# B Neutron stars and black holes

1. Jun 14, 2017

### phinds

Could be a couple of things. First, you get notifications after the posts so if you are active on the site you may see a new post and then a bit later get an email saying that there's a new post but actually it's one you've already seen. Second, sometimes a post will be deleted but it sends out an email when posted so that can cause confusion.

The thing to do is to look at the BODY of the email and see what post you are actually being notified of.

2. Jun 14, 2017

### Jason R Carrico

Why can I not see newer posts on this thread? I keep getting emails saying there have been newer replies but I don'tsee anything. Why?

Could be a couple of things. First, you get notifications after the posts so if you are active on the site you may see a new post and then a bit later get an email saying that there's a new post but actually it's one you've already seen. Second, sometimes a post will be deleted but it sends out an email when posted so that can cause confusion.

The thing to do is to look at the BODY of the email and see what post you are actually being notified of.

The above showed up in my email, but shows up nowhere when I open this thread.

3. Jun 14, 2017

### Jason R Carrico

I see it now. Sorry and thanks

4. Jun 14, 2017

### stefan r

Suppose the falling object broadcasts a radio message of it's current location. The broadcast starts at one gigahertz but will shift to one megahertz, then kilohertz, hertz etc. The location message was always transmitted at one gigahertz. Now you can make two measurements of velocity. Suppose location A to location B is 2 meter. Light would be able to travel that distance in 6.7 x 10-9 seconds which is also 6.7 cycles at 1 gigahertz. The distant observer who gets a 1 hertz signal will also observe 6.7 cycles but that will take 6.7 seconds. So the distant observer is seeing the messenger drop into the hole at 0.15 meters per second while the messenger is claiming 150,000,000.
The example is not exactly correct for a drop from infinity. Also the signal and velocity would not be linear from point A to point B.

5. Jun 14, 2017

### Staff: Mentor

Phinds is correct. I had to delete multiple posts from this thread.

Hmmm. You sure about this? It doesn't sound right to me, but I confess I'm not sure how to do the math.

6. Jun 14, 2017

### stefan r

No. Not sure of anything. I have not personally made any observations of black holes. The world looks fairly Newtonian in my house.

Also sure that a linear measurement will be wrong. Just trying to describe time dilation. Most descriptions use the word "clock". I am using a radio broadcast frequency as a "clock".

7. Jun 14, 2017

### phinds

Uh ... really? And where exactly is this happening? How close are A and B to the BH?
It would be helpful if you would draw a diagram of exactly what you are describing. It sounds wrong to me also but I may be misinterpreting what you are describing.

8. Jun 14, 2017

### stefan r

speed of light 299,792,458 meters per second in a vacuum.
Isaac Newton and the royal society did not think of it.
My example is crap because the signal would dilate from both gravity and also doplar effect. For stationary objects:

For a solar mass black hole the Schwarschild radius is 2950 meters. To get a time dilation of 1 billion, 10-9 you need √10-18. So the transmitter is around 3 femtometers from the event horizon. Not a very good example.

Suppose it is broadcasting from 29,500 meters (rs x 10) outside a solar mass black hole or neutron star. The time dilation is 0.949. So a radio station broadcasting at 105.1 FM will show up as 99.7FM to someone listening from far away.

9. Jun 14, 2017

### Staff: Mentor

That looks correct to me. My earlier confusion was mostly from your description of the motion of the transmitter.

10. Dec 22, 2017

### Ken G

I really don't see how the presence or absence of a singularity has anything to do with answering any of those questions, I'm sorry. Also, it does not relate to the presence of the "gap" in stable density, as that does not have to do with black holes at all. Whether or not an event horizon forms relates to what happens after the object has already formed, so is just not relevant to those questions. Also, one must be careful not to mistake the infinity in an arbitrary (Schwarzschild-like) time coordinate with the final state of formation of an actual object, as that final state should be in the object's own proper time.

11. Dec 22, 2017

### Chronos

The difference between neuton star & black hole mass is one of the great questions in astrophysics. According to google, the most massive known neutron star [J0348-0432] weighs in at an impressive 2.0 Msun, whereas the least massive black hole [XTE J1650-500] tips the scales at 3.8 Msun. While this is not necessarily spectacular, it certainly is enough to arouse suspicion. Are gap mass degenerates just inexplicably rare within our observational stewardship, or, are we even more naïve than we suspect? Granted, achieving accurate mass measurements at interstellar distances is not always a trivial matter, but, this is akin to randomly turning up a thousand spades of dirt in your backyard only to find all worms revealed run either less than 2 grams or more than 3.8 grams in mass. It certainly appears to suggest either improbable luck, or your yard is inhabited by separate earthworm species.

