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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].

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15
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4answers
2k views

Event horizons without singularities

Someone answered this question by saying that black hole entropy conditions and no-hair theorems are asymptotic in nature -- the equations give an ideal solution which is approached quickly but never ...
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4answers
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How long can a particle survive inside of the horizon of a black hole?

By examining the causal structure of a Schwarzschild black hole, one can see that a particle in region II is unable to escape to $r=\infty$. Such diagrams do not show, however, how long a particle ...
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2answers
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What does string theory predict for the singularity inside a black hole?

The usual explanation for what's going on inside a black hole goes something like "General Relativity predicts a singularity with infinite curvature, but when matters gets so tightly compressed we ...
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3answers
407 views

Singularity - exactly what is it?

In quantum mechanics and gravity theories one always meets the word "singularity" in connection with talks about black holes and the big bang, etc. Now in mathematics a singularity is well defined – ...
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2answers
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Rotating black holes and naked singularity

In the book The science of interstellar by Kip thorne can be found the following: There is a maximum spin rate that any black hole can have. If it spins faster than that maximum, its horizon ...
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2answers
431 views

Can a sufficiently large black hole be singularity-free?

This came to me after reading that a black-hole that has the mass of the observable universe will also have an event horizon that covers the observable universe. Since the definition of a black hole ...
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6answers
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Why must a singularity form inside a black hole? [duplicate]

What is the exact reason that normal matter can not exist within an event horizon? I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less ...
11
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3answers
740 views

Are there any true discontinuities in physics?

When we first learn physics, it's often presented very 'discontinuously'. For example, pop quantum likes to talk about objects being "either" particles or waves, leading to a lot of confused questions ...
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3answers
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Electrostatic energy integral for point charges

The electric energy stored in a system of two point charges $Q_1$ and $Q_2$ is simply $$W = \frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$$ where $a$ is the distance between them. However, the total ...
6
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2answers
286 views

Naked singularity

Many consider naked singularities as a fundamental problem and that it should be always covered by a horizon (Cosmic censorship hypothesis). But why naked singularities are really a problem? If we ...
4
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1answer
571 views

Spaghettification on an atomic scale?

Spaghettification occurs when an object approaches a singularity. As one comes close enough to the singularity, the gravity at the feet (if this is a human) is greater than that at the head, ...
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5answers
466 views

Are all black holes singularities identical?

There seems to be a problem between a singularity and the event horizons size. My logic is this if u have two collapsing stars with different masses there horizons will be different in diameter yet ...
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3answers
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What happened during the Planck Era of the Big Bang?

If you look at a big bang timeline before 10 to the -43 seconds you can see Planck time - ???? So I googled it and was met with Before 1 Planck Time Before a time classified as a Planck ...
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1answer
357 views

With point particles being smaller than their Schwarzschild radius are they forever cloaked in a black hole?

My understanding of point particles is that they have mass and are dimensionless. If this is so then wouldn't the mass cause the particle to have a Schwarzschild radius which would then make the ...
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3answers
533 views

Black hole as a gravitational spherical shell. Why not?

I think that Leonard Susskind's holography, George Chapline's "dark energy star," the Emil Mottola and Pawel Mazur's "Gravastar," the Polchinski's "firewall," and the recent ideas of nonsingular black ...
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2answers
522 views

Age of the universe and the singularity at the Big Bang

Using the standard model of cosmology we calculate the Hubble time to obtain an estimate of the age of the universe. This model assumes a beginning of time in the past. But that point is a true ...
2
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1answer
232 views

The universe appears to have a lower bound in the time dimension, why not an upper bound?

The Big Bang looks like a lower bound to the "size" of the universe in the time dimension. Could it also have an upper bound, some furthest point in time from the Big Bang?
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2answers
192 views

Do particles in a black hole stay in constant orbit?

Would particles behave the same way as a satellite orbiting earth, only far more compact and rapid correlating to the gravitational force of the black hole?
2
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1answer
114 views

Metric diameter of a ring singularity

In the Kerr metric the ring singularity is located at the coordinate radius $r=0$, which corresponds to a ring with the cartesian radius $R=a$. So the center of the ring singularity in cartesian ...
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2answers
699 views

About the 1D singularity of black hole [duplicate]

I saw some responses here saying that the singularity into the black hole is one dimension object so my question is : is it possible that the singularity is simply a merger of the 4 dimensions of the ...
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2answers
479 views

Is a black hole really connecting two parallel universes? [duplicate]

What is beyond the point of singularity in a black hole and universe expands in all the three $x$, $y$ and $z$ axis? So how can one thing be on top of another when we don't know where the end point ...
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5answers
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Why do physicists trust black hole physics?

Based on popular accounts of modern physics and black holes (articles, video lectures), I have come to understand the following: Black holes are predicted by General Relativity, a classical theory of ...
8
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5answers
1k views

How to understand singularities in physics?

The question is probably two-folded and I will try not to make it too vague, but nonetheless the question remains general. First fold: In most physical laws, that we have analytic mathematical ...
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6answers
2k views

Interpretation of a singular metric

I'm interested to find out if we can say anything useful about spacetime at the singularity in the FLRW metric that occurs at $t = 0$. If I understand correctly, the FLRW spacetime is a combination ...
20
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2answers
594 views

Curvature Invariants in General Relativity and Singularities

Suppose that I want to check if a given metric is singular or not. I'm interested in curvature singularities, not coordinate singularities, so I can look to scalars made with Ricci, Riemann and Weyl ...
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1answer
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How to thoroughly distinguish a coordinate singularity and a physical singularity

In a course on general relativity I am following at the moment, it was shown that the singularity $r=2M$ in the Schwarzschild solution is a consequence of the choice of coordinates. Introducing ...
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3answers
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The problem of infinite energy of electron as point charge?

