How big is a neutron star?
symmetrymagazine.org
symmetrymagazine.org
Author was a physicist, engineer and gravity expert.
If you can treat these books as something like Socratic dialogue, or Medieval theatre, then you can get a feel for Forward's facility with gravitational dynamics. Quadrupole radiation. Relativistic mechanics.
https://www.forbes.com/sites/startswithabang/2018/06/13/the-...
although it did not explain how black holes form then. do they need a sufficient density of bosons? do those only form in supernovae?
[0] https://en.m.wikipedia.org/wiki/Kugelblitz_(astrophysics)
No. Even degeneracy pressure from the Pauli exclusion principle has a limit; it can't hold an object up against gravity for an arbitrarily large mass. So neutron stars, like white dwarfs, have a maximum mass limit; any object over that mass cannot be a neutron star because neutron degeneracy pressure can't hold it up against its own gravity. (The article briefly mentions this; the limit is the Tolman-Oppenheimer-Volkoff limit.)
We don't know exactly what that maximum mass limit is for neutron stars, because we don't know their equation of state with sufficient accuracy (whereas we know the white dwarf equation of state accurately enough to know that the maximum mass limit for them is 1.4 times the mass of the Sun), but we know it's somewhere betweena about 2 and 3 times the mass of the Sun. Objects more massive than that can only be black holes.
As far as how black holes form, they form when a sufficiently massive object collapses under its own gravity. Usually this happens when a star runs out of nuclear fuel. (More precisely, this is how black holes of roughly stellar mass form. For supermassive holes, like the one at the center of our galaxy, things are more complicated, because they probably don't form in one single process, they form over a long period of time as a hole that started out a lot smaller swallows other massive objects.) If the collapsing object is over the maximum mass limit for a neutron star, degeneracy pressure from the Pauli exclusion principle cannot stop the collapse.
There is a theory that black holes can form from direct collapse. In this case, as I understand it, it can skip the star phase and just collapse straight into a black hole.... but I really am not an expert.
You can find more here: https://en.wikipedia.org/wiki/Direct_collapse_black_hole
And I HIGHLY recommend the PBS NOVA episode "Black Hole Apocalypse" (Jan 10, 2018, Season 45 Episode 1). It was on Netflix for a while (and may still be.)
Edit: here is the full episode on PBS (thank you NOVA!!!) https://www.pbs.org/video/black-hole-apocalypse-yj34qi/
One (pedantic) correction: objects more massive cannot be held up by neutron degeneracy pressure, but you can have more massive stars held up by radiation pressure from fusion. Certainly, there are many giant stars in the 2-8 solar mass range, and rarer stars in tens-to-hundreds of solar masses. Of course, they will eventually burn away their fusion fuel, and the core remnant may indeed become a black hole.
Radiation pressure actually isn't significant in the structure of most stars (it might be for huge stars near the Eddington limit). What holds up stars is ordinary thermal pressure due to the high temperatures inside them. The high temperatures are maintained by the fusion reactions in the stellar cores, yes. You're correct that objects like this do not have a maximum mass limit the way white dwarfs and neutron stars do.
Mass losses over life of a star have usually much less effect on the star than composition changes (but there are exceptions). As the star consumes its fuel its internal composition can change drastically with very little change in mass.
Ok, so it is more complicated than that, the speed of any atom or molecule is a Maxwellian distribution, but enough move fast enough that it’s an acceptable approximation, especially over these time scales.
> The Sun does not have enough mass to explode as a supernova. Instead it will exit the main sequence in approximately 5 billion years and start to turn into a red giant. As a red giant, the Sun will grow so large that it will engulf Mercury, Venus, and probably Earth.
It has a noisy gas surface, that goes up and down, and some times is pulled so far out of the Sun that at those places talking about "radius" is meaningless.
That 700000km figure is a coarse average.
The decrease in number density causes the core to contract slightly and heat up so that the pressure remains the same. The increased temperature causes the rate of nuclear reactions to increase, which then increases the luminosity. The increased luminosity then causes the outer envelope of the star to "puff up" and the radius to increase.
This is not a dramatic process, but over billions of years it has a noticeable effect. The Sun is now 15% larger and about 50% more luminous than when it entered the main sequence.
