I just recently read this and enjoyed it. One criticism is that although the physics is "hard" (i.e., relatively accurate), the sociology and psychology of the creatures is silly. Despite dramatically different biology, the creatures act extremely similar to humans with only a few bizarre tweaks (e.g., widespread polyamory and orgies, which play essentially zero role in plot development).
Yes, Forward does not have characters, in terms of agents with motivations and opinions. They are engineering constraints.
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.
Name a book where the sociology and psychology of alien creatures is not silly and similar to that of humans. Seriously, please do, because I'll read it :)
I loved the descriptions on how the move about the world and how they think about it, with "hard directions" and such. It's been a while since I've read it, but really enjoyed it.
> it did not explain how black holes form then. do they need a sufficient density of bosons?
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.
>Objects more massive than [2 to 3 times the mass of the Sun] can only be black holes
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.
> you can have more massive stars held up by radiation pressure from fusion
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.
Imagine what an object would look like teetering on that limit, a tiny mote of frozen hydrogen touches down, and now it's over the max, and FOOOOOOOOP the inwards collapse begins...
For white dwarfs, at least, this process is one possible way to trigger a supernova--a white dwarf right at the limit accretes some more mass and collapses catastrophically; the collapse triggers a supernova explosion.
My understanding is that we're not totally certain if all black holes form from stellar mass black holes.
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.
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.)
It’s actually not really known how these form. Some theories speculate that they’re normal stellar-mass (with “normal” in this case being hundreds of solar masses, because stars were huge back then) black hope that just ate a lot of stuff. Perhaps they merged with other black holes, too. And it’s also possible that a bunch of dust just collapsed under its own gravity early in the universe’s lifecycle and became dense enough to go directly to a black hole.
If you have enough mass (or energy[0]) in a region, it can’t be anything other than a black hole. The relationship between the size of that region and the mass-energy involved is, surprisingly, that the radius (not the volume) is directly proportional to the mass. It gets more complicated for black holes which spin or have a charge, but the basic idea is the same.
The sun has a radius of about 700,000 km, but the question is interesting and there should be a fairly small upper border, since too much mass would end in a black hole.
Too much mass... but if it is spinning maybe it can be bigger. Neutron stars spin extrodinarily fast. And what if the singularity forms in the core, but the spinning shell remains outside to form an acretion disk of neutronium? Boom? Or does it heat/slow fast enough that the star just winks out into a bh?
What you describe is actually a controversial thing.
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.
Neutron stars resist gravity due to the internal pressure just like planets and other stars. Which is why they end up spherical. Put a tiny black hole in any of them and you get the same issue as trying to build a house on thin air.
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
Well, some neutron stars are spinning at a substantial portion of c, the record being 1/4 c. In an object the size of a city, that some serious force pulling against collapse.
The event horizon is like a waterfall, only instead of water it is causality.
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.
The horizon is not anything like hard surface. You can't stack things on top of it. The near-horizon exterior gets extremely dynamical when you put lots of matter there, and the result is almost always a lot less matter there and a bigger horizon area, typically within timescales comparable to the light-crossing time of the horizon diameter. Things really do fall into (rather than onto) black holes, even if some classes of observers might struggle to witness the details and even though it is tempting for ease of calculation or ease of theorizing to treat matter as being smeared onto the horizon rather than crossing through (and/or redefining) 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_
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 believe I fairly explicitly said I wasn’t able to apply GR? That it was above my level? That this was a simplification? And I also believe that simplification is appropriate in this context, especially when so signalled.
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”?
Even classically, the spinning would pull apart the equator, but the poles would fall. You could get a disk of nuclear matter (add electrons and that's a galaxy) or a buzzing cloud where everything just misses the black hole as it orbits (like the stars in the galactic core), but if it's a solid mass with a continuous velocity field, the poles will fall in.
The largest observed angular velocity is 0.24c which sounds like a bigger issue than it is. The centripetal force from that is still significantly weaker compared to the 10^12 to 10^13 m/s^2 you get from surface gravity.
Question: if the sun has a 'fixed' radius but it is radiating constantly doesn't that mean that at some point that radius will change due to the changing radiation pressure from within the sun itself? If so how fast does that change, and how large was the sun say a billion years ago?
At this point in its life the Sun is in equilibrium: it loses mass (which would make it smaller), but this decreases its gravity and pressure (which makes it larger), and these two effects cancel out almost exactly. So the Sun will remain approximately the same size for another 5 billion years or so, until the next phase of stellar evolution.
The pressure balancing gravity in a star like the sun comes from electromagnetism. Neutron stars are so heavy that the pressure comes from the nuclear forces and degeneracy pressure (the same reason there are at most two electrons per orbital in chemistry). They are really fundamentally different objects. A neutron star is more like an enormous nucleus bound by gravity, while the sun is just plasma with an occasional nuclear reaction happening. Future changes in the sun's radius have more to do with its changing composition over time, which alters the reactions that can occur and their rates, which subsequently change the balance between pressure and gravity.
Ignoring changes in time, that nabla9 already explained, the Sun doesn't have a "fixed" radius either.
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.
The main driver of change on the main sequence is the change in composition in the core. Over time the fraction of the core that is hydrogen decreases and the fraction of helium increases. This reduces the number density of particles in the core since four free protons have become a single helium nucleus.
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 sun will grow to a red giant in a billion years or so. The earth will possibly be swallowed by it but at least in a few hundred million years earth will be so hot that oceans boil off and life will be impossible on earth. I hope I got the numbers right...
Per Wikipedia, hydrogen exhaustion will begin in about 5 billion years from now.
> 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.
Boil off where? What would happen to the water vapor if it floats off the Earth into the vacuum of space? Pulled in by the Sun's gravity and forever lost?
There's no water vapor on Venus though. At a certain point in the atmosphere, wouldn't it be cool enough and pressure low enough to make clouds still? Maybe they move around the Earth to the cool side away from the Sun?
Water disassociates into hydrogen and oxygen in UV light, and hydrogen gas move faster than escape velocity, even at current atmospheric temperatures.
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.
I have no idea. I think it should grow with mass loss, but I think there were measurements the have shown that it currently somehow doesn't really change its size.
The response of star to mass loss is highly nonlinear and dependent on other factors than mass.
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.
Does anyone know the meaning of radius here? Does it measure from center to surface along curved spacetime or is it rather the radius that a sphere with the given surface would have if spacetime were flat (i.e. like the Schwarzschild radius of a blackhole)?
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Author was a physicist, engineer and gravity expert.