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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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How to study regularity of a Green's function when solving field equations perturbatively?

Preliminaries Consider a nonlinear differential operator $\mathcal{O}$ acting on a field $\phi$, with source $\rho$ $$\mathcal{O}(\phi)=\rho$$ Let's say the charge density is small, so we can define $\...
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How to deal with the divergence in tree-level diagrams? where the propagator momentum is on-shell

Only consider the interaction term between electron Higgs and $Z$ boson $$ \mathcal{L}_{h ff}=-\frac{Y_f v}{\sqrt{2}} \bar{\psi} \psi\left(1+\frac{h}{v}\right) =-m_f \bar{\psi} \psi\left(1+\frac{h}{...
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 ...
5 votes
2 answers
963 views

What happens to the ring singularities when two Kerr black holes merge?

Imagine two Kerr black holes with ring singularities oriented in different axes (e.g. one horizontal and the other one vertical). If they merge, what will happen to these singularities? Will they form ...
3 votes
1 answer
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What is the physical origin of van Hove singularity?

I am trying to build physical intuition about van Hove singularities. The density of states for a system with energy dispersion $E_\mathbf{k}$ is defined as $$ D(E) = \int_{S(E)} \frac{dS}{4\pi^3} \...
1 vote
2 answers
101 views

Solution to infinite particle creation in EM by classical sources

In this question: Peskin and Schroeder "Particle Creation by a Classical Source" particle creation by a classical source is discussed. Doesn't this mean that a static constant source would ...
1 vote
1 answer
79 views

Was the singularity a boson? [closed]

I was wondering if there is any truth in the perspective that the singularity point at the beginning of our universe would be considered a boson. I have heard it said that the universe at that one ...
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1 answer
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What are spinning black holes orbiting?

I have seen depictions of spinning black holes with the "singularity" spinning around a center of rotation in a flat plane, or moving around an imaginary sphere. Is there anything in the ...
3 votes
6 answers
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Singularity of a black hole: point or solid sphere? [duplicate]

A black hole is defined by its event horizon. The event horizon has a Schwarzschild radius of, $$r_s=\dfrac{2GM}{c^2}$$ Technically, this means that any body of mass, $M$, with a radius smaller than ...
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1 answer
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Regularization of black hole singularities

Hi I have a question: when dealing with the gravitational Lorentz factor from schwarzchild solution to EFE, used in defining gravitaional time dilation and one encounters singularities at $r=0$ or $r=...
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1 answer
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Why domain of Kerr black hole includes negative values for $r$ coordinate?

I understand the domain of $t$ is all real numbers but mathematically, how to prove the domain of $r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two ...
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Can ring singularities form a Hopf link?

Can ring singularities form a Hopf link?
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Is there any observational evidence for the existence of Schwarzschild black holes?

So as far as I know, the objects that have been confirmed to be black holes by direct observation of the event horizon("black hole shadow"), like M87 for instance, also show observable ...
1 vote
1 answer
436 views

Energy density of a 0D point particle vs. a 1D string

As I understand there is a problem in physics where point-like massive (or charged, etc.) particles would have infinite mass/energy (or charge, etc.) density. I'm curious how in the context of String ...
2 votes
1 answer
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A question on IR divergence in Peskin-Schroeder chapter 6

In equation 6.64 of Peskin Schroeder, it computes $f_{\text{IR}}(q^2)$ in the limit $-q^2\to\infty$. Now, if we try to simplify the integral: \begin{align} f_{\text{IR}}(q^2) &=\int_0^1d\xi\;\frac{...
3 votes
0 answers
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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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1 answer
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Black holes, singularities and topology in relativity

General relativity is defined on a base manifold which, viewed as a topological space, is simply connected (which means there's no holes). However, we know that inside a black hole there's a ...
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1 answer
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We say the big bang (initial singularity) didn't happen at a point, but is it the same with the singularity of a black hole?

I have read this question: The simple answer is that no, the Big Bang did not happen at a point. Instead, it happened everywhere in the universe at the same time. Consequences of this include The ...
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1 answer
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Can super heavy elements form inside black holes?

I have read that heavy elements like gold and uranium are formed due to extreme pressure, through a process similar to nuclear fission. I wonder if something like atomic no. 500 or 5000 could form ...
1 vote
1 answer
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Divergences in tree-level diagrams?

Consider the Feynman diagram in $\phi^4$ theory where there are three incoming momenta ($p_1$, $p_2$, and $p_3$), three outgoing momenta ($q_1$, $q_2$, and $q_3$), and one internal line so that this ...
1 vote
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Types of singularities

I am confused about the types of singularities. According to my limited knowledge there are two types of singularity. One is space like singularity ( a curvature singularity enclosed within a null ...
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1 answer
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Why do correlation functions involving composite fields require special analysis?

For simplicity I will be considering $\phi^4$ theory. To analyze correlation functions of the form $$\langle \phi(x_1)\phi(x_2)\ldots\phi(x_n)$$ with $$x_1 \neq x_2 \neq \cdots \neq x_n \tag{1}$$ we ...
1 vote
1 answer
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Diverging Scattering Amplitudes and Transmission/Reflection Coefficients

I am currently studying scattering theory from Sakurai and Griffiths and I have noticed that for the 1D Dirac potential, the transmission and reflection coefficients diverge when the energy ...
1 vote
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How does renormalization affect divergent subdiagrams?

Suppose we have a theory that is super-renormalizable and let $\Gamma^n$ denote the sum of all 1PI diagrams of this theory with $n$ amputated external legs. In such theories, for all $n$ sufficiently ...
7 votes
6 answers
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Do black holes have a size?

