# 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 ...
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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 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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