# 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 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 ...
1 vote
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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
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### 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 ...
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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{...
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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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### 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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### 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 ...
1 vote
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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
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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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### 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
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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 ...
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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 ...
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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 ...
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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 ...
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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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### 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 ...
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### 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 $$E_n=\frac{-13.6eV}{n^2}$$ ...