# "Dragons egg" by Robert L Forward

1. Sep 16, 2015

### k!rl

The book is about humans comming into contact with intelligent life on a neutron star, who due to their homeworlds massive gravity evolve incredibly fast relative to the human time frame in higher orbit. It's written by Robert L Forward, a physicist, however shouldn't higher gravity cause time to slow down relative to the outside observers?

This puzzles me to no end

2. Sep 16, 2015

### Staff: Mentor

Time dilation on neutron stars is a small effect compared to other factors.

Bacteria evolve (for some suitable metric) thousands to millions of times faster than humans, for example.

3. Sep 16, 2015

### SteamKing

Staff Emeritus
I think Forward's explanation was that the creatures on the neutron star, the Cheela, functioned at a high rate due to their bodies being composed of nuclear, rather than biological, material. That is, their metabolism functioned at the rate of a nuclear, rather than a chemical, reaction.

https://en.wikipedia.org/wiki/Dragon's_Egg

4. Sep 17, 2015

### k!rl

Thanks for the explanations, I can't believe i've read this far while misunderstanding this point.

5. Sep 18, 2015

### Czcibor

I'm not a physicist, but a while after reading your post I had one afterthought. Shouldn't on a neutron star the time actually slow down a bit? So any hypothetical star neutron beings shall actually evolve slower?

The holy book says that:
https://en.wikipedia.org/wiki/Gravitational_time_dilation

6. Sep 18, 2015

### SteamKing

Staff Emeritus
Yes, there is some time dilation on a neutron star, but not to the extent that the imaginary creatures experienced in the story. The lifespan of one of the Cheela was only about 40 minutes in proper time, which is a dilation factor much higher than suggested by the size of the neutron star which these creatures inhabit.

Forward was a physicist and an aerospace engineer before he turned to writing science fiction. The novel Dragon's Egg contained a scientific appendix which explained many of the strange physical effects one would experience on a typical neutron star. However, due to the strange biochemistry of the Cheela, their metabolism supposedly was greatly accelerated over that typically experienced by creatures which exist through conventional chemical reactions.

While seemingly plausible, one must remember that this work is a novel, not a scientific treatise, and that the author has undoubtedly taken certain liberties in order to spin a more compelling tale.

7. Sep 18, 2015

Staff Emeritus
Did you read the book? Forward explains all this in it.

8. Sep 18, 2015

### Staff: Mentor

Exactly this point. I found Dragon's Egg a very interesting book on the basis of the time difference between the Cheela and humans. It was fascinating to consider any sort of relationship between species that are separated by their perception of time. I found the Cheela a bit too human-like but beyond that quite interesting.

9. Sep 21, 2015

### Loren

I gave up on the book when he started talking about black holes inside suns.

10. Sep 21, 2015

### Staff: Mentor

I don't remember that bit, it has been several years since I read it. What was the context and why did it bother you?

11. Sep 21, 2015

### Loren

It's been a little while, but I think the Sun had at least one black hole in it, which I could not fathom how a small black hole could exist in a star without soon gabbling up the star.

The mass of a star determines its type, so a significant part of that mass would need to be part of the black hole, which leaves insufficient mass for a G-type main-sequence star. That assumes that a black hole in the center of a star could even exist in equilibrium.

While it's been proposed that a micro black hole might be created under the conditions of the big bang, the observable data for those conditions have pretty much ruled out that possibility. That leaves the minimum mass for an observed black hole as 3.8 solar masses, which is much more massive than our sun.

12. Sep 21, 2015

### SteamKing

Staff Emeritus
I just scanned a copy of Dragon's Egg, and I find no mention of any black holes inside the sun. I think you have this novel confused with something else ...

13. Sep 21, 2015

### Loren

I was just thinking that you might be right when I reviewed the book on my iBook and found the passage where it states in the chapter Pulsar from the book Dragon's Egg, " ...the Sun had a case of indigestion. It had eaten too many black holes." Try searching on that string. The following paragraphs describe four dense masses (probably primordial black holes) circling inside our Sun.

14. Sep 21, 2015

### Staff: Mentor

Observations have ruled out small black holes (or any other compact massive objects) as primary source of dark matter for a large range of masses. They could still exist if they contribute only a small fraction to the total matter density.
That doesn't mean I would trust any "black hole in a star" model without proper simulations to estimate their lifetime.

