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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What happens when you shine circularly polarized light at a pole of a rotating black hole?
Circularly polarized light carries spin angular momentum (SpAM 😉), so shining it into a pole of a spinning black hole from a point on the rotation axis of the BH should raise the angular momentum of ...
2
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0
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Pole at Infinity of a 1-loop scalar bubble diagram
In What is the $i\epsilon$ for the $S$-matrix, chapter 3, they discuss over the singularities of a 1-loop scalar bubble diagram (3.12),
$$\mathcal{I}_{\text{bub}} = \Gamma(2-D/2)\lim_{\epsilon\...
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Why do IR divergences only appear on external legs of a Feynman diagram in the discussion of Bremsstrahlung?
On p. 203 in section 6.5 of Peskin and Schroeder, the diagrams below are given as examples of when an infrared divergence occurs.
'Soft photons' are photons with energy below some cutoff that we ...
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Can we be alive in spinning Black Holes? [duplicate]
I was studying about black holes and I get to know that we can be alive in black holes if the black hole is spinning. I didn't understand the reason. Can anyone explain.
I mean to ask that if is it ...
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Correct Expression for Centripetal Force
Assume we have a car of mass $m$ with an initial velocity of $u$ ms$^{-1}$ about to travel on a loop-the-loop that is made up of two semicircles, AB and BC, of different radii $R_1$ and $R_2$ where $...
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Singularity structure being valid for all QFTs?
I'm trying to understand this paper in which the authors try to build a wavefunction for the universe without assuming locality and unitarity, so they would be rather emergent from geometrical ...
- 2,818
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Quantum field theory in 2 spacetime dimensions
I have a question. Let us consider a two dimensional disc of finite radius as our spacetime. In a very simple case, we take a $\phi^3$ massless scalar field theory.
Consider a tree-level scattering of ...
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What is the meaning of divergent quantum fisher information?
I've recently come across this example, and it has me confused. I've computed the quantum fisher information (QFI) for a qubit initialized along the $\hat x$ axis ($|\uparrow_x\rangle=\frac1{\sqrt{2}}\...
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Black hole event horison diameter to steller mass
are event horizon diameters linear as compared to stellar mass? it seems as if there were singularities involved billion star mass black holes would have a relatively smaller event horizon diameter ...
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Can dark matter in neutron stars cause the formation of naked singularities?
I've been studying the concept of dark core collapse, particularly as discussed in the paper "Low Mass Naked Singularities from Dark Core Collapse" on arXiv. The paper explores the idea that ...
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When Does a Singularity Become Naked in Space-Time?
A singularity within a space-time 𝑀 is typically hidden behind an event horizon, preventing any information from the singularity from reaching distant observers. However, a singularity may be "...
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Why does null geodesic incompleteness indicate the breakdown of GR?
If a spacetime in general relativity (GR) is null or timelike geodesically incomplete, it is said to be singular (more precisely, there is a more general notion of a "b-incompleteness" of ...
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Integral of first and second normal derivative of $1/r$
Problem:
I want to numerically compute the deceiptively simple looking surface integral of the second directional derivative of the source function $1/r$, namely $\mathbf{n} \cdot \nabla (\mathbf{n} \...
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Insertions of the action inside correlators
Suppose I have a scalar field theory described by an action $S[\phi]$ that can be massive $\lambda\phi^4$ theory, what is the effect of inserting a power of the action inside of correlators?
Like:
$$\...
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Necessity of Singularity in General Relativity
The Schwarzschild solution is the standard example used to describe a black hole, its important points being the event horizon and the central singularity. But this solution is derived by assuming an ...
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Can you calculate the radius of a hypothetical singular surface inside a black hole from observing changes to its linear momentum?
Say there is a ball of unknown radius surrounded by a bubble. The ball represents a hypothetical singular surface inside a black hole and the bubble represents the event horizon.
If you threw marbles ...
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Is the size of a black hole singularity smaller than a fundamental particle?
I am wondering about the size of a black hole singularity. We know that a classical black hole is infinitely dense. I am not asking about size of event horizon. I am asking about actual size of the ...
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Hydrogen radial equation solution's boundary condition for $r \to 0$ [duplicate]
I am studying the hydrogen atom and I am analysing the radial equation: $$\left[\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial r^2} + \frac{\hbar^2l(l+1)}{2m}+ V(r)\right]u=Eu$$ with $V(r)$ equal to ...
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As per Friedmann Equations, is big-bang singularity necessary?
