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 [tag:black-holes] and [tag:wormholes] for certain kinds of singularities occuring in [tag:general-relativity]. For the procedure of "getting rid" of singularities, consider [tag:regularization].

76 questions with no upvoted or accepted answers
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254 views

Why is the Taub-NUT instanton singular at $\theta=\pi$?

Consider the following metric $$ds^2=V(dx+4m(1-\cos\theta)d\phi)^2+\frac{1}{V}(dr+r^2d\theta^2+r^2\sin^2\theta{}d\phi^2),$$ where $$V=1+\frac{4m}{r}.$$ That is the Taub-NUT instanton. I have been ...
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178 views

What is the state-of-the-art on spacelike singularities in string theory?

What lessons do we have from string theory regarding the fate of singularities in general relativity? What happens to black hole singularities? What happens to cosmological singularities? Which ...
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1answer
189 views

In string theory, what replaces the black hole singularity?

In string theory, what replaces the black hole singularity? I know that it is possible for a single string to have arbitrarily large energy. Is a black hole just a single string?
5
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709 views

What is a branch cut singularity in QFT?

Peskin & Schröder say on page 216: The poles in $p^2$ come only from one-particle intermediate states, while multiparticle intermediate states give weaker branch cut singularities. In order to ...
5
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378 views

Heat kernel expansion for entanglement entropy

Can somebody please let me know where I can find a reference for calculating heat kernel coefficients on a manifold with conical singularities? I am trying to compute the entanglement entropy for ...
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93 views

How does the renormalization group justify the renomalization process?

I recently learned "Renormalization" and "RG". My textbook says "RG allows us to make sense of why a renormalized quantum field theory describe Nature." To me, it sounds like "RG justifies the ...
4
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171 views

What is the physical meaning of the derivative of the norm of a Killing vector?

Initial considerations Consider a metric of the form $$ ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}=-\alpha^2(r,t)\,dt^2+a^2(r,t)\,dr^2+r^2\,b^2(r,t)\,d\theta^2+r^2\,b^2(r,t)\,\sin^2\theta\,d\varphi^2\ .\quad (...
4
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146 views

Where does chiral matter at conical singularities “come from” in M-theory?

It seems to be accepted that to produce chiral fermionic matter in a compactification $\mathbb{R}^4\times X$ of M-theory/11d SUGRA to four dimensions, we need the seven-manifold $X$ to have isolated (...
4
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1answer
169 views

Contradiction between Geroch's theorem on topology change and formation of naked singularity?

It's been known since Oppenheimer and Snyder's work in 1939 that it's easy to get a naked (i.e., timelike) singularity in models of spherically symmetric gravitational collapse, for forms of matter ...
3
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0answers
40 views

Must collapse to a singularity proceed through a strong curvature singularity?

A strong curvature singularity (s.c.s.) can be defined as one for which a geodesic is incomplete at affine parameter $\lambda=0$, with $\lim_{\lambda\rightarrow0}\lambda^2R_{ab}v^av^b\ne0$, where $v^a$...
3
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2answers
176 views

Location of event horizon in moving black hole

Say a black hole is travelling at $c/2$, does the shape of the event horizon change? What about the location of the event horizon? If it is travelling at a hypothetical $c$, does the event horizon ...
3
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0answers
133 views

No-hair theorems for naked singularities?

For black holes, we have no-hair theorems that say, under certain assumptions about the matter fields, that they are uniquely characterized by just a few parameters. Are there any such theorem for ...
3
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1answer
245 views

A question on IR cancellation calculation in Peskin & Schroeder

In Peskin and Schroeder Introduction to Quantum Field Theory book, above equation 6.64 on pg. 200, it was said that "to gain better understanding, of the divergence, let us evaluate the coefficient of ...
2
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1answer
36 views

Discontinuities in electric fields

I'm a mathematician self-studying physics for fun and I'm trying to wrap my head around a simple concept, which is a consequence of approximations. Basically, by Coulomb's law, if I have a point ...
2
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52 views

Adding up gravitational fields of infinitely many objects?

