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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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 ...
Gopal Kaushik's user avatar
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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 ...
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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 ...
zahra's user avatar
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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 ...
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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 ...
CBBAM's user avatar
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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 ...
StackUser's user avatar
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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 ...
Daniel Vainshtein's user avatar
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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 ...
MiltonTheMeme's user avatar
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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 $T_{\mu\nu}=0$. ...
Zjjorsia's user avatar
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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 ...
MiltonTheMeme's user avatar
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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 ...
ldfjglfkgj's user avatar
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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 ...
TOAA's user avatar
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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 + \...
posfn0319's user avatar
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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 ...
mmesser314's user avatar
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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 ...
jazamm's user avatar
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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 ...
Bhavya Panda's user avatar
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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 ...
gatiskandis's user avatar
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 \...
User13114's user avatar
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2 answers
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Field of an Uniformly Charged Infinite Plane Sheet

Let's consider two cases: Let's say that we have two positive point charges. If we get those charges together very very very close to each other, the repulsive force goes to infinity between those ...
Emzar Chichoevi's user avatar
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7 answers
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How to handle divergences in Poisson's equation in the presence of a point charge?

I'm looking for a (fairly) mathematically-rigorous resolution to the following). Suppose an electron is moving through an electric field in some region: $$\Omega \subset \mathbb{R}^d \ ,$$ where $d = ...
Zachary Candelaria's user avatar
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Black hole singularity [duplicate]

Suppose a cloud of dust of sufficient mass and density collapses to form a black hole. As this mass falls within the event horizon, to an outside observer it enters an area of infinite time dilation. (...
Rich's user avatar
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If field strength (magnitude) is: $E=kq/r^2 $, what happens at $r=0$?

The formula for the Electric field strength (magnitude) is: $$E=kq/r^2$$ where $k$ is a constant, $r$ is the distance from a point charge, and $q$ is the magnitude of the point charge. Given this ...
user45664's user avatar
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Question about Kerr's recent paper regarding Penrose et al.'s works on gravitational singularities [duplicate]

R. Kerr posted an essay on arxiv recently. Kerr claims: The consensus view for sixty years has been that all black holes have singularities. There is no direct proof of this, only the papers by ...
Daddy Kropotkin's user avatar
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1 answer
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Will this hypothetical circular singularity FTL travel warp drive work? [closed]

Not a physicist, but just wanted to know if this would work in theory: Since nothing can practically travel faster than the speed of light (for now until proven otherwise), the only way for ...
notorious-raccoon's user avatar
-2 votes
1 answer
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About Second-Order Poles of Matsubara Sum

I would like to ask about the calculation regarding Matsubara sum of the form \begin{equation} \frac{1}{\beta}\sum_{i\omega_n} \frac{1}{(i\omega_n-\xi)^2} \end{equation} which is a second order pole ...
HereXD's user avatar
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Can the gravitational singularities of black holes be solved by potential or self-energy?

In Newtonian Mechanics, the energy density of gravitational field is negative in comparison with the positive energy density assigned to mass density, meaning that that the total positive energy of ...
Manuel's user avatar
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33 votes
8 answers
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Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?

In a preprint posted on the arXiv, Roy Kerr claims that there is a widespread misunderstanding related to the singularity inside the black hole that bears his name. Can anyone explain his argument in ...
noir1993's user avatar
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4 votes
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Eigenvalues of the geodesic deviation equation, curvature invariants, and singularities

The geodesic deviation equation tells us what tidal forces freely falling observers experience in a local Lorentz reference frame. The tidal deformation tensor is $$E^{\alpha}_{\gamma}=R^{\alpha}_{\...
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Is the scalar-field Feynman propagator at the origin ($x=0$) equal to 1?

I was reading about Feynman rules for scalar field in $\phi^4$ theory in section 4.6, pages 113-114 of Peskin & Schroeder, and, calculating amplitudes for processes, the authors show that Feynman ...
dallla's user avatar
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Two-dimensional Ising model for square lattices

Consider Onsager's exact solution of two-dimensional Ising model for square lattices with nearest neighbour interaction energy ‘J ‘being equal in the horizontal and vertical directions. At the ...
sangara's user avatar
1 vote
2 answers
71 views

Does that the regularized sums of series and integrals divergent to infinity appear in measurements prove that they represent actual infinite values?

There is a philosophic debate about whether there could be infinite quantities in nature. Definitely we cannot measure infinite quantities with measurement instruments. But we know the regularized ...
Anixx's user avatar
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2 answers
115 views

Why do we defer to GR when describing black holes rather than rely on QM?

This is a broad question but it's well documented that GR and QM are very well tested in their own domains but they conflict around black holes. Picture a neutron star slowly accreting matter until it'...
Daniel Piggott's user avatar
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1 answer
146 views

If it's a common myth that a black hole contains a singularity, what does a black hole actually (likely) contain?