Imagine empty infinite universe with just a single resting electron - let's ask the question about configuration of electric field in such empty universe. The standard answer would be $E\propto 1/r^2$...
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7answers
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What does an undefined formula in physics mean?

I am trying to figure out how undefined formulas in mathematics relates to physics. Take the following formula for terminal velocity. $$V_\text{terminal} = \sqrt{ mg \over{c \rho A}} $$ Say we have ...
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1answer
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Geometry inside the event horizon

I'm trying to understand intuitively the geometry as it would look to an observer entering the event horizon of a Schwarszchild black hole. I would appreciate any insights or corrections to the above. ...
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0answers
255 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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4answers
982 views

“Center of a black hole is a time”

$\newcommand{\d}[1]{\mathrm{d} #1}$In one lecture (around 1:33:15) of the series of lectures "Theoretical Minimum" of Prof. Susskind he talks about black holes and the Schwarzschild metric: $$\d \tau^...
4
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3answers
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Why doesn't $\vec{E} =\frac{1}{4\pi\epsilon_0} \int\frac{\rho \hat{r}\;dxdydz}{r^2}$ blow up at $r=0$, when $\rho$ is finite?

Electric field at $(x,y,z)$ produced by a continuous distribution of charges is given by:$$\mathbf{E}(x,y,z) =\dfrac{1}{4\pi\epsilon_0} \int\dfrac{\rho(x',y',z') \mathbf{\hat{r}} \;\mathrm{d}x'\mathrm{...
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5answers
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Does red shift evidence necessarily imply that the universe started from a singularity?

We are taught that the universe began as a singularity - an infinitely small and infinitely dense point. At the beginning of time there was a 'Big Bang' or, more accurately, 'Inflation'. The main ...
6
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1answer
204 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
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1answer
219 views

Why is the natural singularity $r=0$ in Schwarzschild geometry a spacelike one?

Why is the natural singularity $r=0$ in Schwarzschild geometry a spacelike one?
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2answers
482 views

Problem with Maxwell's theory

What exactly is the problem with classical Maxwell theory and the blowing up of energy at $r=0$? Does it have any other problems on the classical level?
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1answer
289 views

Technically, what is a spacetime singularity? [duplicate]

In popular science books and articles, one often finds that the BigBang is a singularity of spacetime, and it is expected to be solved by a successful theory of Quantum gravity. Technically what is a ...
16
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1answer
807 views

Current status of Penrose-Hawking “thunderbolts?”

I recently came across the interesting statement that most definitions of cosmic censorship (CC), and most work on proving it, don't exclude something that Hawking calls a "thunderbolt" (Penrose 1978, ...
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4answers
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If an anti-matter singularity and a normal matter singularity, of equal masses, collided would we (outside the event horizon) see an explosion? [duplicate]

If an anti-matter singularity and a normal matter singularity, of equal masses, collided would we (outside the event horizon) see an explosion?
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1answer
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Reconciling “The Big Crunch” with the 2nd Law of Thermodynamics

Assume "The Big Crunch" scenario (the universe will collapse to a singularity). In this case, I think of the entire universe as an isolated system; in the "Big Crunch" scenario, it seems to me gravity ...
4
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1answer
456 views

How can black holes have electric charge and spin? [duplicate]

If the star's mass supposedly collapses into a single point, and it ends up having "said" zero volume, then how can people say that the hole has a specific spin or that it can have an angular momentum?...
4
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1answer
175 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 ...
4
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1answer
230 views

A true singularity at $t=0$, coordinate independent Big Bang

Consider a flat Robertson-Walker metric. When we say that there is a singularity at $t=0$, clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is ...
3
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2answers
213 views

For a collapsing star, at what mass is the formation of a black hole inevitable?

Stellar mass black holes are formed from the collapse of stars. I have read figures, normally around 2-3 solar masses, that correspond to the mass at which it becomes inevitable that a star will ...
3
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3answers
236 views

Kruskal-Szekeres Coordinates and the Singularity

On the wikipedia page for Kruskal-Szekeres coordinates, it states: [Kruskal-Szekeres] coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended ...
3
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1answer
799 views

Ring singularity of Kerr metric

I have been reading about the Kerr metric using various sources (Wald's textbook, Visser's The Kerr spacetime: A brief introduction etc.). I could not understand exactly why the singularity structure ...
2
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1answer
96 views

Can a curvature singularity (i.e. BH), as defined in terms of geodesic incompleteness, actually exist in nature?

A curvature invariant is a scalar representation of curvature derived from a curvature tensor. The classic example is the Kretschmann scalar derived from the Riemann curvature, where $K=R_{μνλρ}R^{...
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4answers
145 views

Does Newton's Law of Universal Gravitation work when particles are very close?

By Newton's Law of Universal Gravitation, the gravitational force between two particles is $Gm_1m_2/r^2$. Let's assume that the numerator is constant and happens to equal $1$. Imagine that two ...
2
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1answer
228 views

Showing $I=\int d^3k\int dk^0\frac{1}{k^4}$ to be logarithmically divergent

Consider a momentum integral of the form $$I=\int d^3k\int dk^0\frac{1}{k^4}$$ where $k^2=(k^0)^2-(\vec{k})^2$ and the integral over $k^0$ runs from $-\infty$ to $+\infty$. This integral is common in ...
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3answers
792 views

light entering a black hole's singularity

I already understand that light cannot escape a black hole after passing the event horizon, so please do not explain that to me. What I would like to know is this: a well known fact about light (a ...