This is actually the source of an open problem in astronomy called the Faint Young Sun Paradox [1]. Because the Sun was much less luminous in the past, the temperature on Earth should have been about 20 K cooler in the past, but geological measurements don't seem to bear that out. Somehow the Earth managed to stay warmer in the past given the same level of solar irradiation.
The only way it could be stable is a tiny body which is supported based on the structural integrity of the material. This is why asteroids can have very odd shapes.
PS: As to spinning, Neutronium really wants to blow up. Neutron stars are stable due to gravity and internal pressure. Start spinning them around a black hole and you just get a normal accretion disk
To a first approximation (because time and space melting into each other in a wildly non-Euclidean environment isn’t something I can do justice to), unless the neutron star is spinning so fast it is a torus with a black-hole-sized gap in the middle, a black hole inside a neutron star will doom it.
Stress-energy can find itself inside a black hole horizon with no noticeable local effects for some time. One could in principle collapse a perfectly uniform shell of ultrarelativistic matter around some victim, for example, such that the victim is inside the horizon -- that is, the victim's outgoing radio signals cannot reach the rest of the universe -- hours before the matter reaches the victim. Neutron stars require "signals" (QCD and other interactions) exchanged among its deepest components in order to stabilize the entire structure, and the system can find itself in a configuration wherein signals from region A cannot reach region B, so signals from B are wrong to stabilize region C and so on, and the result can be some combination of implosion and explosion. This doesn't fit well with the analogy of going over the edge of a waterfall.
As to your neutron-star-matter torus around a BH, it's hard to contrive even a toy a stress-energy tensor where the generating non-interacting matter doesn't stray onto plunging geodesics, and I struggle to imagine how real interacting matter with inelastic collisions could be more stable. Another salient feature of even the toy version of such system is that there would be enough moving matter in the torus for it to be subject to self-gravitation. Consequently, you're into the task of combining at least a pair of substantially different metrics in the limit where you can't just linearize, resort to perturbation theory, or drop in a Darmois-Israel junction -- that is, you're into the realm of a full numerical relativity task and a full relativistic hydrodynamics task. A taste for what this involves can be had at https://www.mpa-garching.mpg.de/181055/Core-Collapse-in-CFC_
For example, waterfall of causality was meant as an analogy, a point of no return made of time rather than stuff, not a literal waterfall.
Firstly, a torus of ultradense matter is almost certainly unphysical. Such a torus surrounding the near-horizon of a black hole is even less physically plausible.
Secondly, the waterfall analogy only (and only barely) works for an infaller who starts outside an already existing horizon. But in a black hole formed by gravitational collapse there are inside-the-horizon observers (collections of particles, essentially) who never cross from the outside of an event horizon to the inside of an event horizon: they do not fall in any meaningful sense of the word past any point of no return. They are just in a region of the universe with no horizon and suddenly in a region of the universe with a horizon, and unfortunately for them they are on the much less comfortable side of the horizon (the inside). The events that trigger the appearance of the horizon can be at a substantial distance from these unfortunate observers.
I am still confused as to why you felt the need to write “The horizon is not anything like hard surface. You can't stack things on top of it.”, given I cannot see how my words could have led you to think I thought it was solid.
Actually, this leads to an important question: given that my attempt at signalling the limits of my knowledge failed, can you tell me what the right way is to signal the equivalent of “I have been comfortably following the Susskind lectures on my commute at faster than real-time, but my actual degree is not physics”?
You can largely ignore relativity at 1/4c so centripetal acceleration ~F=V^2/r. F ~= (0.24 * 300,000,000 m/s)^2 / 16,000m = 3.2 * 10^11 m/s^2. https://en.wikipedia.org/wiki/PSR_J1748%E2%88%922446ad
Which means the Star has a significant bulge but the minimum and maximum surface gravity ends up well within the range for neutron stars.
PS: I am sure someone has done a fairly detailed analysis of the forces involved but a quick search did not find anything.
You are describing a "naked singularity", it doesn't matter what exactly is spinning, but the theory is: anything with a singularity in the middle, that is spinning fast enough, would become a torus, and the singularity would be exposed.
Problem is, IF, those are possible (noone is sure yet), they create a huge problem for physics: as far as we know, singularities destroy information and what comes out of them is random, if naked singularities are possible, ANYTHING is possible, and if ANYTHING is possible, physics is meaningless.
Seemly in the 70s Stephen Hawking gave a mindblowing talk about that, and Ringworld author was present on that talk.