How to calculate fusion conditions for a miniature star and avoid black holes

[MichaelCadeOwen]

I’m wanting to write a realistic sci-fi book but there are a few concepts I don’t understand how to apply. I’m not good with physics so what I’m wanting to know is how to calculate what pressure and temperature would be required for sustained nuclear fusion for something comparable to a star shrunken down to a few meters in width or would something that size and pressure cross the Schwarzschild radius and create a black hole? Also any tips on calculating things like time dilation at relativistic speeds. I’m a history major but I have a layman’s knowledge of some theoretical physics and am very interested in it. Thanks!

 

[jedishrfu]

Do you mean like a neutron star?

https://www.popularmechanics.com/sp...n-stars-before-collapsing-into-a-black-holes/

The subtle difference between when a massive dying star compresses into a core and when it collapses entirely may have been found. In a study published in Astrophysical Journal Letters, researchers at the Goethe University in Frankfurt say they’ve found the dividing line between compact objects called neutron stars and black holes.

When a massive star reaches the end of its life, it goes out with an immense bang called a supernova. From there, one of two known things Can happen: it either becomes a black hole, which has so much gravity not even light can escape, or a neutron star, which is a city-sized corpse of a formerly large star that’s made out of incredibly dense neutron matter.

But astrophysicists have struggled to find out exactly what variations cause a large star to compress into a dense stellar remnant, a neutron star, rather than the inescapable void of matter-eating fury that is a black hole. According to the Goethe researchers, the difference is simple: 2.16 solar masses. Any leftover object after a supernova that is less than 2.16 times the mass of the sun will star a neutron star, while anything more than 2.16 solar masses will become a black hole.

Most neutron stars are between one and two solar masses, and most black holes discovered so far (or at least suspected so far, since we can’t directly see something that gives off no light) are four solar masses or above.

https://en.wikipedia.org/wiki/Neutron_star

A neutron star is the collapsed core of a large star which before collapse had a total of between 10 and 29 solar masses. Neutron stars are the smallest and densest stars, not counting hypothetical quark stars and strange stars.[1] Typically, neutron stars have a radius on the order of 10 kilometres (6.2 mi) and a mass between 1.4 and 2.16 solar masses.[2] They result from the supernova explosion of a massive star, combined with gravitational collapse, that compresses the core past the white dwarfstar density to that of atomic nuclei. Once formed, they no longer actively generate heat, and cool over time; however, they may still evolve further through collision or accretion. Most of the basic models for these objects imply that neutron stars are composed almost entirely of neutrons (subatomic particles with no net electrical charge and with slightly larger mass than protons);

 

[russ_watters]

...what pressure and temperature would be required for sustained nuclear fusion for something comparable to a star shrunken down to a few meters in width or would something that size and pressure cross the Schwarzschild radius and create a black hole?

It isn't clear to me what you mean: do you want a small ball of hydrogen a few meters in diameter, like a few tons of material from the core of the Sun, behaving in the way it does in the core of the Sun? Or do you want the entire mass of the Sun compressed into a few meters diameter? Recognize that when you crush a star like that, you no longer have atoms, so you no longer have fusion.

This black hole calculator might be of use, depending on exactly what you are looking for:
https://space.geometrian.com/calcs/black-hole-params.php

One thing it will tell you is that a black hole with the mass of the Sun has a Schwarzschild radius of 3 km.

 

[happyhacker]

Like you I am trying to put together a Sci-Fi Space fiction book. And Physics does form a basis for some of the story. I could recommend ISBN-10: 978-1-4447-9565-3 by Adam Roberts. It's a 2014 book so pretty good i.e. not too old. General advice seems to be not to try and prove anything using physics we know just create your tech. Research is easy and there is loads of stuff on You Tube. I just put things in a 'subatomic' physics where 'spooky things' happen and leave it at that. Best of luck.