# B Angular momentum, degeneracy pressure, and cosmic inflation

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1. Jul 30, 2017

### stoomart

Considering the angular momentum of a collapsing star preventing it from resulting in a black hole by degeneracy pressure, are there ekpyrotic universe models that include angular momentum and degeneracy pressure as key factors of cosmic inflation?

2. Jul 31, 2017

### Staff: Mentor

Where are you getting this from? Can you give a reference?

3. Jul 31, 2017

### stoomart

I was reading through a bunch of different material while researching pressure and inflation for another thread when these concepts started coming together, so I'm not positive they are even related. Here are some of the sources I was reading:

Wikipedia: Gravitational collapse
Wikipedia: Degenerate matter
arXiv: Induced Compression of White Dwarfs by Angular Momentum Loss

Last edited: Jul 31, 2017
4. Aug 1, 2017

### Staff: Mentor

None of these explain where you got the idea that angular momentum can prevent collapse to a black hole. Where did you get that idea from?

5. Aug 1, 2017

### stoomart

I will do some more digging to find the source, but it may have just been a misunderstanding of something I read, since I perceive all of this stuff heuristically and not mathematically.

6. Aug 1, 2017

### stoomart

Correct me if I'm wrong, but my understanding is a black hole requires a/m < 1, so if the ratio is much higher than 1, the object may collapse to degenerate matter or a naked singularity.

Wikipedia: Stellar rotation
Yale.edu: Angular momentum and the formation of stars and black holes
SAO/NASA ADS: Gravitational collapse and rotation. I - Mass shedding and reduction of the a/m ratio

Mass shedding can be effective in reducing the a/m of a collapsing configuration, but there is a limit in this reduction. For cases where the precollapse model is a uniformly rotating Newtonian spheroid, a/m cannot be reduced to less than ~40% of its initial value, unless there is significant redistribution of specific angular momentum on the collapse time scale...If follows that if the initial a/m is greater than 2.5, mass shedding alone cannot reduce the ratio sufficiently in a single collapse phase to allow a black hole to form, unless there is significant redistribution of specific angular momentum during that phase...
A second possibility is that the collapse could continue to situations of unbounded gravitational potential with a/m still greater that 1. A supporter of the cosmic censorship hypothesis would like to be able to positively exclude this, but we are unable to do so on the basis of our present analysis.​

7. Aug 1, 2017

### Staff: Mentor

More precisely, for a Kerr solution to be a black hole requires $a / m \le 1$. Yes, that's correct. If $a / m > 1$, the solution describes a naked singularity.

First, we do not know of any exact solution for a rotating object like a planet or star (whereas we do have exact solutions that describe a non-rotating, perfectly spherical planet or star). Nor do we have an exact solution describing a rotating object that collapses to a Kerr solution for any value of $a / m$ (whereas we have an exact solution, the Oppenheimer-Snyder model, that describes the collapse of a perfectly spherical object to a Schwarzschild black hole). We can only simulate such a collapse numerically.

Second, "collapse to degenerate matter" is not really "collapse" in the sense you're using the term. If the process stops with a rotating white dwarf or neutron star, then there is no singularity or horizon anywhere, so there's no issue.

Third, while the $a / m > 1$ Kerr solution, describing a naked singularity, is mathematically consistent, AFAIK nobody believes it is physically reasonable. A naked singularity basically destroys the predictability of the solution--anything could come out of it. So I would not expect "collapse to a naked singularity" to be physically reasonable either.

Finally, although, as I said above, we do not have any exact solutions describing a rotating planet or star, all known rotating objects have $a / m < 1$ by a large margin. And it's straightforward to show that you cannot convert a Kerr solution with $a / m < 1$ to a Kerr solution with $a / m > 1$ by any continuous process (heuristically, the reason is that to increase $a / m$ you have to add more angular momentum to the object than you add mass, and the closer $a / m$ gets to 1 from below, the harder it gets to do this--you end up always adding more mass than you are trying to add because of the way spacetime curves close to the Kerr black hole's horizon). I don't know if anyone has tried to study a similar restriction on ordinary rotating objects, but I would expect there to be one--in other words, I would expect that it is impossible for any collapse process to convert a rotating object with $a / m < 1$ to a Kerr solution with $a / m > 1$.

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