The Friedmann Equations do not directly require that the scale factor $a(t)$ was zero in the beginning. Since Einstein's static universe is still a valid solution, is it possible that before the Plank ...
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Under what circumstances can a 4D singularity occur in General Relativity?
I've tried to find on the literature about 4D (single point) singularities, but most of the theorems about singularities pertain to either space-like or time-like singularities, which always have some ...
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Where is the mass in a Black Hole without a "central" curvature singularity?
Not all black holes have a curvature singularity at their center (an example). But in principle, I thought that the curvature singularity was a direct result of the fact that the mass is concentrated ...
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Realistic black holes
If I understand the answers provided in this Link Why singularity in a black hole, and not just "very dense"?
Then the singularity at $r=0$ may just be a mathematical artifact, and may not ...
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Can a Kerr black hole become super-extremal?
Let's assume there is a large Kerr black hole, which is almost
extremal and would become extremal with the addition of a small
amount of mass $M$ with spin $J$ to make the final $J=M$.
What if this ...
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Deriving OPE between vertex operator: Di Francesco Conformal Field Theory equation 6.65
How does one get Di Francesco Conformal Field Theory equation 6.65:
$$ V_\alpha(z,\bar{z})V_\beta(w,\bar{w}) \sim |z-w|^{\frac{2\alpha\beta}{4\pi g}} V_{\alpha+\beta}(w,\bar{w})+\ldots~?\tag{6.65}$$
...
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Removing the cosmic horizon in the de Sitter metric
The metric for de Sitter spacetime in static coordinates is
$$ds^2 = \left(1-\frac{r^2}{\ell^2}\right)dt^2 - \frac {1}{1 - \frac{r^2}{\ell^2}}dr^2 - r^2\,d\Omega_2^2.$$
It is evident that there exists ...
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Explain to a non-physicist what goes wrong when trying to quantize gravity
I am not a physicist, but I'm trying to get a little bit of an understanding of why it is hard to extend the standard model with quantum gravity (i.e. why it's hard to combine QM and GR), cf. e.g. A ...
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How to deal with the divergence in tree-level diagrams? where the propagator momentum is on-shell
Only consider the interaction term between electron Higgs and $Z$ boson
$$
\mathcal{L}_{h ff}=-\frac{Y_f v}{\sqrt{2}} \bar{\psi} \psi\left(1+\frac{h}{v}\right)
=-m_f \bar{\psi} \psi\left(1+\frac{h}{...
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How to study regularity of a Green's function when solving field equations perturbatively?
Preliminaries
Consider a nonlinear differential operator $\mathcal{O}$ acting on a field $\phi$, with source $\rho$
$$\mathcal{O}(\phi)=\rho$$
Let's say the charge density is small, so we can define $\...
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How do black holes move if they are just regions in spacetime?
If black holes are just regions of spacetime, how can black holes even move? When matter moves through spacetime, it bends the spacetime around it, but if black holes are just regions of spacetime, ...
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What happens to the ring singularities when two Kerr black holes merge?
Imagine two Kerr black holes with ring singularities oriented in different axes (e.g. one horizontal and the other one vertical). If they merge, what will happen to these singularities? Will they form ...
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Was the singularity a boson? [closed]
I was wondering if there is any truth in the perspective that the singularity point at the beginning of our universe would be considered a boson.
I have heard it said that the universe at that one ...
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What are spinning black holes orbiting?
I have seen depictions of spinning black holes with the "singularity" spinning around a center of rotation in a flat plane, or moving around an imaginary sphere. Is there anything in the ...
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Singularity of a black hole: point or solid sphere? [duplicate]
A black hole is defined by its event horizon. The event horizon has a Schwarzschild radius of,
$$r_s=\dfrac{2GM}{c^2}$$
Technically, this means that any body of mass, $M$, with a radius smaller than ...
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Regularization of black hole singularities
Hi I have a question: when dealing with the gravitational Lorentz factor from schwarzchild solution to EFE, used in defining gravitaional time dilation and one encounters singularities at $r=0$ or $r=...
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Is the Schwarzschild singularity a limit of the Kerr singularity?
In a Schwarzschild black hole, the singularity is spacelike. In a Kerr black hole, it is timelike.
Is there any continuous transformation between those solutions? Can the Schwarzschild solution be ...
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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 ...
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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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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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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 ...
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1
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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 ...
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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 ...
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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 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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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 ...
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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 $T_{\mu\nu}=0$.
...
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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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