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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Black Hole Singularity Other Universe

It is thought that there is another universe beyond the singularities of black holes. Is it because width of the light cones become zero at the singularity, meaning that you can cross infinite ...
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Thinking about singularities and the speed of light

I apologize that this takes so much explanation. From what I understand about the idea of the "singularity" in a black hole, it's not taken literally as Infinite mass in zero density or ...
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Singularity in coordinate transformations

Ok. I would like to apologise if the question is somewhat 'stupid'. So, initially I didn't pay much attention to it, but we know that when the Jacobian vanishes for a particular point, we say that the ...
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Why does the electromagnetic repulsion between protons in the nuclei fail to prevent the formation of a black hole singularity?

The process of forming a black hole requires all matter to be crushed into a point by gravitational attraction. But the electromagnetic repulsion between protons inside the nuclei of the atoms is way ...
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How can a singularity move?

When an object approaches the event horizon of a black hole from the point of view of a remote observer time of this object freezes. (Does it also stop? Since it has a finite speed even at the event ...
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Electrostatic potential resolving singularity

I'm trying to determine the electrostatic potential caused by a specified charge density function: $$ \rho_c(\vec{r}) =\begin{cases} 1 & \vec{r} \in V\\ 0 & \text{otherwise} \end{cases} $$ The ...
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Big Bang and the Pauli Exclusion Principle

Due to some of the basic principles of quantum mechanics, we have the Wolfgang Pauli exclusion principle, where two fermionic bodies cannot occupy the same quantum state simultaneously. If that is ...
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1answer
101 views

Can Hawking Radiation occur at the Big Bang singularity or at the Big Crunch singularity?

While reading about Hawking Radiation which occurs due to the quantum effect (quantum fluctuations) at the event horizon of the black hole,I was thinking whether this radiation can take place at the ...
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Is there any reason that the Schwarzschild radius of a 5(+)-dimensional object would require different math?

$$R_g = \frac{2GM}{c^2}$$ It doesn't seem to me that the gravitational constant or speed of light particularly care how many dimensions there are in this context. Mass is mass whether it comes in ...
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If the universe started from a singularity expanding based on pressure, how did physics decide which direction each thing would expand toward?

Two entities truly captured within a singularity would have no positional offset from each-other, nor volume to differ either. Yet for two things to push away from each-other, they must have either ...
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Can there be singular subtensors in the elasticity tensor and what would it mean in that case?

Can the elastic tensor $C_{ijkl}$ describing the stress strain relationship as $$\sigma_{ij} = C_{ijkl} \, \varepsilon_{kl}$$ contain singular subtensors? In that case, what would it mean mechanically?...
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Time and causality at the beginning of the universe

I have been, quite a few times, been caught up in arguments on the internet, where my opponent posits causal events existed before the "singularity" at the "beginning" of the ...
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Doubt regarding the existence of conjugate points on timelike geodesics

The expansion of a timelike geodesic congruence with (normalized) tangent vector field $\xi^a$ is defined as $\theta=\nabla_a\xi^a$. Assuming the strong energy condition, $R_{ab}\xi^a\xi^b\geq 0$, and ...
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Topologically, is a curvature singularity just a hole?

Topologically speaking, a hole can be introduced into a manifold and it will still be a manifold, e.g. remove points within a 2-sphere of some radius from the cartesian plane and you'll still have a ...
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Does the physical singularity of the Reissner-Nordstrom metric have a ring structure?

The physical singularity of the Kerr metric has a ring structure due to the axi-symmetric nature of the metric. The Reissner-Nordstrom metric is the solution for a non-spinning, electrically charged ...
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Singularity at the centre of Black hole [duplicate]

Why we assume that there is a singularity at the centre of Black hole? Isn't it possible that there is a different state of matter exist at such a high pressure which we haven't able to explain using ...
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152 views

Aren't Black Holes Just Neutron/Quark Stars?

