# 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 [tag:black-holes] and [tag:wormholes] for certain kinds of singularities occuring in [tag:general-relativity]. For the procedure of "getting rid" of singularities, consider [tag:regularization].

514 questions
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### Curl and circulation of a vector field that is ill-defined at the origin: any interesting physical effects?

In the cylindrical polar $(\rho,\phi,z)$ coordinate, suppose the velocity field in a liquid is given by $$\vec{v}=\frac{K}{\rho}\hat{e}_{\phi}, \qquad K=\text{constant}.\tag{1}$$ It can be easily ...
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### Does time stop inside a black hole? How about at it's singularity?

I'm a layperson who just read Brief Answers to Big Question and in the book, Hawking proposes that: A typical black hole is a star so massive that it has collapsed in on itself. It’s so massive ...
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### UV divergence integral

Could anyone please explain how to calculate integral such as $$\frac{\Omega}{2}\int_{-\infty}^{+\infty} \frac{d^3k}{(2\pi)^3}\ln\left[{1+\frac{a^2}{k^2}}\right]=-\frac{\Omega a^3}{12\pi}+I_0~?$$ ...
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### Why is the singularity not taken into account?

In this article "Reflections on Maxwell’s Treatise", Section 4.2, it says: He replaces $\mathbf{m}$ with a volume element of magnetization $\mathbf{M}\ dV$ , integrates over $V$ , and lets the same ...
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### Would a cellular-automata universe allow singularities to exist?

It is usually assumed (almost always) that cosmological singularities (like black hole singularities) are impossible and do not exist in the universe. If the universe was like a cellular automata (...
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### BH singularity? Infinite density

How can the density of a region of space go from finite density to infinite when there are no numbers larger than any Aleph0 number but smaller than any Aleph1 number (no decimal point in front of it, ...
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### How to find electric field at a point on an arbitrary surface charge $(\sigma)$ due to it?

Electric field at any point due to any volume charge $(\rho)$ Electric field at a point outside a volume charge is given by Coulomb's law: $$\vec{E}=k \iiint_V \dfrac{\rho}{r^2} (\hat{r})dV \tag1$$ ...
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### Is the Big Bang a naked spacelike singularity?

While reading some answers on similar topics, I was wondering about the nature of the Big Bang singularity in the standard cosmological model. I know it's a spacelike singularity that have a ...
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### Silly question about Schwarzschild Black holes and scientific communication

Well, in scientific communication literature often we encounter the following phrase about black holes: A Black Hole is a body that have infinite curvature and infinite density So, with basic GR ...
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### Naked singularity

Many consider naked singularities as a fundamental problem and that it should be always covered by a horizon (Cosmic censorship hypothesis). But why naked singularities are really a problem? If we ...
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### Can the gravitational field be considered conservative despite the existence of singularities?

Assuming singularities are physical objects as opposed to mathematical artifiacts, can the gravitational field still be considered conservative? And if not, does this open a possibility of breaking ...
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### Functions unbounded at a point on the domain: How to show electric field exists for any continuous volume charge density?

My understanding after reading Mike Stone's answer: \begin{align} \vec{E} &= k \iiint_{V} \dfrac{\rho(x',y',z')[x-x'\hat{(i)}+y-y'\hat{(j)}+z-z'\hat{(k)}]}{[(x-x')^{2}+(y-y')^{2}+(z-z')^{2}]^{...
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### Does time exist at the center of a Black Hole?

A black hole is a wormhole resulting from a dead Star which is capable of sucking any mass/matter along its path due to Gravity. I was wondering what time would be like at the central point of the ...
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### Magnetic field at points on the circuit

I know magnetic field lines due to a circuit always form closed loops. Therefore $\nabla \cdot \vec{B}=0$ everywhere (even at points on the circuit). However due to singularity, magnetic fields are ...
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### Weyl anomaly in 2d CFT (string theory lectures by D.Tong)

In his lectures on String Theory (http://www.damtp.cam.ac.uk/user/tong/string.html), Tong gives a proof of the Weyl anomaly, using equation $(4.36)$. It seems wrong to me. Here he uses the OPE ...
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### Electric field at source points of any continuous charge distribution

In classical electromagnetism, is there a way to find the electric field at source points of a line, surface or volume charge? If there is a way, please explain in detail My idea: I don't really ...
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### Doesn't the fact that elementary particles are not black holes prove they are not point structures?

De Schwarzschild radius of a mass $m$ is defined as $$r_s=\frac{2mG}{c^2}(m).$$ So if we insert in this formula the mass of an electron (a point particle, according to mainstream physics), which ...
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### Are singularities' behaviour really unpredictable?

If a real/true singularity existed our models and theories would become useless to predict what would happen in that singularity. For example if naked singularities really existed, we could not ...
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### Can we “stir” space-time?

Depending on the energy-momentum density of a given region in space there is an intrinsic curvature to it. I can't help but feel like space-time is a like fluid, which begs the question whether it is ...
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### Would a 5-dimensional black hole actually break laws of physics?

I discovered a paper by, Figueras, Kunesch, and Tunyasuvunakool, "End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture." A Cambridge University press release is here. The ...
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### Does infinite mass exist? [closed]

So when I search up if infinite mass exists, google provides me with a source that states infinite relativistic mass does exist at the speed of light which is why it is impossible to ever reach to ...