from Hacker News

The Gravo-Thermal Catastrophe

by terryf on 9/21/24, 5:45 AM with 35 comments

• by jessriedel on 9/21/24, 4:28 PM

  Is 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.

• by AnotherGoodName on 9/21/24, 4:14 PM

  My 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.

• by mikhailfranco on 9/22/24, 6:18 AM

  This idea has been explored by Julian Barbour in his book The Janus Point.

  http://www.platonia.com/books.html

  The related math and modelling goes under the name Shape Dynamics:

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

  Shape Dynamics - An Introduction

  https://arxiv.org/abs/1105.0183

• by pfdietz on 9/21/24, 5:35 PM

  As I understand it, those simulations did not include three-body interactions that could leave particle pairs bound. If this happens, those binaries can now inject energy into the cluster as a whole, keeping it inflated and preventing collapse. Of course, the binaries' orbits shrink over time, so this doesn't go on forever.

• by keskival on 9/21/24, 3:38 PM

  I 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.

• by kazinator on 9/23/24, 1:09 AM

  Something doesn't add up, obviously.

  For one thing, squeezing the sphere smaller against pressure requires work. That's an external energy input. The system is not closed if some agent is available that can squeeze the sphere smaller.

• by trhway on 9/21/24, 6:04 PM

  Application of the 1/R2 gravity formula to the pointwise mass with R->0 can easily power your Romulan ships. In similar vein applying that classical gravity formula - which is valid only to spherical masses or masses at such large distances that they can be treated as such - to the stars inside disk galaxies gets you the "dark matter", and thus not surprisingly the flatter the disk galaxy the more "dark matter" :)

• by bbor on 9/21/24, 6:14 PM

  A) …why? What makes this interesting to physicists? I understand this as “if stars weren’t stars but instead rigid spheres, and if they were in an impossibly-impervious giant sphere, then weird stuff happens”. And…?

  B) “since stars rather rarely collide” still blows my mind. I did some napkin math on Reddit a while back on why there will be very few stellar collisions (really, one star falling into another’s orbit?) when andromeda collides with the Milky Way, and the answer is that space is just mind-bogglingly huge. Even the most dense clusters in our galaxy are akin to ~70 1cm diameter spheres per olympic swimming pool.

  If god is real, he is surely a giant.

• by phkahler on 9/21/24, 2:15 PM

  >> 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.