# Tag Info

26

Short answer is yes. But if you want to nit pick, I could argue that when a star collapses to form a BH, it first forms a horizon before the singularity forms (cannot form a "naked singularity"). And since time inside the horizon is essentially frozen with respect to that of an observer outside, the singularity NEVER forms. Yet from the point of view of the ...

16

If something is infinitely dense, must it not also be infinitely massive? Nope. The singularity is a point where volume goes to zero, not where mass goes to infinity. It is a point with zero volume, but which still holds mass, due to the extreme stretching of space by gravity. The density is $\frac{mass}{volume}$, so we say that in the limit ...

15

A popular assumption about black holes is that their gravity grows beyond any limit so it beats all repulsive forces and the matter collapses into a singularity. [...] Is there any evidence for this assumption? It's not an assumption, it's a calculation plus a theorem, the Penrose singularity theorem. The calculation is the Tolman-Oppenheimer-Volkoff ...

12

The many comments have covered the main points about the question, but I thought it would be worthwhile explaining how the behaviour is calculated. If we solve the Einstein equation for a point mass we get the Schwarzschild metric: $$ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1}dr^2 + r^2 d\Omega^2$$ All equations look scary to ...

11

I) The substitution $f=r\psi$ is the standard substitution to get a radial 3D problem to resemble a 1D problem, see e.g. Ref. 1. II) From the perspective of the normalization of the wavefunction $\psi(r)$, a $1/r$ singularity of $\psi(r)$ at $r=0$ is fine because $|\psi(r)|^2$ is suppressed by a Jacobian factor $r^2$ coming from the measure in 3D spherical ...

11

You are correct when you concluded that two classical point electrons could never touch each other. It would take infinite energy.

10

No. Firstly, weak cosmic censorship can only hold in the generic sense, as there are known examples of nakedly singular space-times. (See, e.g. Christodoulou 1993, and Christodoulou 1999.) Observe in particular that the nakedly singular space-time constructed in the 1993 paper is spherically symmetric with a central axis, and the initial data is ...

10

We don't know what will happen when a photon or any other particle hits a singularity of a black hole. The singularity is a phenomenon of classical general relativity and the singularity is really is an indication that classical general relativity breaks down there. To really understand what happens near a singularity we need a full quantum mechanical ...

10

In classical General Relativity, once an event horizon forms, every particle inside that event horizon will inevitably travel in the direction of the center of the black hole. This is what is meant by "gravitational collapse" and how matter comes to form a singularity in the center- no matter how small it is, or how close to the center it is, nothing can ...

9

Black holes and "anti"-black holes are the same objects. A black hole resulting from the collapse of normal matter, and a black hole resulting from the collapse of antimatter, are indistinguishable. Recall that black holes only have charge, mass, and spin and there is no way to tell that a black hole originally was matter or not (e.g., we can't measure B or ...

9

It's important to understand the context in which statements like "there must be a singularity in a black hole" are made. This context is provided by the model used to derive the results. In this case, it was classical (meaning "non quantum") general relativity theory that was used to predict the existence of singularities in spacetime. Hawking and ...

9

If the Universe is spatially infinite, it always had to be spatially infinite, even though the distances were shortened by an arbitrary factor right after the Big Bang. In the case of a spatially infinite Universe, one has to be careful that the singularity doesn't necessarily mean a single point in space. It is a place - the whole Universe - where ...

8

It's difficult to know what happens on the other side of a black hole, since no information can cross back through the event horizon (the radius at which light and therefore any information can no longer escape). The leading idea is that near the center of every black hole lies a singularity, or a point where the density (and therefore the curvature of ...

8

While there is a general consensus aligned with the Big Bang theory's historical and current stages of the universe. To note, there are three theories with focus on this topic regarding the future, namely: the open universe, flat universe and closed universe theories. Ultimately, the fate of the universe depends on the outcome of the competition between the ...

8

As dmckee says in his comment, the answer is no, a stationary spherical shell isn't possible. This is because not even the interparticle forces in neutronium are strong enough to support it. The problem is that once inside the event horizon there is no way to travel away from the singularity, or even maintain your distance from it, without travelling faster ...

