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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 [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].

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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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2answers
71 views

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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1answer
45 views

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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0answers
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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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4answers
69 views

Solutions to Newton's laws with unbounded kinetic energy for inverted harmonic oscillator potential

In a one dimensional setting, Hooke's Law, together with Newton's 2nd law, results in a differential equation of the form (setting the constants $m$ and $k$ equal to 1 for notational simplicity) $x''(...
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2answers
66 views

Black hole fundamental laws [closed]

As the Laws of physics breakdown during inside a black hole, would we have to create new fundamental Laws?
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1answer
128 views

If a black hole cannot have a diameter smaller than Planck length (a finite and non-zero length), then how can we call it a singularity?

As title. If a black hole has a minimum finite diameter, than it should not mathematically be a singularity.
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0answers
64 views

Does a Black-hole Represent a Limit To The Value of Energy-density? [closed]

I've recently read an article that stated the singularity of a black hole could be a string, which is stipulated to be pure energy. If that's the case, does this mean that the singularity of a black ...
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0answers
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singularity blow up in supersymmetric theories

I have been doing some reading on algebraic geometry, in particular singularity resolutions. All the examples I am familiar with in physics correspond to singularities of the extra dimensions (e.g. ...
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2answers
77 views

If a Black Hole Singularity is a 1 Dimensional Object, How Does it Affect 4 Dimensional Space

If the center of a black hole is an one-dimensional point, gravitational singularity, where density and gravity become infinite and space-time curves infinitely, then / why: If spacetime is warped ...
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1answer
121 views

Could the singularity of a black hole just be an iron / dark matter sphere? [duplicate]

A singularity would break physics wouldn't it? How does a massive star collapse and suddenly fall into a point in space with no dimensions what so ever when it had a core and perfect balance between ...
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0answers
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According to the actual understanding, was the Big Bang a singularity in space or rather in density? [duplicate]

Often in cosmology erroneous pictures are transmitted by the recurrent hearing from various sources or by sentences taken out from bigger discussion, and even by omitting adjectives and the likes. I ...
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1answer
38 views

Moving singularities

I am aware that black holes can move through space-time. Is there a way to move a naked gravitational singularity artificially? Sorry if this is a little stupid, trying to figure out the feasibility ...
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2answers
42 views

Was the singularity just a mini model of our current unvierse? [duplicate]

Did the singularity just "containe" the matter, the energy and the space-time or it created them. If it just contianed them and then the expansion hppened, can we say it was just a mini model of our ...
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2answers
81 views

Where is the Physical Singularity under the Holographic Principle?

From this article, it states that The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself ...
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6answers
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Why exactly are singularities avoided or “deleted” in physics?

What is the real reason that make us reject singularities everytime we see them in a theory/model? For example, in GR, it is predicted that black holes singularities have infinite density. This makes ...
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2answers
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Naked singularities and mass distribution of a black hole

Do naked singularities also appear mathematically if the mass of a black hole is uniformly spread around its Schwarzschild surface? I recently heard about the concept of a naked singularity and it ...
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2answers
64 views

Is the zero distance limit of Coulomb's law something to worry about?

Coulomb's law fails when the distance $r$ between to point charges vanishes. As $r\to 0$, the electric field between two point changes increases without limit. I should be bothered about the limit $r\...
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0answers
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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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3answers
578 views

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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3answers
92 views

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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1answer
81 views

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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1answer
81 views

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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2answers
215 views

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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1answer
50 views

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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1answer
78 views

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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3answers
175 views

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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1answer
50 views

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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2answers
230 views

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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1answer
46 views

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 ...
4
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2answers
196 views

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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0answers
55 views

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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1answer
107 views

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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1answer
116 views

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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1answer
68 views

Equation for the field of a magnetic dipole

In my electrodynamics class, my professor derived the equation for the field of the magnetic dipole $$\vec{B}(\vec{r})=\frac{\mu_0}{4\pi}\frac{1}{r^3}[3(\vec{m}\cdot\hat{r})\hat{r}-\vec{m}]+\frac{2\...
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1answer
81 views

Timehole - Black hole physics [closed]

If someone could shed some light so that I can think straight again that would be appreciated.. Anywho, since watching a video on what the universe may look like in trillions of years (each atom ...
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2answers
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How to plot the graph of this expression which involves Dirac delta function?

I was doing a problem on electrostatics which required finding the charge density from the given electric field and then plot a graph of the charge density. I was able to find the charge density which ...
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1answer
33 views

Where is mass density information of a Black Hole?

Have read that all the information of a black hole is contained on the Event Horizon. Does that include mass density of interior as a function of position? The shape of an event horizon depends on the ...
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0answers
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Normal ordering in 2D thermal CFT

I am trying to understand the notion of normal ordering in thermal CFT in 2D CFT, for instance I consider a two-point function of scalar primary operator with $\Delta$ dimension at finite temperature $...
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0answers
77 views

Black hole interior [closed]

Had a few questions about the "interior" of the black hole. I've read that all the mass of a black hole is concentrated at it's center and that you can't isolate an object to an area of space ...
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1answer
154 views

In string theory, what replaces the black hole singularity?

In string theory, what replaces the black hole singularity? I know that it is possible for a single string to have arbitrarily large energy. Is a black hole just a single string?
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1answer
60 views

Uncertainty cannot be calculated?

I'm doing an experiment on resonance. The phase difference between the driving force and the one oscillating is given by $$\varphi=\arcsin\left(\frac{y_1}{y_2}\right)$$ where $y_1$ and $y_2$ are ...
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1answer
123 views

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 ...
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3answers
218 views

Electron falling into proton approaches infinite kinetic energy why?

Foreword I believe this question to be different from the usual "Why don't electrons fall into the nucleus" because this A: asks about the details of explanations for why electrons don't fall into ...
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1answer
72 views

Can a curvature singularity (i.e. BH), as defined in terms of geodesic incompleteness, actually exist in nature?

A curvature invariant is a scalar representation of curvature derived from a curvature tensor. The classic example is the Kretschmann scalar derived from the Riemann curvature, where $K=R_{μνλρ}R^{...
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4answers
452 views

How can infinite density exist?

Thinking in mind, infinite density is where there is no space between particles correct me here if i'm wrong. Inside a blackhole at the core. So if there are 2 particles touching each other Then ...
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1answer
61 views

Are the actual singularities with geodesic incompleteness the same as curvature singularities?

Types of singularities include curvature singularities and conical singularities. So, for a curvature singularity(black hole) with geodesic incompleteness, is it the same as a physical singularity? If ...
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1answer
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General Theory of Relativity [duplicate]

Why is General Theory of Relativity not applicable in the singularity of Black Hole?
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3answers
173 views

Kruskal-Szekeres Coordinates and the Singularity

On the wikipedia page for Kruskal-Szekeres coordinates, it states: [Kruskal-Szekeres] coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended ...
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1answer
52 views

Why is electric field inside a charge distribution not infinite?

Let's consider electric field due to a charge distribution at a point $P$ inside the charge distribution. Due to inverse square nature of electric field, electric field due to an element volume charge ...