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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Why does S-matrix have poles?

Why does unitarity require amplitudes to have singularities? I can see this by constructing amplitudes for specific processes, but what is the rationale behind the general rule? For concreteness, ...
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Is this case a failure of Stokes' theorem?

In the presence of a hypothetical magnetic point charge at the origin of coordinates, it turns out that an irremovable physical singularity of the vector potential ${\bf A}({\bf r})$ exists for any ...
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Curvature Singularities in Geodesically Complete Manifolds

Do there exist manifolds which are geodesically complete, and yet have a curvature singularity? While I don't believe this is the case, I have yet to find a proper proof of the same.
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1answer
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Black hole supernova [closed]

This is a question about my intuition of black holes. Assumption: The creation of a black hole follows the same physics as the creation of stars. A star can supernova, I'm assuming a black hole also ...
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2answers
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What is the gravitational acceleration inside the event horizon?

Inside the event horizon is a singularity and it has a surface. Given that even light can't escape the pull once the event horizon is crossed, does that mean that anything that crosses the event ...
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7answers
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Why doesn't physics like infinity (or does it)? [duplicate]

I was recently told that in physics, if your equation contains an infinity, it usually suggests that something is wrong. As an example, the infinity around black holes (also) tells us that general ...
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2answers
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What happens to graviational force when separation between 2 objects is very small?

I recently learned about gravitational force and found out the equation for gravitational force on a object by an object according to Newton's law of universal gravitation. $$ F = \frac{Gm_1m_2}{r^2}. ...
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1answer
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How does Eddington-Finkelstein Coordinates solve coordinate Singularity

Hi i am reading about Eddington-Finkelstein coordinates and i read that they do remove the coordinate singularity at $r=r_s$ but still there is some problem with these coordinates which can be removed ...
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Why was Einstein wrong about black holes?

In 1939, Albert Einstein published a paper entitled "On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses." In it, he considers the problem of whether it is ...
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Noncollisional orbital near-singularities in general relativity

One of the most counterintuitive results in Newtonian mechanics is the existence of many-body systems in which one mass accelerates to infinite velocity in finite time, without colliding with any of ...
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Identifying Black Hole Horizon from metric tensor

Suppose we have a spherically symmetric and static metric given by: \begin{equation} ds^2=-B(r)dt^2+A(r)dr^2+r^2d\theta^2 +r^2\sin^2(\theta)d\phi^2 \end{equation} where: \begin{equation} B(r)=1-\...
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Are there any real examples of Infinite, or possible infinite, in our universe? [duplicate]

infinite small or large, infinite slow or fast, infinite long time or short, any kind of infinite counts. Are there any real-life example out of Math, that is infinite? This is the whole knowledge I ...
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How does mass increase in black holes? [closed]

In the center of a black hole is a gravitational singularity, a one-dimensional point which contains a huge mass in an infinitely small space, where density and gravity become infinite and space-time ...
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Does time stop in black holes? [closed]

I was going through Hawking's incantations on black holes, where black holes get defined as follows: Black Hole: A region of spacetime from which the escape velocity exceeds the velocity of light. I ...
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1answer
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UV divergences in perturbation theory

I've seen people claim that UV divergences appear in perturbation theory are due to taking the continuum limit "too soon" or "sloppily". What does this mean?
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Are black holes exploding just like the singularity at the big bang did, we just can't see it because of time dilation?

There is only a few question about exploding black holes but that does not address my question. Can a black hole explode? Is there a relationship between Black Holes and the Big Bang? Did the Big Bang ...
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1answer
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A simple, easily understandable example of infinities making trouble in physics?

I have heard that many physical theories (such as quantum gravity) suffer from infinities arising everywhere, which for some reason cannot be regularized or renormalized. Is there a simple example of ...
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Are ultraviolet divergences an infinity of “energy” or of “energy-density”?