I'm reading a book introducing gravity and find something I don't understand. Please check the attached image. The sentence in red bracket claims that if one adding up gravitational fields of ...
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127 views

Minkowski Space is not truly conformally compact

We say a manifold $(M,g)$ is conformally compact if it is the interior of some $(\overline M, \overline g)$, such that $$g = r^{-2}\overline g|_M,\quad \mathcal Z(r) = \partial M,\quad \text{and}\quad ...
2
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2answers
88 views

What is the energy required to create a gravitational field equivalent to that a mass $m$ shows?

If the mass of a neutron star in its collapse becomes a singularity, then the resting energy of this gravitational field must be $E = mc^2$ ($m$ = star mass). Is this possibility wrong?
2
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96 views

How many types of Singularities has string theory successfully resolved?

Except for proposing the fuzzball as a solution for black hole singularity, has string theory successfully explained/dealt with any other form of spacelike or timelike singularities? Kindly explain
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69 views

Singularities not allowed in classical geometry of general relativity because of topology?

While looking at Prof. Brian Greene's research work I came across the statement regarding the difference between quantum geometry and the geometry underlying general relativity, "...topology change (...
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212 views

What is the Planck Pressure?

What exactly is the Planck Pressure? According to wikipedia the Planck pressure "is not found except for shortly after the big bang or in a black hole". But wouldn't the pressure inside a black hole ...
2
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66 views

Can fractional D-branes be described in F-theory?

In Type IIB string theory, there can exist fractional D-branes at singularities. Additionally, F-theory is in some sense an alternative description of Type IIB string theory. So there should be an F-...
2
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1answer
105 views

Singularities of matrix element of composite local operator in QFT

Consider a state $|\psi\rangle$ in a quantum field theory and a local operator $\mathcal{O}(x)$. It's known that the $n$-point function $\langle \psi | \mathcal{O}(x_1) \cdots \mathcal{O}(x_n) | \...
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179 views

Gravitational singularity

Is it possible that the gravitational singularity actually turns out to be a genuine singularity once we have a true theory of quantum gravity in place. There is a lot of talk about singularity but ...
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593 views

How to calculate topological charge?

For a complex vector field in two dimensions with one or more phase singularity - a point where the field amplitude is zero and the phase is undefined - how do you explicitly calculate the total ...
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100 views

Is sonoluminescence relevant to the behaviour of Navier-Stokes (or converse)?

More precisely, could Sonoluminescence be a singularity of Navier-Stokes(NS)? Is there some other connection that might be interesting, or is it completely irrelevant? Wiki page mentions NS, but says ...
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1answer
55 views

Does the second-order correction to degenerate perturbation theory vanish?

Consider a degenerate two-state system with states denoted by $|1\rangle$ and $|2\rangle$. If we apply a perturbation $H^\prime$, the first order correction to the energy is obtained by choosing two ...
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42 views

How shall we show the surface integral approaches a limit (or does not blow up) at a field point near $S'$

Consider the electric field due to volume charge distribution in volume $V'$: $\mathbf{E}=\displaystyle \int_{V'} \rho' \dfrac{\mathbf{r}-\mathbf{r'}}{|\mathbf{r}-\mathbf{r'}|^3} dV'$ The integrand ...
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116 views

Would a cellular-automata universe allow singularities to exist?

It is usually assumed (almost always) that cosmological singularities (like black hole singularities) are impossible and do not exist in the universe. If the universe was like a cellular automata (...
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25 views

Normal ordering in 2D thermal CFT

I am trying to understand the notion of normal ordering in thermal CFT in 2D CFT, for instance I consider a two-point function of scalar primary operator with $\Delta$ dimension at finite temperature $...
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0answers
85 views

Derivation of the Raychaudhuri equation following Wald - taking the trace

I am following the derivation of Raychaudhuri's equation as in Wald. There it is stated (Wald: General Relativity on page 218, equation 9.2.10), that from the relation $v^c \nabla_c B_{ab} = -B^c_b B_{...
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60 views

Would naked singularities have a complex irreducible mass?

