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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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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2
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Understanding the Singularity of Black Holes [duplicate]
Could someone please explain how we know the singularity has an infinite density and zero size/volume? From reading around online black holes have a defined radius (the event horizon) but this isn't ...
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Where does the singularity go in an Einstein-Rosen Bridge?
I've been reading up on some material about black holes and Einstein-Rosen bridges. Generally it is said that a black hole is defined by the event horizon (boundary in space where the gravitational ...
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Order by order renormalization
This post is a little bit related with my last post, where I don't totally understand one point. I think it's better to write a new post specialized for this point.
For a renormalized $\phi^4$ theory, ...
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Peskin & Schroeder Introduction to Quantum Field Theory, two-loop renormalization example
In Peskin & Schroeder's An Introduction to Quantum Field Theory, section 10.5, page 338, the book gives a two-loop renormalization example (in scalar $\phi^4$ theory).
Before we start the two-...
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Dirac string and nature of singularities
The Dirac magnetic monopole is defined as
\begin{align}
\vec{B}=\frac{g\vec{r}}{r^3}\,,
\end{align}
where $g$ is the strength of the monopole and $\vec{r}$ a vector. It is possible to show that the ...
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How to obtain the line element with inverse metric coefficient than that of Schwarzschild line element?
The Schwarzschild solution could simply be expressed as
$$ds^2=-(1-2GM/r)dt^2+(1-2GM/r)^{-1}dr^2+r^2d\phi^2 \; .$$
Is it possible that we could obtained a new metric into the form as
$$ds^2=-(1-2GM/r)^...
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Books on singularity theorems
could someone recommend me from basic to advance level books on Singularity theorems on Black holes and laws of thermodynamics on Blackholes for selfstudy?
my professor has given me "general ...
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1
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Magnetic field $B$ becomes infinity at the center of an electromagnetic coil?
Suppose that there is a long wire carrying a current. According to Ampere's law, there one can determine the magnetic field (B) on a circular path around the wire given its radius (R).
Consider the ...
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Is it possible for a black hole singularity to interact gravitationally with other celestial bodies (if we analyze it using the concept of gravitons)? [duplicate]
It is known to all that the travelling speed of gravitons (the propagation speed of gravitational field) is not instant. So for black holes, the gravitons (the gravitational field) generated by the ...
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Expansion at first order ${\cal O}(\alpha_s)$ in counterterms for the QCD vertex renormalization at 1-loop
What is the meaning of the expansion at first order ${\cal O}(\alpha_s)$ in $\delta_2$ and $\delta_3$ at the second step in the last line? These quantities are not "small" - on the contrary,...
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Is there a cutoff for Newtonian gravity?
When I study the (conventional) quantum field theory, I learned about the short distant cutoff in renormalization in order to regularize the momentum integral and remove the infinities. I'm thinking ...
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Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
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Is there any evidence black holes can grow (gain mass) by accretion?
When LIGO detected GW150914, we saw for the first time the merger of 2 black holes and the gravitational wave evidence fit with our models and understanding for such an event. (Horizon meeting horizon)...
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Proof of Landau Conditions
I was reading this Quantum Field Theory book written by Claude Itzykson and Jean-Bernard Zuber. In section 6-3, page 304, the authors introduced analytic properties of Feynman integrals.
Consider the ...
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Star collapses to a singularity or is collapsing into singularity?
This has bothered me for a while now, however I barely have a vocabulary to ask it. Please let me try.
When a star, at the end of its life starts to collapse into the black hole, all the atomic forces ...
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Collinear Divergences and SCET (Soft Collinear Effective Theory)
Can someone elaborate on how to treat collinear divergences in massless fermionic theories, such as the massless QED? Some very basic words on where do we can find such divergences and how to cure ...
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In the Lorentz force equations, can the magnetic field be assumed to be singular at one or more points?
