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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 ...
Yossarian's user avatar
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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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7 votes
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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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7 votes
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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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5 votes
2 answers
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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 ...
haael's user avatar
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Why poles of two-point function corresponds to bound states?

In this article Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms the author has: Let $\mathcal{G}$ be fourier transform of the green function $$ \begin{array}{r} \...
amilton moreira's user avatar
5 votes
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223 views

Imaginary poles of the Green's function

I am dealing with a theory with the Green's function that has infinitely many poles on the imaginary axis: $$G(\omega)= \sum_{n=1}^{\infty} \frac{1}{\omega-i\mu_n}$$ where $\mu_n=\cosh(n\beta/2)$, and ...
danport's user avatar
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How does the renormalization group justify the renomalization process?

I recently learned "Renormalization" and "RG". My textbook says "RG allows us to make sense of why a renormalized quantum field theory describe Nature." To me, it sounds like "RG justifies the ...
J-Gan Kim's user avatar
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232 views

Where does chiral matter at conical singularities "come from" in M-theory?

It seems to be accepted that to produce chiral fermionic matter in a compactification $\mathbb{R}^4\times X$ of M-theory/11d SUGRA to four dimensions, we need the seven-manifold $X$ to have isolated (...
ACuriousMind's user avatar
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Heat kernel expansion for entanglement entropy

Can somebody please let me know where I can find a reference for calculating heat kernel coefficients on a manifold with conical singularities? I am trying to compute the entanglement entropy for ...
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Eigenvalues of the geodesic deviation equation, curvature invariants, and singularities

The geodesic deviation equation tells us what tidal forces freely falling observers experience in a local Lorentz reference frame. The tidal deformation tensor is $$E^{\alpha}_{\gamma}=R^{\alpha}_{\...
bkocsis's user avatar
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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 ...
ziv's user avatar
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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 ...
John's user avatar
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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 ...
Roger's user avatar
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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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What is the physical meaning of the derivative of the norm of a Killing vector?

Initial considerations Consider a metric of the form $$ ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}=-\alpha^2(r,t)\,dt^2+a^2(r,t)\,dr^2+r^2\,b^2(r,t)\,d\theta^2+r^2\,b^2(r,t)\,\sin^2\theta\,d\varphi^2\ .\quad (...
L. Werneck's user avatar
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1 answer
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Why does a pole in the Green function correspond to a bound state?

Consider the many-body (zero temperature) fermion Green function $$ G(a,b;t)=-i\theta(t)\langle\psi_a(t)\psi_b^\dagger\rangle $$ Where I'm restricting $t>0$ for causality and that the free ...
Andrew Yuan's user avatar
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Confused about a derivation in Proposition 8.3.1 in Hawking and Ellis

I'm working through the proof of Proposition 8.3.1 in Hawking and Ellis (1973, pp. 278-80) about the equivalence between $b$-completeness of a Lorentzian manifold and $m$-completeness of its ...
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Hypothetically, could the interior of a black hole look exactly like the universe that surrounds us?

I do understand that we can't experimentally verify anything we imagine about the interior of a black hole. If we were to apply what we know about the physics of the observable universe and assume ...
Amber Lily's user avatar
3 votes
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80 views

Universality of leading singularities in QFT

I have now seen at several places claims of the form "each state looks like the vacuum at short distances" or similiarly that the "leading singularity of correlation functions is ...
DerHutmacher's user avatar
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0 answers
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References for Subtleties in Electromagnetism: Infinities

There appears to be some infinities in classical electromagnetism: The total energy contained in the electric field of a point charge diverges. The potential at a point charge diverges. The potential ...
3 votes
0 answers
134 views

Is there a physical interpretation of the connection between the scattering matrix and bound states?

The square integrability condition of a scattering wavefunction can be written for imaginary wavenumber $k = -\mathrm{i}\kappa$ as $$\int_0^\infty \mathrm{d}r\left|(-1)^l \mathrm{e}^{-\kappa r} - S_l(-...
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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. ...
Powder's user avatar
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3 votes
1 answer
322 views

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 ...
Ashley Chraya's user avatar
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669 views

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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3 votes
0 answers
64 views

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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3 votes
0 answers
169 views

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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3 votes
0 answers
1k views

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 ...
David Ding's user avatar
3 votes
1 answer
340 views

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 ...
Árpád Szendrei's user avatar
3 votes
2 answers
415 views

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 ...
usmans's user avatar
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2 votes
0 answers
429 views

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 ...
Sonia Llambias's user avatar
2 votes
0 answers
36 views

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 ...
Mark Highton Ridley's user avatar
2 votes
1 answer
94 views

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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2 votes
1 answer
320 views

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 ...
Stefano98's user avatar
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2 votes
0 answers
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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 ...
Rick's user avatar
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2 votes
0 answers
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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 ...
benholstder's user avatar
2 votes
0 answers
77 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 ...
Hierarchist's user avatar
2 votes
0 answers
192 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 ...
TaeNyFan's user avatar
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2 votes
0 answers
106 views

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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2 votes
0 answers
339 views

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 ...
Everything's user avatar
2 votes
1 answer
114 views

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 ...
del's user avatar
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0 answers
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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 ...
shinotakatoshi's user avatar
2 votes
0 answers
323 views

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 ...
Harambe's user avatar
  • 500
2 votes
2 answers
118 views

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?
João Bosco's user avatar
2 votes
0 answers
85 views

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 (...
M111's user avatar
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2 votes
0 answers
85 views

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-...
diracula's user avatar
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2 votes
0 answers
3k views

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 ...
docscience's user avatar
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2 votes
0 answers
112 views

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 ...
Dilaton's user avatar
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2 votes
0 answers
109 views

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 ...
kbb's user avatar
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1 vote
0 answers
45 views

Can ring singularities form a Hopf link?

Can ring singularities form a Hopf link?
Michael's user avatar
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