I'm wondering if one can say that a black hole is an object "made of matter" that has a size (as a size, I'm not talking about the size of the event horizon). I would like to know if one can ...
9 votes
1 answer
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What is a branch cut singularity in QFT?

Peskin & Schröder say on page 216: The poles in $p^2$ come only from one-particle intermediate states, while multiparticle intermediate states give weaker branch cut singularities. In order to ...
6 votes
1 answer
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How to find that there is a conical singularity in the BTZ black hole?

Considering a non-rotating and non-charged 2+1 dimensional black hole, known as the BTZ black hole which obtained by adding a negative cosmological constant $\Lambda=-\frac{1}{l^2},l\ne0$ to the ...
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2 answers
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What happens if $ a^2 > M^2 $ in Kerr metric?

(Boyer-Lindquist coordinates and $ c = G =1 $ taken) As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \...
7 votes
1 answer
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Curing spacetime singularities by a higher-curvature gravitational Lagrangian

It is well known that the self-energy of a point charge is diverging in the classical (Maxwell) electrodynamics. In 1930's, Born and Infeld introduced their nonlinear electrodynamics (with a ...
0 votes
1 answer
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Don't Geodesics change due to other geodesics?

So the geodesics that point towards the Earth brings space-time towards the Earth and then back out again, but then the moon has its own geodesics so wouldn't it be kind of like geodesics affecting ...
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1 answer
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Range that the Schwarzschild metric is valid

The Schwarzschild metric is the metric calculated from the field equation outside of the black hole. This condition of region (outside of the matter) was the reason why we could use $T_{\mu\nu}=0$. ...
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 ...
5 votes
4 answers
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Aren't places where geodesics end singularities?

So of course when stuff falls into black holes, the geodesic for anything ends in that singularity. However, isn't it technically true that a light ray that originates from the sun and then hits the ...
8 votes
2 answers
1k views

Partition Function of a Hydrogen Atom [duplicate]

I'm trying to figure out how to write the partition function as a function of temperature for just a single hydrogen atom with a bound electron. I know the Energies will be $$E_n=\frac{-13.6eV}{n^2}$$ ...
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What physical quantity is a black hole singularity refering to and why is it special?

What mathematical term actually shows a "singularity" in a black hole and why is this so special compared to other singularities? It seems super hard to find any concrete formulas about the ...
17 votes
3 answers
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Partition function of a hydrogen gas

Hi I have a doubt (I'm not very expert in statistical mechanics, so sorry for this question). We consider a gas of hydrogen atoms with no interactions between them. The partition function is: $$ Z=\...
4 votes
0 answers
132 views

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 ...
1 vote
0 answers
38 views

Partition function of Hydrogen atoms problem

I know there are several questions asking this problem, but I found this problem has not been solved yet to me. I will repeat the problem and state my view. Consider the statistical mechanics of a ...
19 votes
3 answers
6k views

Can we have a black hole without a singularity?

Assuming we have a sufficiently small and massive object such that it's escape velocity is greater than the speed of light, isn't this a black hole? It has an event horizon that light cannot escape, ...
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2 answers
115 views

Use of infinity in physics [closed]

There have been lots of questions on this site about the use of infinity in different ways in physics. Infinitely big - Physics near null infinity Infinitesimals - Using differentials in physics ...
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2 answers
173 views

Do physicists commonly believe that any potential infinities such as those which come up in General Relativity can be real in nature?

What is the consensus on whether or not nature actually has functional infinities such as an absolute singularity, or the multiverse itself as a whole, or even some potential for reality always ...
24 votes
7 answers
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Given that matter cannot escape a black hole, how did the big bang produce the universe we see today?

Extrapolation of the expansion of the Universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. If the matter contained within our ...
2 votes
3 answers
301 views

Can objects escape black holes by waiting?

Assuming that Hawking radiation cause black holes to become less massive over time, it should follow that the event horizons of black holes should shrink over time as well. In this case, what would ...
1 vote
2 answers
164 views

How do black holes infinitely bend space-time when the bending is mass dependent and not density dependent?

According to Einstein, mass bends the fabric of space-time. And nothing in the universe has infinite mass to infinitely bend space-time. So how do remnants of supermassive stars, i.e black holes ...
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0 answers
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Is there a point where the electric field strength is zero for two point charges of opposite signs put together?

I searched online that there is no 'neutral point' in the electric field of two charges of opposite signs, unlike the electric field of two positive charges. However my question is when you put 2 ...
2 votes
1 answer
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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 ...
2 votes
1 answer
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Discontinuity in integrand while calculating the electric field of a uniformly charged sphere

Suppose you wanted to calculate the electric potential of a uniformly charged sphere with radius $R$ at a point $r$ inside the sphere. In Griffith's EM this is done by integrating $\frac{1}{4 \pi \...
1 vote
3 answers
688 views

Is this case a failure of Stokes' theorem?

In the presence of a hypothetical magnetic point charge at the origin of coordinates, it turns out that an irremovable physical singularity of the vector potential ${\bf A}({\bf r})$ exists for any ...
0 votes
2 answers
79 views

Black holes / density [duplicate]

If a star explodes to form a black hole how does the gravitational field become infinite from one state to the next? ie: it seems additional mass has been added or is this simply a function of density?...
0 votes
1 answer
288 views

Angular Deficit of a Conical Singularity

I'm currently studying the Bonnor solution starting with this paper on Black Diholes. The metric is given by : $$ ds^2 = \left(1-\frac{2Mr}\Sigma\right)^2 \left[-dt^2 + \frac{\Sigma^4}{(\Delta + (M^2 +...

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