Consider the relativistic Lorentz force equation (in a simplified form) given by
\begin{equation}\
\left(\frac{u'}{\sqrt{1-|u'|^2}}\right)'= E(t,u)+u'\times B(t,u).
\end{equation}
Here, $E$ and $B$ ...
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Why is Griffiths using ordinary power series to solve Hydrogen atom problem?
The hydrogen atom problem leads to a differential equation of the form
$$\rho\frac{d^2v}{d\rho^2}+2(\ell+1-\rho)\frac{dv}{d\rho}+[\rho_0-2(\ell+1)]v=0\tag{4.61}$$ where $\rho_0$ is a constant. In ...
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What is spinning in a spinning black hole? [duplicate]
When a rotating star collapses into a neutron star, the resulting object spins at a huge number of rpm due to its much smaller volume and the conservation of angular momentum. What happens when a ...
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Why can infinite quantities not be shown in an experiment or observed in physics?
To modern physicists knowledge, there are no truly infinite quantities that can be shown with an experiment or observation. Time is not infinite, it had a beginning. Matter and energy is finite (...
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Existence of a Trapped Surface to the Existence of a Black Hole
Does the existence of a trapped surface in a region of space (not necessarily either of the vacuum or symmetric spacetime) indicates (theoretically) the existence of a "black hole" there? ...
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Could subatomic particles exist in a black hole singularity?
Hypotheses of black hole singularities imply infinite density because a singularity is a dimensionless point with mass. However, subatomic particles constantly move. In this case, I see no possible ...
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How accurate are astronomical observations around black holes? Can they distinguish between the following two scenarios?
Scenario 1
As Schwarzschild imagined. All of the matter in the black hole is at the centre, forming a singularity. The formula for the event horizon that bears his name is
$$R = \frac{2GM}{c^2}$$
...
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Motion of opposite electric charges
I have what seems like an obvious question, but I have gotten a completely paradoxical answer to it. My goal is to understand what would happen if two particles with opposite charges $q_1$ and $-q_2$ ...
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References for Subtleties in Electromagnetism: Infinities
There appears to be some infinities in classical electromagnetism:
The total energy contained in the electric field of a point charge diverges.
The potential at a point charge diverges.
The potential ...
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1
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Divergence not defined
I’m currently working on the practice problems in Introduction to Electrodynamics by Griffiths. I got confused by the solution to this problem.
What does “ill-defined divergence” even mean? I ...
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Do the different generations of fermions correspond with the epochs of the very early universe?
Up and down quarks as well as electrons and electron neutrinos currently dominate. Is it possible, that during the electroweak epoch, charm and strange quarks dominated? and that during the gut epoch, ...
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What do we mean when we say that black holes aren't made of anything?
I have read this question:
It turns out that black holes aren't really objects, but rather regions in spacetime. In fact, this is so true that black holes are what we call vacuum solutions: there isn'...
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Why does curvature somewhat determine the topology?
I thought the topology of a manifold is defined before we define the tensor fields that live on it. A manifold can be defined by the atlas, and the atlas fixes the topology. The metric tensor is then ...
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Rewriting an asymptotic series as a convergent integral [closed]
I am given the function
$$
f(x) = \sum_{n=1}^{\infty} \frac{\Gamma(2n)}{\Gamma(n)}(-x)^n
$$
and I need to show that it can be rewritten as an integral that is convergent for a range of values of x. I ...
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How to obtain (interacting) time-ordered correlation functions from the S-matrix - reverse of the LSZ formula?
The LSZ formula shows how to obtain the S-matrix elements from the time-ordered correlation functions of the interacting fields.
I wonder if there is a reverse formula; that is, can we find the ...
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Checking if an integral converges (or diverges) using dimensional analysis
Cross posted at Math.SE
I have been watching some online lectures, and the lecturer uses dimensional analysis to make claims such as the following:
Consider the integral
\begin{equation}
I(\xi, d) = \...
