68

I'm not a quantum cosmologist, but I am an early-universe cosmologist, so I can give you my opinion after having read this paper. The article claims that Bohmian trajectories is a valid replacement for geodesics. This was claimed in the very beginning of the paper and not much is offered in the way of defense for this assumption. That's not to say that it's ...


57

If we are talking about stellar-sized black holes, then the object that collapses to form a black hole will have a high concentration of iron (and other iron-peak elements like manganese, nickel and cobalt) at its core, and it is the core-collapse that begins the black hole formation process, but much more material than this will eventually form that black ...


47

The phrase black hole tends to be used without specifying exactly what it means, and defining exactly what you mean is important to answer your question. The archetypal black hole is a mathematical object discovered by Karl Schwarzschild in 1915 - the Schwarzschild metric. The curious thing about this object is that it contains no matter. Techically it is a ...


44

Yes, the particle would continue to accelerate and would never reach a terminal velocity. But that is not what this equation tells you. This equation tells you what the terminal velocity is, given the parameters of the function. When in a vacuum, there is no terminal velocity. It is not zero, it is not infinity. A terminal velocity literally does not exist ...


40

Iron can undergo fusion. However, iron is the point where fusions starts to cost more energy than it yields, so in a typical star it doesn't fuse. In a supernova, and the abundance of energy available in one, iron will continue to fuse to heavier materials, which is probably how we got heavier metals here on earth in the first place (it has to have fused ...


38

At first many people didn't care much for black holes. But later people showed that they were pretty unavoidable features of the theory of general relativity and that theory made other quite precise predictions that were tested and found good. So when you are told that black holes are required if you have GR and GR looks like the best game in town then it ...


37

When you ask most working physicists this type of question, the answer you get tends to be an oversimplified one that is partly just based on experience and conservatism. There were singularities and acausal behaviors in the classical electrodynamics of point particles, but this eventually got pretty much cleared up by QED, so the moral that people took to ...


30

"To me it seems like negative or complex numbers. We used to hate these things but now they are more generally accepted. " Indeed. And in a general context, the infinite answer that some equations return might not be a problem. We have all kinds of rigorous notions of infinite quantities in set theory; see, for example, aleph and beth numbers and infinite ...


29

Indeed you made one mistake: the infalling observer does not see the outside universe "speed up". Look at what happens in a space-time diagram. At the spacetime point where your astronaut passes the horizon, he can only see what's in his past light cone, and that's the universe at early times only. It's the signals that he sends back (or tries to) that reach ...


28

While this work certainly investigates an interesting point, I think simply replacing geodesics in GR with similarly looking quantum trajectories does not solve the issues here. Finding the Friedmann equations while assuming large-scale homogeneity and isotropy is no surprise to me. There are a number of people working on so-called Big-Bounce Cosmologies. ...


27

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 ...


27

The answer is we don't know. I think it is uncontroversial to say that the prediction of singularities by GR is a sign that the theory is failing: we don't expect there actually to be singularities. But we don't have a theory which works (which does not predict singularities in other words) where GR predicts singularities -- such a theory would need to ...


26

Actually, it turns out to be incorrect that the optimal strategy is to free fall. There is an optimal strategy for firing your rocket engine which maximizes your proper time from the event horizon to the singularity, and extends it beyond the proper time of a free falling observer. Here is a paper that discusses the issue and describes strategies for ...


25

It's true that a point particle with finite charge is problematic in electromagnetism because of the infinite field and associated energy near such a particle. However, we don't need that concept in order to make a defining statement about the electric field. Rather, we can use $$ {\bf E} = \lim_{r \rightarrow 0} \frac{\bf f}{q} $$ where $\bf f$ is the force ...


24

...why do we trust black hole physics? ... (physics which is derived by combining quantum mechanics and GR such as Hawking Radiation, things relating to the Information Paradox, etc. ) Formally, there isn't quite a reason to because we've not observed these things yet. But that's also perfectly okay as well because that is how science sometimes works: we ...


22

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 $volume\...


22

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 ...


21

Strictly speaking geodesic incompleteness doesn't mean the worldline of the particle ends at the singularity, but rather that we can't predict what happens to it. The trajectory of a freely falling particle is given by an equation called the geodesic equation: $$ \frac{d^2x^\alpha}{d\tau^2} = -\Gamma^\alpha_{\,\,\mu\nu}\frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\...


20

In solving the Schroedinger radial equation there is no boundary condition applied at $r=0$. At $r=\infty$ yes, $R(r)$ must tend to zero - so we reject the positive exponential solution; any change in that would have massive consequences. But there is no constraint laid on $R(r)$ or indeed $R'(r)$ as $r \to 0$. So there's not a change in the boundary ...


19

This is actually a common question. Many websites have been setup to try to explain this. I like this one for instance. I shall attempt to do my own layman explanation. First of all, in order to have a black hole, you need to have a place for it to be in. Since there was no such thing as a universe, there isn't a place for the black hole to actually ...


19

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 limit ...


19

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 ...


19

Coordinates are not sacred objects in GR. Any coordinate system is just as good as any other coordinate system. So to ask whether the Schwarzschild coordinates are valid or not is a meaningless question ${}^1$. However it is reasonable to ask if coordinates have an intuitive meaning for some specified observer. So for example if we take an observer far from ...


18

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 its own gravity towards its centre of mass. Also ...


18

Need for a coordinate-independent definition multiple coordinates may refer to a single point Normally, the way we define this kind of thing in GR is that we have an atlas, and the atlas is made of charts. Each chart is required to be invertible, so no, we can't have multiple coordinates that refer to a single point. In any case, when we define ...


17

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 ...


16

The obvious interpretation of black hole density is the mass of the black hole divided by the volume inside the event horizon. We need to be a bit cautious about taking this too literally because the volume inside the horizon is not coordinate independant so different observers will measure different densities. However we can easily calculate the density ...


16

The nature of singularities in GR is a delicate issue. A good review of the difficulties presented to define a singularity are in Geroch's paper What is a singularity in GR? The problem of attaching a boundary in general to a spacetime is that there is not natural way to do it. for example, in the FRW metric the manifold at $t=0$ can be described by two ...


16

There are only four known stable black hole geometries: Schwarzschild, Reissner-Nordstrom, Kerr and Kerr-Newman. We expect that any random assemblage of matter dense enough to form a black hole will relax into one of these four geometries by emission of gravitational waves. None of these geometries has two distinct singularities, so (as far as we know) it is ...


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