I'm thinking about this more as it relates to the problem of the renormalisation of gravity at very high energies. To my mind, it seems as though, if we're taking the very early universe into ...
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1answer
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Why can we set the external momenta to zero while calculating the 1-loop correction to non-abelian theory coupling?

Refer to the second diagram in figure 73.2 on page 440 of Srednicki's Quantum Field Theory book. On page 441 he proceeds to calculate the amplitude and argues that since the divergent part is ...
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Can the vector potential be written as $\mathbf A = \nabla \chi$ for some singular function $\chi$?

Consider a magnetic field $\mathbf B= \Phi\delta(x) \delta(y) \hat z$. The corresponding vector potential becomes $\mathbf A = \frac{\Phi}{2\pi r} \hat\theta$ in the cylindrical coordinates. ...
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1answer
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Can a gauge transformation eliminate singularity of gauge potential?

Suppose I have a gauge potential $A$ which goes to infinity at some point $x_0$. Can I use a gauge transformation \begin{equation} A'=U^{-1}AU+U^{-1}dU,~~~U=\exp\{-i\alpha^a(x)T^a\} \end{equation} to ...
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Is there physical reason for a stably causal spacetime, or the existence of a Cauchy surface?

In their 1979 essay Global structure of spacetimes, Geroch and Horowitz describe methods of determining the topology, causal structure and singularity of spacetimes. Their (mathematical) arguments are ...
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Are the Infinities in QFT Perturbation (closed loop diagrams) a Consequence of Point Interactions?

I have heard (and read) that the infinities that arise in QFT interactions using higher-order perturbations are "a problem that comes down to the fact that the interactions occur at a single ...
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Singularity in a BH - pointlike? [duplicate]

This answer https://hsm.stackexchange.com/a/12505/13669 has the curious sentence The singularity of a black hole is not a point at its center, it's a spacelike singularity. What is that supposed to ...
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Is there a limit to how much spacetime can be curved?

My question is about the fact that general relativity predicts bending of space and time. However, I have not seen anything regarding the limits to how much space or time can be bent. So my question ...
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1answer
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How to apply Feynman rules of counterterms to calculate amplitudes?

Consider $\phi^4$-theory with counter-terms and renormalized mass, field and coupling constant, described by the Lagrangian $$\mathcal{L}= \underbrace{\frac{1}{2} \partial_{\mu} \phi_{r} \partial^{\mu}...
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Do black holes exist in 1+1 dimensional spacetime?

I'm currently working in 1+1 dimensional spacetime and would like to know if black holes can exist in such a manifold? I think they can because the Schwarzchild metric has the coordinate singularity, ...
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1answer
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Centre of a black hole

In a text intended for people without background in general relativity or quantum mechanics, I read two statements which are false or do not make sense, if I'm correct. Am I correct, and why (not)? ...
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1answer
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How did the Holm 15A Galaxy BH reach 40 Billion Solar Masses?

The most massive supermassive black hole discovered to date lies within the Abell 85 galaxy cluster. At the heart of this cluster is the galaxy Holm 15A, containing an estimated 2 trillion solar masse ...
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Race to the singularity, who wins, the photon or the neutrino?

There are a lot of questions and answers about speed falling into a black hole, none of them answer my question. Most of them only talk about speeds outside the event horizon. The only relevant answer'...
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1answer
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Does string theory remove the singularity of black holes? [duplicate]

One of the reasons we want a theory of Quantum gravity is to understand black holes and string theory is the most popular approach, but so far I haven't seen any attempt of the theory to remove the ...
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1answer
132 views

Is there any example from physics, supporting $\int_0^1\frac1xdx=\int_1^\infty\frac1xdx$? [closed]

This question is related to the potential possibilities of classification of divergent integrals more precisely than just "divergent to infinity" and the like. Improper divergent integrals ...
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How is rotational information transferred to a singularity? [duplicate]

If some mass spirals into a black hole the conservation of angular momentum means that the result will have to spin (at least to my albeit limited understanding). But if the singularity is a point, ...
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Do Singularities really exist? [duplicate]

This question has been on my mind for quite some time. I don't really have in-depth knowledge about singularities, but from what I understand they rupture the spacetime and they are hard/impossible to ...
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Regular black hole with an evanescent horizon

I'm reading a great paper named Geodesically Complete Black Holes by R. Carballo, F. Filippo, S. Liberati and M. Visser about regular black holes and I'm trying to understand a particular situation. ...
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Why are constant electric fields considered when their energy is infinite?