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Two-loop renormalization Peskin and Schroeder
In section 10.5 of Peskin and Schroeder, Peskin and Schroeder says the value of the last diagram in (10.51) is just a constant, which we can freely adjust to absorb any divergent terms that are ...
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LSZ reduction formula in Peskin and Schroeder
In derivation of the LSZ reduction formula in Peskin and Schroeder, on page 227, the book says
Let us analyze the relation between the diagrammatic expansion of the scalar field four-point function ...
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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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Is it legitimate to use analytic continuation to equate a diverging series with a finite number in a physical theory of nature?
Analytic continuation can be used in mathematics to assign a finite value to an infinite series that diverges to infinity. Is it correct and legitimate to equate this value to a diverging infinite ...
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Infrared divergence in electron self-energy
On Peskin and Schroeder's QFT book, page 319, the book discussed various situations of QED divergence.
On the first paragraph of p.319, the book considered Taylor series of electron self-energy ...
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Prove the causal future of a compact subset of a globally hyperbolic spacetime is closed (Wald's Theorem 8.3.11)
In Wald's GR, theorem 8.3.11 states that
Let $(M,g_{ab})$ be a globally hyperbolic spacetime and let $K\subset M$ be compact. Then $J^+(K)$ is closed.
Let me present my own proof, first. I am not sure ...
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How Existence Of Matter Is Possible Inside The Black Hole? [closed]
According to Chronology of the universe, origin of the universe initiated as per below sequence:
Big bang (at 0 sec) occurs in the black hole (10^-35 m in size, Planck Length) at the center of the ...
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What happens to the matter already at the very center of the star when it turns to a black hole?
I was wondering whether when an object collapses into a black hole, the matter in the position $r=0$, instantly becomes part of the singularity, or does it take time to fall into the singularity, and ...
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How do we know the field strength renormalization factor $Z$ is infinite for $\phi^4$ theory in 4D? [duplicate]
I am following Peskin and Schroeder and consider for simplicity only the $\phi^4$ theory in 4D.
The field strength renormalization factor seems to first appear p.214 and be defined by $$Z= \left| \...
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Computing $\langle 0|S |0\rangle$ in $\phi^4$ theory [closed]
$\newcommand{\bra}[1]{\langle #1|}$
$\newcommand{\ket}[1]{|#1\rangle}$
I have been reading David Tong's QFT notes. As part of an exercise, I am asked to examine $\bra{0} S \ket{0}$ to order $\lambda^2$...
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When falling freely into a black hole, how far does space extend out in front of you? [closed]
Falling freely into a black hole (assuming we survive or being point-sized) all particles in front of you are accelerating away from you in the direction of the singularity which seems flying towards ...
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How to verify the corectness of a renormalization scheme?
I am currently studying renormalization and have the above question about the renormalization scheme. So as far as I understand when we renormalize, we come from the realization that there are ...
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How do infinitely dense singularities evaporate trough hawking radiation?
If we assumed that a black hole with a singularity of infinite density eventually evaporates due to Hawking Radiation, does this affect the singularity itself?
If mass is preserved in the singularity ...
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1
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Mass in the LSZ reduction formula
I'm reading wikipedia's page on the LSZ reduction formula
https://en.wikipedia.org/wiki/LSZ_reduction_formula
For the scalar LSZ reduction formula, after performaing a Fourier transform on the $n$-...
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Is singularity without black hole possible?
I read things related to the topic I am asking and I found the idea of a "Naked Singularity" but naked singularities can't be created without black hole.
I need to know whether it is ...
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About the Euler's Disk
I'm a physics student who got an interest in Euler's disks. As you may know, an Euler's disk is basically a big fat coin spinning upon a (smooth) surface. As the disk loses energy due to friction with ...
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Imaginary part of IR divergence in gravitational S-matrix
I was recently studying Weinberg's computation of the IR divergence in QED and gravity from virtual soft exchanges (https://doi.org/10.1103/PhysRev.140.B516). He does the computation where the matter ...
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