Comment by kannanvijayan
4 days ago
Oh I have so many questions on this topic.
I've often wondered about this. I don't have any direct physics training, but it's something that felt really plausible after I learned that the mass of a black hole is linearly proportional to its swarzschild radius.
As the size of the black hole goes up, its overall density must decrease. Combined with the other observation that our universe has uniform density at large scales, it seemed really obvious to me that there existed some threshold at which the decreasing density of a very large black hole, and the fixed density of our observed universe.. would cross.
I used to muse about this question with some other tech colleagues that liked talking about physics stuff but never really got a clear answer to this.
On a side note - I'm absolutely fascinated by the implications relating to this. I'll post a follow-up thought I'm hoping somebody else has also thought about:
I've seen discussion of dark energy mostly presented as a surrogate for real energy. That there is some underlying energy "accelerating things away from each other".
I always felt uncomfortable with that characterization. It seems more reasonable to me to think of dark energy as _negative energy_ - i.e. a loss of overall energy.
In a classical system, two things moving away from each other stores potential energy that can be recouped at some later time. Dark energy doesn't work this way - things accelerate away from each other the further apart they are. From a global perspective, it's an energy loss.
The energy loss pervades to the quantum world as well - photons that start off high frequency arrive low-frequency.
It somehow feels more appropriate to me to think of dark energy as energy being extracted out of the universe, in some form never to return. Maybe like a black hole evaporating as observed from the inside?
When I asked this of some people in real life, I was pointed to answers that indicated that the "energy" component in dark energy is normalized into the "tension" of space somehow. As I mentioned before I'm not really studied in physics, but that explanation felt unsatisfactory to me.
Plug estimated mass of universe to your schwarzschild formula and be amazed how close it is to observable size of the universe.
I tried once, but I'm not sure what terms to throw in there. Visible matter, estimated dark matter.. anything else?
I think my estimate came out to less dense than the required threshold but it was a while back now and cobbled together with some queries to wolfram.
This is true almost by definition, and doesn’t tell us anything interesting about black holes.
There was a thread a while ago on here where the hypothesis for why things are moving apart at faster rates is down to time moving at different speeds due to mass.
So time in the void between galaxies is moving quicker than time in the galaxies, but on the grand scale of the universe the differences as up a lot.
I quite liked this theory, think is make sense, at least from my very limited understanding of this stuff.
Aka Timescape Cosmology, https://en.m.wikipedia.org/wiki/Inhomogeneous_cosmology
Would make sense if our universe is a simulation. It takes more compute power to simulate areas of high density so time naturally flows slower there.
Yeah, but also that's how time actually works too, time runs slower for us on earth than say GPS satellites so adjustments need calculated to sync the two. Again caveat is I'm more than likely either just wrong or misunderstanding it or massively oversimplifying it.
> It somehow feels more appropriate to me to think of dark energy as energy being extracted out of the universe, in some form never to return. Maybe like a black hole evaporating as observed from the inside?
But in this story the black hole increases in size as matter falls into the horizon and shrinks as it evaporates, so cosmic expansion would be associated with more energy falling into the black hole than leaving it.
I thought about this part. I'm not sure we can link apparent size from outside the event horizon to apparent size from inside.
Apparent distance is something that's affected by relative frames of reference and the frames of reference are as different as as can be in this case.
A black hole is really just a singularity with infinite density by definition, but finite mass.
The size and density of the Schwarzschild volume is determined only by mass (stationary, non-rotating). It's proportional to the inverse square of mass. Density = 3c⁶/32πG³M².
SMBHs have densities ~0.5 kg/m³ between thin air and water.
Stellar BHs are ~1e19 kg/m³ several orders of magnitude more than a neutron star.
>follow-up thought I'm hoping somebody else has also thought about [...] dark energy as _negative energy_ [...] Maybe like a black hole evaporating
Another layman's thoughts: Isn't the energy theoretically lost by black holes so faint it's currently undetectable? And isn't the amount of dark energy theorized to be the major component of the observable universe? It seems like the numbers wouldn't add up?
I don't have enough of the background to speculate about the numbers. Dark energy feels "big" if we think of it in terms of the actual energy it would take to accelerate the universe away from itself at the rate that we see.. but the rate that we see is affected by our frame of reference, along with distances and everything else.
I'm gonna pull out my lay understanding again. An evaporating black hole, as it gets smaller, should get more dense and be associated with a higher local spacetime curvature, no? The effect of which would be to slow down apparent time for observers within the system. Maybe that affects observed distance and rates of speed at which things seem to be happening when we look out into the sky?
Sometimes I regret not caring enough about calculus in university.
> Combined with the other observation that our universe has uniform density at large scales
s/has/had at the time of recombination
It is largely an assumption of LCDM that we can treat the universe as practically homogeneous throughout its entire evolution but potentially not a very well-founded at that [0, 1].
> I always felt uncomfortable with that characterization. It seems more reasonable to me to think of dark energy as _negative energy_ - i.e. a loss of overall energy.
Your intuition is correct. If the Lambda term in the Einstein field equations is moved over to the side of the energy momentum tensor, it takes on the role of a negative contribution (provided Lambda > 0, as observations seem to indicate).
> In a classical system, two things moving away from each other stores potential energy that can be recouped at some later time. Dark energy doesn't work this way - things accelerate away from each other the further apart they are. From a global perspective, it's an energy loss.
Note that there is no global energy conservation in General Relativity[2], only at a local scale[3]. Heck, you'll already struggle to define what the energy is of a given piece of spacetime in a meaningful and generic manner[4, 5]. In other words, violations of energy conservation due to spacetime expanding or contracting (a strictly non-local phenomenon), like in the case of the cosmic redshift, are expected and our intuition from classical mechanics only takes you so far.