Last edited: Dec 22, 2017
12. Dec 22, 2017

### Ken G

What doesn't make sense about that is that it usually doesn't matter to the mass if you get a neutron star or a black hole, the mass is set first, and then you get what you get. If there really is a gap from 2 to 3.8, it implies that the mass you end up with is controlled by the object that is created, rather than the other way around. I would find it much easier to believe that either the masses between 2 and 3.8 are hard to pin down, or that they simply aren't classified as either a neutron star or a black hole because it isn't known which to classify them as. If it is true that the mass is pretty well known, and there really is a gap in mass, then I agree that would be of great significance to the formation process of whatever these objects are. Perhaps the neutron star is capable of "bouncing out" any mass that would raise it just a bit above 2 solar masses, but if you really pile on about 4, then it cannot be bounced out. But all that would involve extremely complex physics including rotation, magnetic fields, and equations of state-- not just a treatment of gravity.

13. Dec 23, 2017

### Chronos

The issue is beyond a mere curiousity. In fact,t.one of the leading authorities on stellar mass black holes has already asserted evidence for a preferred mass range of.stellar mass black holes, as discussed in this paper; https://arxiv.org/abs/1006.2834,The Black Hole Mass Distribution in the Galaxy. Ozel also comments on the mass gap between black holes and neutron stars. A variety of methods have been developed to enhance the reliability of black hole mass estimates as discussed here; https://arxiv.org/abs/0902.2852,Determination of Black Hole Masses in Galactic Black Hole Binaries using Scaling of Spectral and Variability Characteristics.and as touched upon in this article https://www.theregister.co.uk/2008/04/01/smallest_black_hole_known_discovered/. For a discussion more specific to the mass gap issue, this may prove interesting; https://arxiv.org/abs/1110.1635,Missing Black Holes Unveil The Supernova Explosion Mechanism. We remain in interesting times.

Last edited: Dec 23, 2017
14. Dec 23, 2017

### Ken G

That's quite interesting, thank you!

15. Dec 23, 2017

### Ken G

General relativity is normally thought to imply that anything that creates an event horizon around itself will also collapse into a singularity. I personally don't know what theorems are needed for that conclusion, but I still don't see in the above any evidence that the mass of the remnant is determined by the equation of state of the remnant in the range 2 - 5 solar masses, that feedback is missing from the argument. Intermediate mass black holes are much more massive than that.

16. Dec 24, 2017

### Ken G

The interesting gap is between 2 and 5 solar masses, not 15 and 50,000, as the latter is expected from stellar mass issues. Also, there is not a direct connection between a mass gap and a density gap, as the latter is expected and the former is not.

17. Dec 25, 2017

### Chronos

Last edited: Dec 25, 2017
18. Dec 26, 2017

### Chronos

There is always uncertainty in data - especially astrophysical data. But strong outliers [like 5000-7500] must be taken seriously when uncertainty of the data is more tightly constrained than those of any assumptions underlying predictive models. The lack of prolific exceptions is less noteworthy than the existence of any confirmed exception..

Last edited by a moderator: Dec 29, 2017
19. Dec 28, 2017

### PAllen

This gap seems to have been bridged by the LIGO neutron star merger, which is believed by most subject matter experts to have produced a 2.7 solar mass BH within about 10 to 100 milliseconds after initial merger.

20. Dec 29, 2017

### Staff: Mentor

A few misconceptions/open questions that have appeared in this thread need to be cleared up:

This is not possible; there is not a continous series of stable (i.e., non-collapsing) states between any neutron star and any black hole. The reason is something called Buchdahl's Theorem, which says that no stable configuration of matter can have a radius smaller than 2.25M, where 2M would be the Schwarzschild radius of a black hole with the same mass. So there's no way for a stable object like a neutron star to be "just short" of being a black hole, because that would correspond to a stable configuration of matter having a radius of, say, 2.0001M--i.e., just a bit larger than a black hole of the same mass--and that is ruled out by Buchdahl's Theorem.

This is not correct. No locally measured speed will be faster than light, even inside the horizon. A coordinate speed in particular coordinates might be greater than $c$, but this has no physical meaning. And none of this has anything to do with whether a singularity is present or how long it takes an infalling observer to reach it.

It is, relative to an observer "hovering" at a constant altitude just above the horizon. Only local relative speeds are physically meaningful in a curved spacetime.

Because no compact body can exist with a radius smaller than 2.25M. See above.

The Einstein-Bohr debate is irrelevant, as is the uncertainty principle; we are talking about classical GR here, not QM. If you want to talk about how quantum gravity might affect possible black hole states, please start a new thread (and it should be either in the QM forum or, more likely, the Beyond the Standard Model forum, since there is no established theory of quantum gravity at present).

The Hawking-Penrose singularity theorems are the ones that establish this conclusion: a good brief statement of the conclusion is that the presence of a trapped surface implies geodesic incompleteness. The assumptions required are an energy condition (which one depends on what kind of geodesic incompleteness is being addressed--timelike or null) and a condition on the global structure of the spacetime (typically that there is a Cauchy surface with certain properties). The Wikipedia page gives a decent brief overview:

https://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

21. Dec 29, 2017

### Staff: Mentor

A number of posts relating to an unacceptable reference given by a particular member have been deleted. This thread is closed as the OP question, which was based on a simple misconception, has now been answered. If further discussion of the gap between known neutron star and black hole masses is desired, please start a new thread.