The Gravo-Thermal Catastrophe
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The Gravo-Thermal Catastrophe
1–10 of 36 posts
Re: The Gravo-Thermal Catastrophe
#2>> Also suppose they’re ‘gravitationally bound’. This means their total energy, kinetic and potential, is negative. That means they couldn’t all shoot off to infinity even if the sphere wasn’t there holding them in.
This seems like an invalid assumption. We know that clusters of stars can eject some of their members. Lot of hand waving in this one.
Re: The Gravo-Thermal Catastrophe
#3>> Also suppose they’re ‘gravitationally bound’. This means their total energy, kinetic and potential, is negative. That means they couldn’t all shoot off to infinity even if the sphere wasn’t there holding them in. This seems like an invalid assumption. We know that clusters of stars can eject some of their members. Lot of hand waving in this one.
That's only an initial condition -- that requirement states only that the total energy is negative.
We are gravitationally bound to Earth, but the Voyagers have left the solar system.
Re: The Gravo-Thermal Catastrophe
#4>> Also suppose they’re ‘gravitationally bound’. This means their total energy, kinetic and potential, is negative. That means they couldn’t all shoot off to infinity even if the sphere wasn’t there holding them in. This seems like an invalid assumption. We know that clusters of stars can eject some of their members. Lot of hand waving in this one.
That sentence does say "couldn't all shoot off to infinity".
Re: The Gravo-Thermal Catastrophe
#5I suppose in the real world such stars would collide in the center of the sphere and possibly form a black hole before achieving the required density approaching infinity, and also catapult stars out so that they leave the system by exceeding the escape velocity without encountering an elastic wall returning them to the system.
Re: The Gravo-Thermal Catastrophe
#6My favourite along these lines is that the mass vs diameter relation for black holes scales in such a way that we are absolutely in a black hole right now according to current theory. As in the current mass of the universe is enough for a black hole with an event horizon diameter that extends beyond the universe.
Re: The Gravo-Thermal Catastrophe
#7I suppose in the real world such stars would collide in the center of the sphere and possibly form a black hole before achieving the required density approaching infinity, and also catapult stars out so that they leave the system by exceeding the escape velocity without encountering an elastic wall returning them to the system.
> in the real world such stars would collide in the center of the sphere and possibly form a black hole
Yes, the article mentions that towards the end.
Re: The Gravo-Thermal Catastrophe
#8Is this right?:
* Although you can make the enveloping sphere as large as you want, the (anti-)equilibration process requires a sphere of some finite radius because if you wait long enough a few stars eventually get launched at escape velocity, and if these actually escaped they would effectively cool the remaining stars.
* Therefore, the characteristic time scale for this process (i.e., the timescale on which the average kinetic energy rises substantially) gets longer and longer as the sphere gets larger.
* In order for the pressure and average speed of the stars to keep rising, the gravitational potential needs to keep falling, so at least some stars need to get and stay very close. In real life, these turn into black holes, which cuts off the process by limiting the amount of gravitational potential energy that can be unlocked in any given volume with a given mass.
Re: The Gravo-Thermal Catastrophe
#9Is this right?: * Although you can make the enveloping sphere as large as you want, the (anti-)equilibration process requires a sphere of some finite radius because if you wait long enough a few stars eventually get launched at escape velocity, and if these actually escaped they would effectively cool the remaining stars. * Therefore, the characteristic time scale for this process (i.e., the timescale on which the av…
> In real life, these turn into black holes
I think this is right, and I think he explicitly calls out that these calculations were done with Newtonian physics modeling point particles - and we know that those two factors severely limit the application of this to the real-world.
Re: The Gravo-Thermal Catastrophe
#10My favourite along these lines is that the mass vs diameter relation for black holes scales in such a way that we are absolutely in a black hole right now according to current theory. As in the current mass of the universe is enough for a black hole with an event horizon diameter that extends beyond the universe.
This mass to event horizon radius relationship is a property of a Schwarzschild
spacetime geometry, globally the universe has a FLRW spacetime geometry