# Tag Info

25

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 ...

15

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 ...

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

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 ...

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 ...

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

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 ...

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

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 ...

7

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 ...

7

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 ...

7

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 ...

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

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 ...

6

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 ...

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 ...

5

The ring singularity (assuming traditional GR is the whole story of gravity) is a definitive fact. It will remain a ring no matter what its observer does. This is in an absolutely identical sense to the objective difference between an inertial frame of reference (no pseudo-forces whatsoever) and a non-inertial frame (some kind of pseudo-forces).

5

Having $r = 0$ is only a poblem if you have infinitely small, infinitely dense bodies. For any body with a finite radius, at $r = 0$ you will be inside the body and the gravity will be finite. In fact for a spherical body like a planet or star the gravity is zero when $r = 0$. So the problem only arises if you're prepared to accept other infinities like ...

5

The problem with questions like this is that you can't answer the question unless you specify what observer you mean. This may sound nit picking, but if you drop an object into a black hole you'll see it freeze at the event horizon i.e. the acceleration that you measure falls to zero as the object approaches the event horizon (NB this is the surface of the ...

5

The word "singularity" is generally used to denote that some quantity becomes infinite or in general becomes undefined (i.e. cannot be expressed as a finite real number). One particularly common use is in general relativity. At the event horizon of a black hole (the surface of no return), often coordinates that were well behaved far away run into trouble. ...

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

Once inside the Schwarzschild horizon, it is immaterial to observers outside whether what went in was "matter" (fermionic stuff with a rest mass) or "pure energy" (bosonic stuff): it all adds to the black hole's mass by the amount $\sqrt{m_0+(p^2/c^2)}$ where $m_0$ is the rest mass and $p$ its momentum (at infinity). After this, all the body's energy stays ...

4

If there is a trapped null surface, and one of the energy conditions like the null energy condition, or the weak energy condition is satisfied, and space outside is noncompact, there has to exist either a singularity or closed timelike curve inside the black hole. See Penrose and Hawking.

4

J.M. Hure addressed parts of the problem in Solutions of the axi-symmetric Poisson equation from elliptic integrals (2005), giving a form of the electric field in the vicinity of a loop charge. I will post his published result here with his notation. These equations are for a mass distributed in a loop with linear mass $\lambda$, radius $a$, and located ...

4

The Schwarzschild metric for $d$ dimensions is the standard form $$ds^2~=~-e^{2\phi}dt^2~+~e^{2\gamma}dr^2~+~r^2d\Omega^2$$ These metric terms in the Einstein field equation gives $$R_{tt}~-~\frac{1}{2}Rg_{tt}~=~G_{tt}~=~ -e^{2\phi}\Big((d~-~1)\frac{e^{2\gamma}}{r} ~+~\frac{(d~+~1)(d~-~2)}{2r^2}(1~-~e^{2\gamma}\Big)$$ A multiplication by $g^{tt}$ ...

4

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 ...

4

Extreme gravity essentially equates to extreme pressure. We see a progression in stellar evolution. The high pressures of the huge gravitational pull of a star is at first counteracted by electromagnetic/thermal interactions between gas particles. However, at a certain point (with enough gravitational pull) these interactions are not enough and the ...

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