It's a common myth (especially in popsci) that a black hole contains a singularity. However, I cannot find an explanation for what we think a black hole actually does contain. The best I've seen is &...
cat pants's user avatar
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3 answers
175 views

Equivalence principle near a black hole

At every spacetime point, there is a locally inertial frame in which the effect of gravitation is absent. Can this point be taken near the center of a black hole?
Hamed Hilal's user avatar
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1 answer
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How does Planck's Constant solve the ultraviolet catastrophe?

I am studying black body radiation and a high school level for a class. My understanding of it is this: There is a finite frequency light and therefore amount of ultraviolet light objects can emit. ...
Msamericana1's user avatar
2 votes
1 answer
176 views

Why can't the answers to equations be infinity?

When talking about black holes and singularities, most books say that combining relativity and quantum mechanics gives the answer of infinity in some equations. They also say that: Infinity is the ...
P R Das's user avatar
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6 votes
4 answers
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What does it mean for the laws of physics to "break down" at a singularity? [duplicate]

When the statement says: As you get to the center of a singularity the laws of physics "break down". What exactly does that mean?
Perleedee's user avatar
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1 answer
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How can the distance to the event horizon, as measured by a tape attached to a falling mass, be reconciled with the mass passing through it?

When hovering 2km. above the horizon of a black hole with a mass of the sun, at r=5km., the distance you measure with a measuring tape attached to a mass you throw in the hole will tell you the ...
Il Guercio's user avatar
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0 answers
103 views

How far does a particle fall before it hits the singularity of a black hole?

Even though a black hole has a Scwarzschild radius that indicates a finite small distance to the center of the hole, the distance traveled by an infalling particle seems a lot bigger than the ...
Il Guercio's user avatar
1 vote
1 answer
38 views

Can the inertia factor of a black hole be used to infer its density profile?

The Sun's inertia factor of ~0.07 suggests a stark contrast between the density of its outer shells (very low density) and its core (very dense). The same applies to the rest of the solar system. ...
Mike Davis's user avatar
4 votes
1 answer
658 views

Total cross-section for Bhabha scattering

The Bhabha scattering differential cross section is given by $$\frac{d\sigma}{d\Omega}=\frac{\alpha}{2s}\left(\frac{3+\cos^{2}\theta}{1-\cos\theta}\right)^{2}$$ where $\theta$ denotes the angle of the ...
Yair's user avatar
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1 vote
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Peskin and Schroeder Pg. 228: Expanding resummed propagator around the physical pole

I am having difficulty wrapping my head around this particular statement and equation (7.44) on pg. 228 of P&S, I think I understand that "~" sign here is trying to denote at under $p^0 ...
QFT_groupie's user avatar
3 votes
0 answers
59 views

Hypothetically, could the interior of a black hole look exactly like the universe that surrounds us?

I do understand that we can't experimentally verify anything we imagine about the interior of a black hole. If we were to apply what we know about the physics of the observable universe and assume ...
Amber Lily's user avatar
5 votes
1 answer
212 views

Why poles of two-point function corresponds to bound states?

In this article Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms the author has: Let $\mathcal{G}$ be fourier transform of the green function $$ \begin{array}{r} \...
amilton moreira's user avatar
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1 answer
235 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 +...
Boreanaz's user avatar
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1 answer
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Does The Big Bang Require An Infinitesimal Point, Or Is Another Shape Possible? [duplicate]

Einstein's Spacetime has four dimensions. If the size of one of these dimensions is zero, then the four-dimensional 'volume' - or whatever the corollary to 3D volume is called in 4D - would be zero. ...
Keith Payne's user avatar
1 vote
2 answers
89 views

How come mass is conserved if the universe is formed from singularity? [duplicate]

If mass is conserved then how come there happened singularity? since singularity is a point of infinite density and gravity.
Xlee's user avatar
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3 votes
2 answers
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How can we be sure that black hole's singularity is not a missunderstanding? [duplicate]

The Newtonian gravitational potential is given by: $$\phi=-\dfrac{GM}{r}$$ Which appears in the Schwarzschild metric tensor with a so-called singularity at $r=0$. Nonetheless, I can't get why is it ...
Antoniou's user avatar
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1 vote
1 answer
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Non-Compactness in Penrose Singularity

I've been studying singularities in GR, and (obviously), came across PST. Let us state it as the following: Let $(M, g)$ be a connected globally hyperbolic spacetime with a noncompact Cauchy ...
Johann Wagner's user avatar
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1 answer
90 views

Apparent singularity of Magnetic field generator by a ♾️ conductor [closed]

Let's assume two perpendicular wires: one is infinitely long and the other's length is $l$ (finite). The second wire is placed vertically on top of the infinitely long wire and there is a distance of ...
Tutai Koley's user avatar

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