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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Infrared divergence in electron self-energy

On Peskin and Schroeder's QFT book, page 319, the book discussed various situations of QED divergence. On the first paragraph of p.319, the book considered Taylor series of electron self-energy ...
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Prove the causal future of a compact subset of a globally hyperbolic spacetime is closed (Wald's Theorem 8.3.11)

In Wald's GR, theorem 8.3.11 states that Let $(M,g_{ab})$ be a globally hyperbolic spacetime and let $K\subset M$ be compact. Then $J^+(K)$ is closed. Let me present my own proof, first. I am not sure ...
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How Existence Of Matter Is Possible Inside The Black Hole? [closed]

According to Chronology of the universe, origin of the universe initiated as per below sequence: Big bang (at 0 sec) occurs in the black hole (10^-35 m in size, Planck Length) at the center of the ...
6 votes
4 answers
249 views

What happens to the matter already at the very center of the star when it turns to a black hole?

I was wondering whether when an object collapses into a black hole, the matter in the position $r=0$, instantly becomes part of the singularity, or does it take time to fall into the singularity, and ...
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How do we know the field strength renormalization factor $Z$ is infinite for $\phi^4$ theory in 4D? [duplicate]

I am following Peskin and Schroeder and consider for simplicity only the $\phi^4$ theory in 4D. The field strength renormalization factor seems to first appear p.214 and be defined by $$Z= \left| \...
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1 vote
1 answer
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Computing $\langle 0|S |0\rangle$ in $\phi^4$ theory [closed]

$\newcommand{\bra}[1]{\langle #1|}$ $\newcommand{\ket}[1]{|#1\rangle}$ I have been reading David Tong's QFT notes. As part of an exercise, I am asked to examine $\bra{0} S \ket{0}$ to order $\lambda^2$...
2 votes
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Dirac delta function at singularities in spherical coordinates [migrated]

Background Information Let $\delta^3(\vec x-\vec a)$ represent a point density at $\vec a$. It satisfies $$ f(\vec a)=\int \delta^3(\vec x-\vec a)f(\vec x)|J(\vec x)|\mathrm d^3\vec x, $$ where $f(\...
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When falling freely into a black hole, how far does space extend out in front of you? [closed]

Falling freely into a black hole (assuming we survive or being point-sized) all particles in front of you are accelerating away from you in the direction of the singularity which seems flying towards ...
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How to verify the corectness of a renormalization scheme?

I am currently studying renormalization and have the above question about the renormalization scheme. So as far as I understand when we renormalize, we come from the realization that there are ...
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How do infinitely dense singularities evaporate trough hawking radiation?

If we assumed that a black hole with a singularity of infinite density eventually evaporates due to Hawking Radiation, does this affect the singularity itself? If mass is preserved in the singularity ...
1 vote
1 answer
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Mass in the LSZ reduction formula

I'm reading wikipedia's page on the LSZ reduction formula https://en.wikipedia.org/wiki/LSZ_reduction_formula For the scalar LSZ reduction formula, after performaing a Fourier transform on the $n$-...
1 vote
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Is singularity without black hole possible?

I read things related to the topic I am asking and I found the idea of a "Naked Singularity" but naked singularities can't be created without black hole. I need to know whether it is ...
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About the Euler's Disk

I'm a physics student who got an interest in Euler's disks. As you may know, an Euler's disk is basically a big fat coin spinning upon a (smooth) surface. As the disk loses energy due to friction with ...
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Imaginary part of IR divergence in gravitational S-matrix

I was recently studying Weinberg's computation of the IR divergence in QED and gravity from virtual soft exchanges (https://doi.org/10.1103/PhysRev.140.B516). He does the computation where the matter ...
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Do strings prevent a black hole singularity? [duplicate]

Spacetime singularities are problematic in quantum gravity. String theory offers a way to construct such a quantum gravity. Do strings offer a solution to this problem in the sense that point-like ...
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1 answer
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Why do we use the complex electric field vector's square to define in following parameters, instand of using a single one to describe it?

