Astronomers Have Found a Star Orbiting a Black Hole at 1% the Speed of Light

I don't know what that formula looks like.

A better way of stating this would be that objects moving solely under gravity have zero acceleration in GR, because in GR, acceleration means proper acceleration--what is measured by an accelerometer. Objects moving solely under gravity are in free fall.

> All bodies are stationary in GR and observe other things moving in reference to themselves.

This isn't correct. There is no requirement that an observer in GR must use coordinates in which they are at rest.

What you're missing is that there's energy potential in nuclear structures, which can be released through nuclear fusion (and in some cases: fission, though that's not materially significant for stars).

What a star is, basically, is gravity and the strong nuclear force duking it out. Eventually, in most cases, the strong nuclear force wins. How long that takes, and where that ends up, depends almost entirely on the initial mass of the star itself.

For low-mass stars ("brown dwarfs"), there's only just barely enough gravitational pressure to stimulate nuclear fusion. The stars may radiate only in the infra-red, and have lifespans of trillions of years, after which they gradually cool to the background temperature of space, having exhausted their hydrogen. These are from a few times the mass of Jupiter to significantly less than the mass of our Sun.

A star such as our Sun has a lifespan of around 10 billion years. Gravity compresses its hydrogen and helium sufficiently that the atoms are no longer distinct, but form a plasma. In that, hydrogen atoms fuse (through several different chains, it can be complicated), producing first helium, then, as lighter elments (or at least their nuclei) are consumed, temperatures rise, and those in turn fuse, through carbon, nitrogen, oxygen, silicon, and finally resulting in iron, with core temperatures increasing all the while.

Iron is at the bottom of the nuclear potential curve -- you cannot release energy by fusing it (as you can lighter nuclei) or fissioning it (as you can heavier nuclei). Which means that gravity at this point wins, and the collapse of the star progresses to its next stage(s).

Incidentally, the rate of energy release by unit mass of the Sun is about 1/5 that of your own body. It's not that the Sun is highly energetic, but that there's so much of it.

Larger stars are fighting a stronger pull of gravity, so must release more energy with time to overcome its pull. They burn faster, and hotter. Basically: the bigger the star, the shorter its life, with some of the largest having a lifespan of only a few tens of millions of years.

There's a maximum star size (through normal formation) given that once a star begins hydrogen fusion the generated pressure drives off any additional potentially in-falling gas. This is roughly 40x a solar mass as I recall.

There may be models in which more massive stars can form through collisions, though I've no specific information on this.

In all of this: the star that forms may have enough mass to form a black hole, but so long as it can undergo fusion it will be able to resist that.

The ability to resist stops when silicon fuses to iron in the star's core. Once the silicon is exhuasted, a life-stage which takes about one Earth day, the core collapses. Depending on total mass, this may result in a white dwarf, a neutron star, or a black hole. It also generates absolutely immense heat (through pressure and kinetic energy) which rips through the rest of the star -- a nova or supernova. Much of the star's mass may be lost, and additional heavy elements (beyond iron) are formed. Which is to say: all of you that isn't hydrogen or helium, was once part of stellar fusion or a supernova (some heavy elements -- gold and platinum-series elements, may come from neutron-star collisions).

Which is how you can have stars more massive than black holes. For a while.

not really. The larger the mass the less dense it has to be when it fits into its Schwarzschild radius. For example, our visible Universe - 46B ly radius - has Schwarzschild radius of 13.7B ly (that number sounds strangely familiar, isn't it? and may give rise to various speculations :), ie. it would have to be just 64 times denser that it is now, ie. like 64 atoms/m3 instead of the current 1 atom/m3.

According to https://en.wikipedia.org/wiki/Schwarzschild_radius :

"The Schwarzschild radius of an object is proportional to the mass. "

Thus we can see that given the same density mass grows as a cube of the radius of containing sphere, and thus Schwarzschild radius of such a mass would grow as a cube of that sphere radius too. So if a mass grows it is possible for it to lose density pretty fast, like the sphere's radius square fast, and still fit into its Schwarzschild radius.