8

Suppose you have some collection of matter that is so dense it has an event horizon where the escape velocity is greater than the speed of light. The escape velocity is obviously due to the strong gravitational field of the matter inside the event horizon, and equally obviously that matter is also pulled by it's own gravity towards it's centre of mass. Also ...

8

A singularity is a condition in which geodesics are incomplete. For example, if you drop yourself into a black hole, your world-line terminates at the singularity. It's not just that you're destroyed. You (and the subatomic particles you're made of) have no future world-lines. A careful definition of geodesic incompleteness is a little tricky, because we ...

8

A sudden singularity is a singularity that forms in the universe in a finite time. This may see like a strange definition. After all, don't the singularities in black holes form in a finite time, so shouldn't they, and indeed all singularities be sudden? Actually, no! For observers like us, floating around the universe, in our frame of reference it takes an ...

8

There is another 'infinity' (among others) lurking in classical electrodynamics which is evident when one calculates the electrostatic energy $W$ of a uniform spherical charge distribution of radius $a$ and total charge $Q$ $$W = \frac{3}{5}\frac{Q^2}{4\pi \epsilon_0 a}$$ Thus, by this result, a point (zero radius) particle of charge Q has 'infinite' ...

7

There are a few errors in your transcription. The first equation you wrote is a valid form of the Einstein field equation, but the version used by dr. Kaku does not have an equal sign. It has a tilde. I think that Dr. Kaku means that there is a relationship of proportionality there. $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R\sim T_{\mu\nu}$$ This is ...

7

Whether it's a black hole or some other more ordinary mass pulling on your rope isn't actually that interesting. Let's think about a cable unrolling above Earth to start with. What we have is a pulley with a rope hanging off one side. The weight of the rope exerts some force on the edge of the pulley, causing it to undergo angular acceleration (starts to ...

7

I think the first few sentences of Landau's Mechanics puts it elegantly: One of the fundamental concepts of mechanics is that of a particle. By this we mean a body whose dimensions may be neglected in describing its motion. The possibility of so doing depends, of course, on the conditions of the problem concerned. For example, the planets may be ...

7

The most common interpretation is that these theorems prove that at the Big Bang and in the astrophysical collapse of a black hole, we really do get densities as extreme as the Planck density. I don't think any professional physicists believe that the process of forming a singularity proceeds as described in the singularity theorems to densities beyond the ...

7

The only definitive answer is maybe. Observations now seem to indicate that the Universe is dominated by dark energy, which leads to the most likely conclusion that the Universe will expand faster and faster, eventually resulting in the disappearance of everything that isn't bound to whatever object in which you reside. In the case of humans, that would be ...

6

Everything that passes the event horizon of a black hole falls into the singularity, including photons. That's why it's a singularity. There is a particular radius outside the event horizon where a photon will orbit, but the orbit is unstable- if the photon gets perturbed a little closer or the black hole's mass increases at all, it will fall in, and if the ...

6

The final stages of star collapse include various stages, but three common ones to consider are white dwarfs, neutron stars, and black holes. White Dwarfs are formed when gravitational forces of the mass of the remnants of the star cannot overcome the repulsion of the electron degeneracy pressure. So think of gravity competing with the electromagnetic ...

6

Basically, the reason is that if the matter is to keep a positive mass, the amount of force required to keep the matter distribution stable tends to infinity once the matter is fit within the schwarzschild radius for that given mass. This was proven in a very strong sense, without much in terms of assumptions about the particular form of the metric, by ...

5

Whenever an amount of mass (or mass equivalent in energy) finds itself inside a volume smaller than the event-horizon for a Schwarzschild black hole of that mass ($R = \frac{Gm}{c^2}$), then you have the necessary and sufficient condition for a black hole. In fact, the black hole may form before the matter reaches this point, provided that it will reach it ...

5

If you stick to the theory of general relativity then what happens to the matter is fairly straightforward. As the matter falls inwards it experiences increasing tidal forces. The matter reaches the singularity in a finite (short!) time, and at the singularity it is compressed into a point with zero size and infinite density. Note that nothing special is ...

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