As the picture showed (coming from an article: Index formulae for singular lines of polarization), here it gives a calculation for the major and minor axis for ellipse polarizations: $$\textbf{A}+i \...
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2 answers
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Why do black holes remain? [closed]

When we think about black holes as not containing matter but being regions of warped spacetime, I can't think why they don't revert to being Euclidian space more quickly. This is because I can see how ...
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Is a black hole a single particle or a bunch of particles that binds together?

We know that in a neutron star all electrons and protons combine together and make neutrons because of the gravitational pulls. We also know that a black hole is much denser than a neutron star, we ...
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Renormalization in $\phi^3 + \phi^4$ theory in $D=4$

While reading notes on renormalization, specifically one-loop renormalization of $\phi^4 +\phi^3$ theory (Real Scalar Field) in $D=4$, In the section about corrections to coupling constants. For the ...
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1 answer
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Prove there are not timelike vectors contained in the tangent bundle of a Cauchy surface

Intuitively, I do not visualize how could it can contain temporary vectors. I imagine that if there were a timelike vector tangent to a Cauchy hypersurface $S$, you could consider an integral curve ...
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Delta function singularity in curvature

Are there 3+1D spacetimes that lead to a $\delta$-function in curvature? Are there any examples that one can provide?
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Singularities/infinities of continuity equation in polar coordinate

I encountered a bit of a difficulty in solving the continuity equation for polar coordinates. For a "fluid" or density of particles moving radially outwards with constant velocity, its flux ...
1 vote
2 answers
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On the singularity of Biot-Savart's law inside a current-carrying conductor

When using Biot-Savart's law to compute magnetic flux density on a field point away from a current source point, the integrand is finite; however when using it to compute the field inside the source ...
2 votes
1 answer
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What does the Penrose diagram of a super extremal black hole (naked singularity) looks like?

What does the Penrose diagram of a super extremal black hole (naked singularity) looks like? I have seen the ones for regular charged/rotating black holes, but I can't find a good clear one for super ...
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How is the singularity of Schwarzschild space-like if a one can take a time like path to it?

It is known that when one crosses the event horizon of a Schwarzschild black hole, one cannot return and is destined to hit the $r=0$ horizon. My understanding is that this can be seen from the ...
1 vote
1 answer
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Can a singular function plus a Dirac delta have be non-infinite?

In QFT we sometimes encounter functions of the form: $$K(x-y) = \delta(x-y) + \frac{k}{(x-y)^n} $$ Where $x$ and $y$ are $d$ dimensional vectors and $k$ is a (possibly imaginary) constant. These can ...
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4 answers
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Does the vacuum really have infinite energy density?

I said: As far as I understand it quantum field theory says that the vacuum has an infinite energy density. r/AskPhysics RedditorAbstractAlgebruh said: But wouldn't that be due to the way we do the ...
5 votes
3 answers
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Where does all the energy in black holes go?

The temperature inside of a black hole is almost absolute zero, so particles inside a black hole have almost zero motion. So if they don't give out any heat or light, where does all the energy it ...
0 votes
2 answers
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Average electrostatic field over a spherical volume due to a point charge inside

When calculating the average electrostatic field over a spherical volume due to a point charge within the volume, how do we account for the electric field arbitrarily close to the point charge? What ...
1 vote
2 answers
144 views

Is it possible the Black Holes to be pure deformations in the fabric of spacetime and not an effect of super-dense matter?

Is there any theory in the literature that supports this hypothesis that BHs in their center do not have a super-dense matter singularity but are pure deformations in the fabric of spacetime itself or ...
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18 votes
5 answers
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How does it make sense for the universe to have started from a big bang?

