happens in Newtonian mechanics when a particle reaches infinite force position?

Suppose a particle of negligible mass is placed at e.g. $x=1$ inside a one dimensional space with a force field generated by the gravitational attraction of a point mass at the origin $0$. I.e. the ...
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0answers
55 views

Free falling into a black hole: time to the singularity doubt!

I have trying to get a more precise insight into the calculation of the time to the singularity of a test mass into a non-rotatic uncharged black hole. Prelude: the lagrangian for a massive particle ...
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0answers
47 views

Are Black Holes high and low entropy?

Some time ago I read that without knowing more about quantum gravity the assumption that Black Holes continue to collapse is valid. That mystifies me somewhat but for the purpose of this question I’m ...
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0answers
80 views

How does the non-degeneracy of the metric imply that gravity is not fundamental?

In his General Relativity notes, on page 149, David Tong remarks that when we look for solutions to Einstein's equations, we can't just take any metric, such as $g_{\mu \nu} = 0$; we must pick one ...
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0answers
78 views

Wavefunction and a central potential $V(r)$ that is singular at origin

I read the following line from Weinberg's Lectures in Quantum Mechanics (pg 34): As long as $V(r)$ is not extremely singular at $r=0$, the wave function $\psi$ must be a smooth function of the ...
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0answers
41 views

What happens if two Naked Singularities collide?

I have seen that there is a likelihood that Naked Singularities may exist (though it is frequently argued). They have a variety of strange effects, such as having infinite density and such. I have ...
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0answers
26 views

How can black hole rotate? [duplicate]

I was reading about black holes and I've found part saying that black hole is a point and anther saying that black hole can rotate. However the points are dimensionless, so they can't rotate - How can ...
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0answers
60 views

Can a singularity really exist?

Okay, so I have an idea and I wanted to know if it works out or not. I imagine a black hole to form from a star, which is rotating. Let's say the star collapses because of some reason, and a black ...
4
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1answer
108 views

On renormalization of $\phi^4$

I am reading Schwartz's chapter on renormalizing the $\phi^4$ theory and I have two questions. We define the renormalized coupling to be the matrix element of all contributing diagrams at a given ...
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1answer
67 views

Covariance and contravariance of a singular metric tensor

I ran across this problem on an exam a couple days ago: Consider the transformation to the new coordinates $(r,u,z,\bar{z})$ $$r=\sqrt{(x^1)^2+(x^2)^2+(x^3)^2} \qquad u = x^0-r \qquad z=\frac{x^1+ix^...
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2answers
40 views

Basic confusion about fields and infinite potential

Consider a system of two electrically charged particles. Their charge doesn’t matter for my question but suppose they are both positive. I am confused about what the correct way to calculate forces on ...
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2answers
35 views

Poles of a transmission coefficient

I stumbled on the question I can't quite grasp: What is the meaning of poles for transmission probability $T(E)$? $$ T(E) = \left( 1+\frac{1}{4}\frac{V_0^2}{E (E+V_0)} \sin^2 \left(\frac{2 a}{\hbar }\...
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1answer
84 views

Why do physicists dislike Naked singularities? [duplicate]

Why do physicists dislike naked singularities? Why do physicists consider the potential existence of Naked singularities as a serious problem?
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2answers
586 views

Local cartesian coordinates on surface of sphere

I am learning differential geometry from Hobson et al, General Relativity: An Introduction for Physicists. In pg. 36 of the book, the author tries to show that the line element on the surface of a ...
2
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3answers
152 views

The meaning of the singularity in Schwarzschild metric

I have been told by many lecturers and many books that in the Schwarzschild metric $$ ds^2=-\left(1-\frac{r_s}{r}\right)dt^2 + \left(1-\frac{r_s}{r}\right)^{-1} dr^2 + r^2 d\Omega ^2 $$ the ...
2
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1answer
76 views

Does the potential of a charged ring diverge on the ring?

I know that the density and potential (in spherycals) of a charged ring is, respectively,: $$ \rho(\textbf{r}) = \frac{\lambda}{a} \delta(r-a)\delta(\theta-\tfrac{\pi}{2}) $$ $$ \varphi(\textbf{r})= \...
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0answers
26 views

What are timelike singularities? [duplicate]

What are timelike singularities? I'm trying to learn about the properties of timelike singularities.
0
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1answer
94 views

Is there any observational evidence for the existence of Schwarzschild black holes?

So AFAIK the objects that have been confirmed to be black holes by direct observation of the event horizon("black hole shadow"), like M87 for instance, also show observable evidence of frame dragging (...
4
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1answer
84 views

Confusions on QED renormalization

In many QFT textbooks, we usually see the calculations of vertex function, vacuum polarization and electron self-energy. For example, one calculates the vacuum polarization to correct photon ...
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2answers
75 views

Physical interpretation of propagator pole

In QFT the propagator is divergent for the on-shell momentum of the particles. When e.g. calculating the amplitude for a box loop, the propagator diverges for on-shell particles running in the box-...
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1answer
64 views

What happens to Coulomb's law at small distances? [closed]

I searched in the forum and found the maximum distance is $r=1.75\times 10^{-15} m$. Ok, imagine an electron hits a plate with charge of 1 proton, the result of Coulomb's law is $230$ Newtons. ...
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0answers
38 views

Question about Renormalization of Ghosts in QCD in MS scheme

During a calculation of the Renormalization constant of the ghosts in QCD I stumbled over the following question: When I calculate the self-energy of the Faddeev-Popov ghosts in $SU(N)$ non-abelian ...
2
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3answers
133 views

Black hole cosmology vs. Big Bang cosmology

The evidence for Big Bang cosmology is an expanding universe. The expansion of the universe is accelerating. Gravity causes acceleration. What evidence is there that proves everything is moving away ...
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1answer
61 views

Why can Stokes theorem be used in Aharonov-Bohm, eventhough there is a singualrity at the solenoid?

One can show that for the phase difference $\Delta$ between the two wave functions (slit 1 and slit 2) it holds the first equality on the LHS $$\Delta=\oint_{\partial\Omega} \vec{A}\overset{!}{=}\...

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