[HN Gopher] The Gravo-Thermal Catastrophe
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The Gravo-Thermal Catastrophe
Author : terryf
Score : 72 points
Date : 2024-09-21 05:45 UTC (17 hours ago)
(HTM) web link (johncarlosbaez.wordpress.com)
(TXT) w3m dump (johncarlosbaez.wordpress.com)
| phkahler wrote:
| >> 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.
| ISL wrote:
| 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.
| pavel_lishin wrote:
| That sentence does say "couldn't _all_ shoot off to infinity ".
| keskival wrote:
| 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.
| pdonis wrote:
| _> 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.
| AnotherGoodName wrote:
| 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.
| Nesco wrote:
| This mass to event horizon radius relationship is a property of
| a Schwarzschild spacetime geometry, globally the universe has a
| FLRW spacetime geometry
| trhway wrote:
| The light has no chances of getting out of the 13.7B ly
| bubble due to Hubble expansion. Sounds a lot like black hole.
| Nesco wrote:
| The universe has no center, a black hole has one. The
| limits of the visible universe is an horizon on _your frame
| of reference_
|
| In nerdspeak, the geometries _are not the same_ , one is
| isotropic the other anisotropic
| jessriedel wrote:
| 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.
| pavel_lishin wrote:
| > _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.
| jessriedel wrote:
| Right, it wasn't criticism, but the point I added (that I
| think was not explicit in the article) is this: black holes
| provide a _lower bound_ on the potential energy, not just an
| indication that the model is breaking down.
| pfdietz wrote:
| 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.
| leephillips wrote:
| What is a three-body interaction in classical gravity? If you
| calculate the force on each particle from every other particle,
| what's left out?
| trhway wrote:
| 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" :)
| meindnoch wrote:
| >In similar vein applying that classical gravity formula -
| which is valid only to spherical masses
|
| What? Newtonian gravity is defined for point masses. Anything
| else you derive from that by integrating a mass density over a
| region.
| trhway wrote:
| it is equivalent formulations - the point masses case is
| obtained from the spherical in the limit. The spherical case
| is just more illustrative to show where the fantom of the
| "dark matter" in the disk galaxies comes from.
|
| >by integrating a mass density over a region.
|
| exactly. When you do that for a disk galaxy you get much
| flatter curves that the 1/R the proponents of the dark matter
| insist on (that 1/R is exactly what one would get if the
| galaxy was spherical or the star was far outside of the disk)
| bbor wrote:
| 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.
| LegionMammal978 wrote:
| For A), if you have a bunch of tiny atoms bouncing around
| within a regular-sized sphere, then thermodynamics predicts
| that the sphere will experience some constant amount of
| pressure, with tiny fluctuations up and down. This result is
| interesting, since it just takes the ordinary system and asks,
| "What if we scale it up so that the atoms (stars) interact
| gravitationally?" Then, there is no equilibrium pressure
| experienced by the sphere, since the gravitational potential of
| the stars keeps increasing.
| trhway wrote:
| > Then, there is no equilibrium pressure experienced by the
| sphere, since the gravitational potential of the stars keeps
| increasing.
|
| And GR fixes that by kind of moving the sphere walls farther
| away, ie. the space geometry changing by the changing
| gravitational potential.
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