Sometimes in some problems (that i am facing in high school physics related to electrostatics) like the problems of finding flux crossing through a cube where magnitude of electric field is some ...
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2answers
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How is the Coulomb potential infinity resolved in quantum field theory?

People always says that the infinity of the coulomb potential $V(r)=\frac{k}{r}$ as $r$ approach to zero is resolved in quantum field theory. I would like to know how this is done.
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1answer
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How can an observer reach the singularity if black hole interiors grow forever?

This article https://www.quantamagazine.org/why-black-hole-interiors-grow-forever-20181206/ describes how black hole interiors grow forever although the exterior volume of the black hole does not ...
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Correct a misunderstanding about the black hole paradox

I think I have misunderstood the black hole information paradox. Here's my view, first of all a black hole is not an actual singularity, the singularity comes from the space-time metric when $r=0$, ...
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1answer
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Why can't we use the line element to distinguish coordinate from gravitational singularities?

I am a bit confused as to why we can't use the line element to identify coordinate from gravitational singularities. My question stems from learning about the Schwarzschild Metric and the singularity ...
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1answer
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Black hole atlases

What sort of atlases of spaces that contain a black hole (that is, including the space inside the event horizon), if any, are there? Does the central singularity have to be excluded? Are there atlases ...
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1answer
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Definition of density of black holes

For a blackhole of mass $M$, radius $R$ and Schwarzschild radius $R^*$ (where $R<R^*$), its density $\rho$ is defined as $$\rho=\frac{M}{(R^*)^3}.$$ One reason I read for using the Schwarzschild ...
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Euclidean Schwarzschild black hole

I am studying the Euclidean Schwarzschild metric and trying to find its isometries. It still has $\partial_{\phi}$ as a Killing vector, but I wonder if the range of $\phi$ is still $0$ to $2\pi$. The ...
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Schwarzschild solution, stress-energy side of Einstein's equation

The Schwarzschild solution in GR only has a singularity at the origin $r=0$: otherwise there is no matter content. The right-hand side of Einstein's equation is hence almost everywhere zero, but I ...
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1answer
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Is Loop quantum cosmology replacing the Big Bang singularity with a big bounce?

Am I correct in understanding that in the cosmological version of Loop quantum gravity, namely Loop quantum cosmology, the universe in all models starts with a big bounce? Are there other models, for ...
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1answer
56 views

Are there 3D singularities in general relativity?

In the commonly considered spacetimes with singularities, the singularities - to my knowledge - always have less than 3 spatial dimensions: The singularity of the Schwarzschild spacetime (describing ...
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1answer
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What is the physical interpretation of self-contraction being divergent?

If we take vacuum expectation value of two scalar field at the same point (2-point correlation function when 2 points coincide) it diverges. what is the physical reason(interpretation)behind this? ...
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Is there a maximum replusion between two electrons?

Coulomb's law says that as the distance between two electrons approaches zero, the force becomes infinite. However this is just an approximation, and electrons are better described as fuzzy clouds of ...
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2answers
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Is Penrose's CCC consistent with Penrose's singularity theorem?

According to Penrose's Conformal Cyclic Cosmology (CCC), there were universes prior to ours, prior to the singularity of our universe. But how is this claim compatible with his famous singularity ...
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What does it mean when people say “Physics break down”?

So I keep hearing people talking about how physics break down at for example the center of a black hole. And maybe I am just to stupid but, why? How can we say that? For all we know a black hole could ...

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