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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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 ...
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Is Singularity corresponds to null space and are forces causing singularity are some transformation matrix?

Some random thoughts: (Disclaimer: i am a complete noob in physics). I was studying linear transformations from linear algebra and just got this thought that there might be some set of transformation ...
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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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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 ...
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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 ...
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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 ...
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2 answers
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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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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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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 ...
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Singularities of $f(z)=\dfrac{z}{\sin\pi z^{2}}$? [migrated]

Consider the function $f(z) = \dfrac{z}{\sin\pi z^{2}}$. It has a simple pole at $z=0$. There are also 4 poles at $z=\pm\sqrt{n}$ and $z=\pm i\sqrt{n}$, where $n\in Z^{+}$. What is the order of the ...
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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}\...
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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 ...
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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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2 answers
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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 ...
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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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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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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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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 ...
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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 ...
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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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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 ...
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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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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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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 ...
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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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Is possible to achieve an infinite speed in real life? [closed]

Is possible to achieve an infinite speed in real life? I know beforehand that relativity theory forbids anything from travel faster than speedlight, so please stay with reading the full question first ...
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Why does gravity seem to get energy out of nowhere?

Most of the forces have an end point. A positively charged object, when it touches a negatively charged object, becomes neutral and stops attracting other negatively charged objects. We need energy to ...
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Could the spin of a Black Hole give us insight into the size of the core? [closed]

As we know the conservation of angular momentum seems to be rather true and applies to black holes as well. We know that they spin and we also know the relationship between angular velocity and radius....
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5 votes
2 answers
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What curves spacetime in Schwarzschild metric? [duplicate]

I understand that the Schwarzschild solution is valid in the outside region of a massive object, with no other masses involved. Therefore the energy-momentum tensor is 0. But then: what curves space? ...
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Are black hole singularities fermions? [closed]

I was just wondering. I apologize if this is a dumb question. Is it possible that the mass of a black hole is converted into quantum energy that gets distributed across the universe uniformly so that ...
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2 votes
2 answers
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Why should a black hole be infinitely dense? [duplicate]

I have been listening to this on Discovery for centuries of my childhood!! That when the heavy core of a star collapses under its own gravity, it shrinks to an infinitely dense point called "...
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1 vote
1 answer
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Does AdS/CFT help solve the singularity of a black hole?

How does thinking of a black hole as encoding its information in its surface help solve what happens inside it, more specifically geodesic incompleteness. Doesn't it tell us that if we can see how ...
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2 votes
1 answer
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Can there exist small black holes in large ones?

Imagine an infinite empty space except for a local mass distribution resembling our observable universe. I don't think there lies no mass behind the horizon but let's imagine that this is the case. ...
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Where does a black hole's event horizon form and when?

In static spherically symmetric perfect fluid solutions of Einstein field equations the central pressure diverges when the compactness parameter $\alpha~(\equiv r_{S}/R)$ reaches some critical value $\...
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2 votes
1 answer
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Normalizable, but singular distribution

I have obtained a probability distribution for the observable $l$ which takes the form: $$ \frac{dP}{dl}=\frac{(1-\sqrt{1-3l^{2}})^{2}}{l^{3}\sqrt{1-3l^{2}}}\exp\left[-\frac{4\pi}{9l^{2}}(1-3l^{2})^{3/...
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3 votes
4 answers
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Black hole singularities and the ultimate destination of matter

Why are black hole singularities posited when we now believe singularities no longer exist? I understand that once we pass the event horizon we fall into what’s been referred to as a singularity, and ...
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22 votes
2 answers
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I'm missing the point of renormalization in QFT

I am a qft noob studying from Quantum Field Theory: An Integrated Approach by Fradkin, and in section 13 it discusses the one loop corrections to the effective potential $$U_1[\Phi] = \sum^\infty_{N=1}...
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1 vote
1 answer
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Expectation value of $r^{-3}$ for $\ell=0$

I'm trying to calculate the hyperfine structure energy for Hydrogen. From Jackson's Electrodynamics book eq. 5.73 we have: $$H_{HFS}=\dfrac{\mu_{0}}{4\pi}\left[\dfrac{-8\pi}{3}\mu_{N}.\mu_{e}\delta(r)+...
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2 votes
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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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What does M-theory predict at the singularity of a black hole?

how does M-theory avoid problems like infinite density and geodesic incompleteness. like, is there a fundamental limit to where matter can collapse or simply does matter decay and form a condensate of ...
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4 votes
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Branch Cut of Wavepacket - LSZ Reducation Formula Peskin

Peskin & Schroeder, An Introduction to Quantum Field, page 224-225, formula 7.41 \begin{multline}\sum_{\lambda} \int \frac{d^{3} k}{2(2\pi)^3 E_{\mathbf{k}}(\lambda)}\Phi (\mathbf{k}) \frac{i}{p^{...
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1 vote
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OPE in the Free Boson Theory

I am following the book by "Conformal Field Theory" by Di Francesco and authors. Consider a free boson theory with the action $$S = \frac{1}{2}g \int d^2x \partial_\mu \phi \partial^\mu \phi$...
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4 votes
2 answers
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Multiplying distributions for QFT

My understanding is that UV divergences arise due to improperly handling the product of distributions. In what sense is it "improper"? And how does its proper handling relate to the notion ...
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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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Is the electron a pointlike particle? And if yes, how is that possible, because the energy then would diverge, wouldn't it?

My problem is that I read (besides others in this post Why are electrons and quarks 0-dimensional?) that the electron is a point-like particle. My question is on the one hand whether that is true and ...
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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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5 votes
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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 ...
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