It has been said that the Big Bang started from a singularity. Think about a balloon radially growing over time. Fix a time $t_0, t_1 > 0$, and let $M_0, M_1$ be two balloons at time $t_0, t_1$ ...
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1 answer
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What do Maxwell's equations tell us about the ultraviolet catastrophe?

I have found it that in elementary discussions of black-body radiation, other than justifying electromagnetic waves should exist from Maxwell's equations, those equations are not used for anything ...
4 votes
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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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Schwarzschild-deSitter horizon singularity

The Schwarzschild-deSitter spacetime in Euclidean signature is given by: $$ ds_{E}^{2}=\left(1-\frac{2M}{r}-\frac{H^{2}r^{2}}{3}\right)d\tau^{2}+\frac{dr^{2}}{\left(1-\frac{2M}{r}-\frac{H^{2}r^{2}}{3}\...
3 votes
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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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How should the singularity of the Coulomb's law be understood? [duplicate]

The electric field at the point $\vec r$ due to a point charge $q$ at the origin $$\vec E=\frac{q}{4\pi\epsilon_0}\frac{1}{r^2}\hat{r}$$ blows up at the origin. In other words, the force between two ...
2 votes
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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 ...
2 votes
2 answers
103 views

Why are we so sure that there is a singularity inside the event horizon of a black hole? [duplicate]

The Schwarzchild solution is derived in vacuum, and we find that light cones always move inward when r < 2M. So if a spherically symmetric, non rotating celestial object of mass M has a radius less ...
0 votes
2 answers
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Logarithmically divergent Feynman diagrams in $\phi^4$ theory

I am going through the lecture notes for my class and I can't seem to follow the logic. Maybe this is considered a homework problem, but I could not find anything that directly answers my question on ...
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2 answers
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Why do we keep referring to the Heisenberg Uncertainty Principle in situations that we don't - and can't - know about? [closed]

In all of my reading in physics, I have been surprised by the number of times that I read "this can't exist" or "that can't exist" because of the Heisenberg Uncertainty Principle. ...
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4 votes
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 ...
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0 votes
2 answers
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Continuity of fields in Electrostatics

I have a bunch of doubts in electrostatics. In gauss law div(E)=rho/epsilon, is it implicitly assumed that the partial derivatives exist at every point in space? Is it always true that a collection ...
1 vote
0 answers
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Does the angular momentum of a Black Hole give insight into a potential solution for the singularity?

Alright so, i want to make one thing clear. I am a bit of a dumbass who watches a lot of PBS Spacetime and read a paper or to on visualising Black Holes. Example image (10k): I asked a very similar ...
4 votes
1 answer
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Coordinate singularity in general relativity and smooth structure of a manifold

I'm a bit confused by the notion of coordinate singularity, or perhaps relatedly, the differential geometry behind GR. In my elementary understanding of differential geometry, one starts with a ...
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2 votes
1 answer
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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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What does it really mean to have infinite tension?

Let an object of mass $m$ lie on a wire. The wire is much smaller in mass than the object and so its mass can be negligible. As the object lies on the wire, the wire is pulled down to a position where ...
1 vote
1 answer
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Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?

Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral? This question is highly related to working with the ...
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7 votes
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Vector Potential that vanishes outside infinite solenoid

Consider the magnetic field $\vec{B}$ generated by an infinite solenoid on the $z$-axis with radius $R$. Then $$\vec{B}(r)=\begin{cases} B_z \hat{z} & \text{ if }r<R, \\ 0 & \text{ ...
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1 vote
3 answers
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Mathematical Definition of Point Source

Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating". The usual definition in Physics describes it just as a source whose ...
-4 votes
1 answer
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Is it possible for a point-like system to behave like $x(t) = \frac{t}{2}\log(t^2)$ near $t=0$? (infinite speed) [closed]

Is it possible for a point-like system to behave like $x(t) = \frac{t}{2}\log(t^2)$ near $t=0$? (infinite speed) I know beforehand that relativity theory forbids anything with mass from travel faster ...
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