Disclaimer: My understanding of general relativity is rudimentary at best, so bare with me and correct me where necessary. Also, any math in the explanation is appreciated, but try to also keep the ...
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What is the dynamic geometry of merging rotating black hole singularities?

In rotating black holes, either Kerr (uncharged) or Kerr-Newman (charged) the singularity is believed to be a one dimensional ring or torus, unlike the single point singularity of a non-rotating black ...
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Is the mass of a black hole somewhere at all?

The Schwarzschild vacuum solution describes the gravitational field and thus the spacetime curvature of a black hole. The mass of a black hole is sometimes associated with its singularity as pointed ...
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If black holes are just empty vacuum of space inside, then what causes the curvature?

I have read this question: The fundamental confusion many have about black holes is thinking that they are discrete "things" surrounded by horizons and other phenomena. But they are ...
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What if black hole is perturbed and it is far from being spherical/symmetric? Can it still sustain a singularity?

Black holes are generally the considered as the most symmetric astrophysical bodies in the Universe. If an intermediate mass black hole consumes a nearby red giant and in the process, for a very short ...
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Violation of weak vs strong cosmic censorship examples

I am trying to better understand the weak vs strong cosmic censorship through simple examples. On the Wikipedia page, it says: "The two conjectures are mathematically independent, as there exist ...
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What is the mathematical description of a point torque (or point couple) singularity?

Suppose that a concentrated (point) force is exerted at the origin of a 3D dimensional space along the direction $\boldsymbol{e}$. Mathematically, this could be prescribed in terms of a delta Dirac ...
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Quantum Mechanic: Sperically symmetric finite well [duplicate]

Consider the following 3D potential: $$V(r)=\begin{cases}-V_0 \ \ \ \ \ \ & r \leq a\\ 0 &r > a\end{cases}$$ we want to find the eigenfunctions for $\ell=0$, in particular we are interested ...
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How can the jerk tend towards infinity?

Consider a block of mass $m$ kept on a rough surface. A time varying force $F =t$ is applied on the block in a direction parallel to the surface. Assuming the coefficient of static and kinetic ...
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Singularities of the Coordinate Systems

We know that, the singularity of the Schwarzschild metric at $r=2M$ can be removable via coordinate transformation to Kruskal-Szekers . Can we apply a similar argument to the Kerr metric? If so, what'...
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What is the problem with a rotating singularity?

In most cases, people ask how can a point spin, resulting in a 'ringularity' as an answer. But I'm not quite sure why a point can't spin. After all, it's like saying how can something with mass have ...
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Am I wrong to conclude that every gravitational field has its origin in a singularity point? [closed]

If all matter "swallowed up" by a black hole becomes a singularity, what prevents this singularity from already being present in matter, in a more discreet, more diluted form? The ...
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Why are the poles of the propagator the masses of bound states and not the masses of unbound states as well?

For a real scalar field $\phi$, the Kallén-Lehmann representation of a two-particle propagator in a translation invariant theory in QFT is: $G(x_1,x_2) = \sum_{m, \; other \; quantum \; numbers} \int \...
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2answers
109 views

How do the counterterms in QED cancel the infinities?

I'm having a hard time understanding how the cancellation of the infinities works in QED at 1 loop level. I think the aim of this procedure is to obtain a Lagrangian such that all the diagrams that ...
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1answer
40 views

Gravitational self-force of rod

Suppose we have a thin rod of density $\rho$ and length $L$, and we want to calculate the acceleration due to gravity at one end of the rod. Let this end of the rod be at $x=0$ and the other end be at ...
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Singular Integrand vs Diverging integral

I am reading Jackson's Electrodynamics and came across this part that I'm not sure I understand. Specifically what is Jackson referring to when he says "it turns out that the resulting integrand ...
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How can QED by predictive if it diverges?

One of the tests of Quantum Electrodynamics is the value of the "Anomalous magnetic dipole moment". The theoretical value is: $$a_e = 0.001\ 159\ 652\ 181....$$ We say that QED "...
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Why can the Reissner-Nordström black hole be naked? [duplicate]

Reissner-Nordström black holes are (non-rotating) black holes with electric charge. The Schwarzschild radius depends on their mass and charge. The metric is given by: $$ ds^2 = -\left(1-\frac{2M}{r}+\...
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What is the physical origin of UV divergences?