15. Sep 21, 2015

### ogg

We have to be careful when thinking of black holes "sucking", "vacuuming up", "gobbling", etc. Who was the sci-fi author (maybe there were several?) who used black holes as weapons? Some aliens dropped one on Earth (Or did we do it to ourselves? IDK) and it slowly, over decades, swallowed the matter of Earth. Its orbit was BELOW the surface of Earth, but being so massive, that didn't slow it down much. The question there would be: as it orbits the barycenter, how much matter flows into it? The viscosity of the matter (solid or molten) in the near-by (extreme) g field, along with its orbital velocity, would determine the inflow. Similarily, for a black hole inside a star, clearly the matter in its direct path would be (mostly) swallowed (I'd guess, I'd have to do the dynamics calculations to verify this, and I don't have the competence to do them) but near-by plasma would be limited to the regular laws of dynamics (in a general relativistic context). As an estimated lower bound, consider two disks, one the radius of the Sun, R, the other of radius of the BH, r. Then assume that each orbit removes the matter equivalent to πr². So the number of orbits required is R²/r². For a BH with an event horizon of 30 km (10X the Sun's mass, a large stellar sized BH) and given Sun's R=700,000 we have 7E5²/900 ~ 600,000 orbits. Assuming velocity is ~√(11GM/r) we can estimate that one orbit takes about 10 years at an orbital r = ½R, or it would take 6 million years for the Sun to be consumed. This is an extremely crude estimate, but it suggests that there's no reason that a bh couldn't exist temporarily inside a star. (Of course, the nasty (radiation) effects would be observable much sooner.)

16. Sep 21, 2015

### SteamKing

Staff Emeritus
I checked out that chapter. I don't know how I missed it the first time.

Forward used the "black holes" as a plot device which led to the discovery of the Dragon's Egg pulsar. The human scientists were tasked with making observations of the sun, and their data showed a periodic "scruff" which appeared but couldn't be accounted for by normal stellar astrophysics. Eventually, they found that this "scruff" was evidence that a previously unknown pulsar was passing close to the solar system, and an expedition was mounted to observe this object. It was while their observatory was orbiting the Dragon's Egg that the alien Cheela were discovered living on the surface of the neutron star.

17. Sep 22, 2015

### Loren

Yes, that rings a bell. I got as far as about 33% through the book when I stopped and started reading a number of novels by Reynolds. Eventually I will get back to it, but I have one novel by Reynolds that I am finishing now, plus one of my own I am still writing, plus my regular day job. :)

18. Sep 22, 2015

### Staff: Mentor

@ogg: How did you get an orbit of 10 years? The earth revolves at 1 AU around a 1 solar mass object and needs 1 year. Clearly the sun revolving around a 10 solar mass object at less than .01 AU would need less than a day.

The matter would be heavily influenced by the black hole over the whole volume of the star - the net gravitational force is always towards the black hole. To pass a free 10 solar mass BH with ~30 km/s initial velocity, you need an impact parameter of the same order of magnitude of the solar radius. Intense radiation from the accretion disk is the only thing that can prevent the star from collapsing within very short timescales.

The Eddington limit still applies: the system should reach a (quasi-)equilibrium where radiation pressure cancels gravitational pressure. That gives a timescale of $\frac{\dot{M}}{M} \approx 0.5 Gy$ (from here). If (!) this equilibrium is reached the black hole cannot consume the star (at 1/10 its own mass) faster than ~50 million years.

19. Sep 25, 2015

### Hornbein

I looked into this once. Time dilation on the surface is small. I would guess less than 1%. At the center of the most massive neutron stars it would be between 30 to 90 percent. (The calculation depends sensitively on the radius of the star, and this is not known.)

This interested me because it seems to create a dilemma. The interior of a neutron star is a superfluid. Essentially this means that all of the neutrons share a single wave function. But if some of the neutrons have such a large time dilation, how can they share of the wave function of the non-dilated neutrons?

I imagine the answer is that they share the function locally. What is happening a kilometer away doesn't matter.

By the way, I think Anders Sandberg's idea that the aliens are living in the superfluid interior of the star is much more realistic. The surface of a neutron star seems to me to be to be the most unfavorable possible environment outside of a black hole. Among other things, there tend to be regular starwide thermonuclear cataclysms.

20. Sep 25, 2015

### Staff: Mentor

In a superfluid, there are no "outer" and "inner" neutrons. All neutrons are the same.