The formula for the irreducible mass, also known as the Christodoulou and Ruffini equation, is $$M_{\rm irr} = \frac{\sqrt{2 M^2-Q^2+2 M \sqrt{M^2-Q^2-a^2}}}{2}$$ where M is the mass equivalent of ...
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83 views

Singularity Theorem and its statements

The singularity theorem is as follows: A spacetime $M$ necessarily contains incomplete, inextensible timelike or null geodesics if, in addition to Einstein's equations, these conditions hold: ...
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1answer
81 views

Singularity and entanglement on surface of event horizon

An entangled pair of particles is created with one particle embedded onto the surface of a singularity. The other particle at some stated epsilon distance above the event horizon of the singularity. ...
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0answers
65 views

What is the singularity of a bathtub whirl?

I have read that at the center of a bathtub whirl the velocity should be infinite and that is a singularity. Could someone explain this and the mechanism that viscosity counteracts this infinite ...
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75 views

Why it is said that the information of a black hole resides on the event horizon, while a singularity resides on the inside?

Doesn't the statement that a black hole's information resides on the event horizon contradict the statement that there exist a singularity in the centre of the black hole? Mass falling into the hole, ...
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0answers
88 views

Do singularities in black holes violate the Bekenstein bound?

Since all matter falling past the event horizon must hit the singularity in a finite time, I'm assuming that this means that all matter will eventually settle down into the singularity. If this is so, ...
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0answers
78 views

What does a zero area element in the metric mean?

Let's consider the metric $$ds^2= \lambda(r) dt^2 - \lambda^{-1} (r) dr^2 -R(r)^2 d\Omega^2$$ where $$\lambda(r)= \frac{r+\omega}{r+h}$$ and $$R(r)^2 = r(r+h)$$ At $r=-h$, the area element ...
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171 views

Does infinity exist in physical systems?

Sometimes people fail at asking a question by being too broad, unclear like here. So I'll take a stab at what I believe to be the same question, but more concise and clearly stated: Does infinity ...
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0answers
313 views

What actually constitutes a 'rip' in the fabric of spacetime?

Science fiction writers often use the term 'rip' in the fabric of spacetime to provide a means of either time travel or instantaneous travel from one corner of the universe to another. But I've also ...
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0answers
121 views

Confusion on meaning of fugacity in scientific publication

in my research project in statistical mechanics, in the context of phase transition and condensation, I was reading the seminal paper of Yang and Lee titled: "Statistical theory of equations of state ...
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1answer
82 views

Do zero gravitational-force points produce Naked singularities?

In between two singularities, does a particle experience gravity? If a particle is exactly at the midpoint between two singularities, will its net experience of the gravitational force (ignoring the ...
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1answer
196 views

Describing the shape of a singularity

Hawking and Ellis write about the difficulty of describing the shape of a singularity when presented with a manifold that has curves of finite length that don't reach a point in the manifold. [...
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1answer
106 views

If there is a point in a past set, does its chronological future interset a future set?

This post concerns the causality of spacetime $\mathcal M$. A future set $F$ is defined to be the chronological future of some set $S\in \mathcal M$, ie., $F=I^+[S]$. Similiarly, a past set $P=I^-[S'...
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87 views

Colliding black holes to an outside observer

We know that a particle approaching an event horizon will appear to an outside observer to slow down and never cross the horizon. What is observed by an outside observer when a singularity approaches/...
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88 views

Force of gravity at quantum level is indetermined?

Newton's law of Universal Gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional ...
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72 views

Topology of a bit

From a math perspective, it seems obvious that the electric field (or voltage which ever) of a bit in a computer, when its in a stable 0, or 1 state, must have a singularity, a set of points where the ...
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0answers
92 views

How to prove this auxiliary lemma to Hawking's singularity theorem?

This theorem is number 44 of chapter 14 in Barret O'Neil's book "Semi-Riemannian Geometry (with applications to relativity)". The proof given, in particular the use of another theorem to justify the ...
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74 views

Singularities in Schwarzchild space-time

Can anyone explain when a co-ordinate and geometric singularity arise in Schwarzschild space-time with the element $$ ds^{2}~=~(1-\frac{2GM}{r})(dt)^{2}-(1-\frac{2GM}{r})^{-1}(dr)^{2}-r^{2}(d\theta)^...
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0answers
197 views

Naked singularity and null coordinates

I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
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1answer
498 views

Electric field at $r=0$

How does classical physics justify the existence of an electric field at $r=0$? Is this an edge case, an ambiguity, a "does not exist"? Is this a trivial case or indicative of an actual fault in ...