I've heard of UV divergences appearing in perturbative calculations as both a mathematical artifact and as having a physical origin (the latter understanding due to Wilson). Could one clarify what ...
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109 views

Computing curvature singularities from a metric

Suppose I have the metric $$ds^2 = f(r)(dt^2-dr^2-dz^2) - \frac{1}{f(r)} d\phi^2. $$ How would you calculate the curvature singularities of this metric if we assume that $f(r)$ takes value $0$ for $...
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A naïve question about spacetime singularities

Very little that I know about general relativity is that there are solutions of its equations with singularities, and these are interpreted as black holes. Mathematically, the most widespread kind of ...
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191 views

Why does General Relativity predict that singularities are infinitely dense?

From my understanding of general relativity, energy curves spacetime to produce an effect that we call gravity. The greater the concentration of energy, the greater the curvature and hence the greater ...
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Cosmic censorship conjecture: Why naked singularities are expected not to exist?

According to wikipedia, the weak form of the Cosmic Censorship Hypothesis says the following: Singularities [...] are typically hidden within event horizons, and therefore cannot be observed from the ...
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Do black holes rip apart even atoms and protons and neutrons?

I am aware that black holes rip apart objects because of spaghettification. What about atoms and protons and neutrons? Do they get ripped apart too? But, in the case of protons and neutrons, wouldn't ...
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How does Planck's curve solve the ultraviolet catastrophe?

I previously asked whether Planck's curve actually reaches zero, to which some of you answered that it only approaches it, which raises the question: doesn't this mean that a photon with extremely ...
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Are there instances where the density matrix is singular?

Are there instances where the density matrix is singular? Can there be cases where a measurement projection onto the density matrix gives a singular matrix?
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Why is the Schwarzschild metric equal to 0 for light at the event horizon?

Carroll & Ostlie's Introduction to Modern Astronomy and Astrophysics provides a derivation on why light and information is frozen at the event horizon: However I noticed that they equated $ds=0$ ...
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What happens to the force and other quantities in cases like the force of gravity between two bodies once they collide and become one single body? [duplicate]

We know that the force of gravity between two bodies brings them closer by attraction and as they come closer their velocities towards each other increases due to acceleration by the force. However ...
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2answers
76 views

If something moves at an infinite speed how long does it take to traverse infinity? [closed]

If something moves at an infinite speed how long does it take to traverse infinity? If the answer is infinite time, then is there something greater than infinity such that something can traverse ...
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1answer
60 views

Infinity in two-point correlator of $\phi^4$ theory

I’m reading Peskin & Schroeder as a first intro in QFT. The first half of chapter 4 is spent on calculating the 2-point correlation function in $\phi^4$ theory: $$\langle \Omega | \phi(x) \phi(y) |...
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Can singularities be ever formed from an outsiders perspective? [duplicate]

As far as I know, as an object gets closer to an event horizon, gravitation time dilation makes it move slower from an outside perspective, so that it looks like it take an infinite amount of time for ...
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Problem of infinities in QED

Other than Renormalization what were the other approaches taken to solve the problem (by physicists of that period)? Why were they not as successful as Renormalization?
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Why is the voltage in inhomogeneous electric fields undefined?

For example I'm thinking about a radial symmetric field like a point charge. The voltage $U$ can be determined by $$\int_{r_1}^{r_2} E(r)\mathrm{ds} = \frac{Q}{4\,\pi\varepsilon_0}\,\left(\frac{1}{r_2}...
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Using $0*\infty=0$ in Griffiths instead of indeterminate?

In all such derivations, Griffiths suggests assuming the constants zero (in this case A) to eliminate the $f(x)$ when it goes to infinity, but zero * infinity is undetermined instead of zero, so how ...

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