# 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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### Why is the Taub-NUT instanton singular at $\theta=\pi$?

Consider the following metric $$ds^2=V(dx+4m(1-\cos\theta)d\phi)^2+\frac{1}{V}(dr+r^2d\theta^2+r^2\sin^2\theta{}d\phi^2),$$ where $$V=1+\frac{4m}{r}.$$ That is the Taub-NUT instanton. I have been ...
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### Contradiction between Geroch's theorem on topology change and formation of naked singularity?

It's been known since Oppenheimer and Snyder's work in 1939 that it's easy to get a naked (i.e., timelike) singularity in models of spherically symmetric gravitational collapse, for forms of matter ...
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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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### What is the state-of-the-art on spacelike singularities in string theory?

What lessons do we have from string theory regarding the fate of singularities in general relativity? What happens to black hole singularities? What happens to cosmological singularities? Which ...
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### Is the Schwarzschild singularity a limit of the Kerr singularity?

In a Schwarzschild black hole, the singularity is spacelike. In a Kerr black hole, it is timelike. Is there any continuous transformation between those solutions? Can the Schwarzschild solution be ...
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### Normalization of zero point energy in string theory

Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
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### Why is the energy of a vortex in a superconductor finite?

I just had a glimpse of the Ginzburg-Landau theory of superconductivity. I am surprised that that the energy of a vortex is finite. This is surprising because as far as I know, in superfluids, the ...
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### Merging black holes: from two singularities to a ring singularity?

In rotating black holes, the singularity is believed to be a ring or torus, unlike the single-point singularity of a non-rotating black hole. Topological change - Imagine we have two distant black ...
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### Partition function of an asteroid gas (gravity)

Consider the classical problem (Newtonian gravity) of a large number of $N$ identical non-interacting asteroids orbiting around a big planet. I wanted to see if the problem was solvable. I wrote my ...
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### Regular black hole with an evanescent horizon

I'm reading a great paper named Geodesically Complete Black Holes by R. Carballo, F. Filippo, S. Liberati and M. Visser about regular black holes and I'm trying to understand a particular situation. ...
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### 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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### What is the Planck Pressure?

What exactly is the Planck Pressure? According to wikipedia the Planck pressure "is not found except for shortly after the big bang or in a black hole". But wouldn't the pressure inside a black hole ...
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### Must collapse to a singularity proceed through a strong curvature singularity?

A strong curvature singularity (s.c.s.) can be defined as one for which a geodesic is incomplete at affine parameter $\lambda=0$, with $\lim_{\lambda\rightarrow0}\lambda^2R_{ab}v^av^b\ne0$, where $v^a$...
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### No-hair theorems for naked singularities?

For black holes, we have no-hair theorems that say, under certain assumptions about the matter fields, that they are uniquely characterized by just a few parameters. Are there any such theorem for ...
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### How to calculate topological charge?

For a complex vector field in two dimensions with one or more phase singularity - a point where the field amplitude is zero and the phase is undefined - how do you explicitly calculate the total ...
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### Do merging BHs have two or just one singularity?

There are a lot of questions about BH mergers on this site, and based on those, there are two main possibilities: 1. Initially, the merged BHs, now a joint single BH, have two singularities, that ...
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### Gravitational singularity

Is it possible that the gravitational singularity actually turns out to be a genuine singularity once we have a true theory of quantum gravity in place? There is a lot of talk about singularity but ...
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### Dirac string and nature of singularities

The Dirac magnetic monopole is defined as \begin{align} \vec{B}=\frac{g\vec{r}}{r^3}\,, \end{align} where $g$ is the strength of the monopole and $\vec{r}$ a vector. It is possible to show that the ...
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### Do the apparent infinities at the center of black holes disappear if instead a phase-change takes the place of its singularity?

When I watch physics documentaries that discuss black holes, they talk of impossible infinities in the singularity at a black hole's centre. I was wondering about the bubbles of water vapour in ...
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### Infinite gravitational potential question

For this question I use Newtonian gravity only. Relativistic gravitational/kinematic effects are ignored. It is known that the gravity surrounding a point particle of mass $M$ can be described by ...
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### Understanding the Kruskal diagram for Schwarzschild spacetime

I am studying Kruskal coordinates for my General Relativity course. On the book Spacetime and Geometry: An introduction to General Relativity by Sean Carroll, the author gives the metric in Kruskal ...
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### How long from event horizont to singularity?

I was reading Quora answers. Someone asked how long it would take to get to the center of a black hole. Their answer (with no explanation or calculations) was 10 minutes for a Supermassive and 6 ...
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### Why do propagators have singularities at the Fermi surface?

Consider the following integral: $$\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\frac{1}{i\omega - E(K)}\frac{1}{i\omega - E(K')}$$ At the Fermi level $K=K_f$, $E(K)=0$ and supposedly we have a ...
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### 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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### 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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### How do singularities combine when two black holes combine?

If we solved GR in the case of two black holes colliding, does each individual black hole have a single pointlike singularity at their respective centres, and would those singularity combine? Trying ...
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### How to calculate the total cross section of a QCD process? (qq->gg)

I want to calculate the total cross section of various QCD processes (let's go with $q\bar{q}\rightarrow gg$ for this question) at tree level for some colliding hadrons at a certain energy (let's go ...
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### Discontinuities in electric fields

I'm a mathematician self-studying physics for fun and I'm trying to wrap my head around a simple concept, which is a consequence of approximations. Basically, by Coulomb's law, if I have a point ...
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### Adding up gravitational fields of infinitely many objects?

I'm reading a book introducing gravity and find something I don't understand. Please check the attached image. The sentence in red bracket claims that if one adding up gravitational fields of ...
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### Minkowski Space is not truly conformally compact

We say a manifold $(M,g)$ is conformally compact if it is the interior of some $(\overline M, \overline g)$, such that g = r^{-2}\overline g|_M,\quad \mathcal Z(r) = \partial M,\quad \text{and}\quad ...
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### What is the energy required to create a gravitational field equivalent to that a mass $m$ shows?

If the mass of a neutron star in its collapse becomes a singularity, then the resting energy of this gravitational field must be $E = mc^2$ ($m$ = star mass). Is this possibility wrong?
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### Singularities not allowed in classical geometry of general relativity because of topology?

While looking at Prof. Brian Greene's research work I came across the statement regarding the difference between quantum geometry and the geometry underlying general relativity, "...topology change (...
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### Can fractional D-branes be described in F-theory?

In Type IIB string theory, there can exist fractional D-branes at singularities. Additionally, F-theory is in some sense an alternative description of Type IIB string theory. So there should be an F-...
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### What actually constitutes a 'rip' in the fabric of spacetime?

Science fiction writers often use the term 'rip' in the fabric of spacetime to provide a means of either time travel or instantaneous travel from one corner of the universe to another. But I've also ...
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### What is the relationship between complex time singularities and UV fixed points?

In this paper it is described how the turbulent kinetic energy spectrum and the flatness (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of ...
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### Is sonoluminescence relevant to the behaviour of Navier-Stokes (or converse)?

More precisely, could Sonoluminescence be a singularity of Navier-Stokes(NS)? Is there some other connection that might be interesting, or is it completely irrelevant? Wiki page mentions NS, but says ...
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