> It somehow feels more appropriate to me to think of dark energy as energy being extracted out of the universe, in some form never to return.
Dark energy aka the cosmological constant term in the Einstein field equations is a constant term, as the name suggests. Yes, there can be energy loss due to spacetime expanding (see above) but that doesn't change the gravitational constant.
[0]: https://en.wikipedia.org/wiki/Cosmic_web
[1]: https://en.m.wikipedia.org/wiki/Inhomogeneous_cosmology
[2]: https://en.m.wikipedia.org/wiki/Conservation_of_energy
[3]: https://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor
[4]: https://arxiv.org/abs/1510.02931
[5]: https://en.m.wikipedia.org/wiki/Mass_in_general_relativity
Interesting reading - this is the first thorough response I've gotten to some of these question. Will check out the reading material.
> As the size of the black hole goes up, its overall density must decrease.
The center of a black hole is infinitely dense. That's why it even exists. The event horizon is not the black hole.
> and the fixed density of our observed universe
Our universe is expanding. It's density is not fixed.
You really want to be thinking about this in terms of entropy and not matter.
Yeah I was referencing the event horizon as the most meaningful measure of size.
And whether the density is fixed over time or not doesn't affect the question. Let's take the universe at its current average mass/energy density - whatever the "true" measure of that is.
To the best of our understanding, at large scales the density is uniform. So if we consider a suitably large spherical volume of space within our (presumably infinite) universe.. that volume will have an average mass/energy content greater than the threshold amount for a black hole of that apparent volume (again, using the external event horizon frame).
So that suggested to me that either we live in a finite universe, or we must be on the inside of an event horizon. It seems like an unavoidable conclusion.
It's a mathematical model, not reality. I don't believe scientists believe an actual infinitely dense object exists at the center of black holes.
> The center of a black hole is infinitely dense. That's why it even exists. The event horizon is not the black hole.
Arguing semantics is rather boring when it's obvious you understood the point he was trying to make.
> Our universe is expanding. It's density is not fixed.
None of that precludes uniform density at large scales.
>> Our universe is expanding. It's density is not fixed.
> None of that precludes uniform density at large scales.
According to observation, the universe is expanding. An argument that it's really static at a large scale would require contradicting observational evidence, but none exists. A theory that requires abandoning observational evidence bears a special burden, which this theory lacks.
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I think a point they are trying to make is that the border of a black hole is only to us outside observers, if you yourself fell into one you wouldn't notice anything specific when you crossed the boundary. The popular example of hawking radiation references a border and pairs of particles, however its actually only to help people understand the idea of what is going on
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>> As the size of the black hole goes up, its overall density must decrease.
> The center of a black hole is infinitely dense. That's why it even exists. The event horizon is not the black hole.
>> and the fixed density of our observed universe
> Our universe is expanding. It's density is not fixed.
These are both correct and germane points. So why was this post downvoted? Physics isn't a popularity contest, it relies on evidence.
I think given time at a blackboard we could walk through Newton's cannon in the context of Poisson gravity, and for extra credit with the cannonball inducing a perturbation of the Poisson vector field. Even without the cannonball's backreaction, the Poisson picture offers a nice image of the gravitational potential energy at the top of the cannonball's inertial (ballistic) curve. We would then consider a cosmology like our own but with a recollapse: at maximum extent there is some (quasi-)Newtonian notion of gravitational potential energy for all the galaxies, since they are at the point where they begin free-falling back into a denser configuration. It's then the usual story of relating kinetic and potential energy, and recognizing that the standard cosmological frame is close to Newtonian by design. (We also have to stop this approach when the galaxies are merging enough that radiation pressure and gas ram pressure become relevant, because the errors become astronomical).
Since we don't have a blackboard in front of us to interact with, I can suggest Alan Guth's lecture notes on Newtonian cosmology. (Guth is credited with discovering cosmic inflation.) https://web.mit.edu/8.286/www/lecn18/ln03-euf18.pdf See around eqn (3.3). You could also borrow a copy of Baumann's textbook <https://www.cambridge.org/highereducation/books/cosmology/53...> which studies the Poisson equation for various spacetimes, however a static spacetime gets most of the focus.
A universe which expands forever, or which expands faster in the later universe, makes a mess of this sort of approach to calculating a gravitational potential energy. So does any apparent recession velocity that's a large fraction of c (inducing significant redshift, whatever the recession (pseudo-)"force" might be).
However, the general idea is that there is a relationship between the kinetic energy a receding galaxy (in a system of coordinates -- a "frame" -- in which these kinematics appear) and a gravitational potential energy still occurs in a non-recollapsing universe. It's just that the potential energy climbs forever, and you get an equivalent to gravitational time dilation between galaxies at different gravitational potentials (i.e., between early-universe galaxies and higher-potential modern-times galaxies).
Accelerometers in galaxies will not show a cosmic acceleration for any galaxy; they're all really close to freely-falling (local galaxy-galaxy interactions are real -- collisions and mergers and close-calls happen -- but wash out over cosmological distances; look up "peculiar velocity" for details). Therefore we can conclude that there's no real force imposing acceleration on the galaxies. However that's also true of a cannonball in a ballistic trajectory, including one on an escape trajectory or one that enters into a stable orbit. Consequently one can draw some practical comparisons between a ballistic launch from Earth into deep space and galaxies spreading out from an initially denser early part of an expanding cosmos.
> Dark energy as energy being extracted out of the universe
No, it's just a way of thinking about whatever is driving the expansion, and that doesn't dilute away with the expansion as ordinary matter and radiation does. It's not even a "real" energy in the sense that it is only an energy in the cosmological frame, and is a frame-dependent scalar quantity, whereas in the fuller theory it's just a multiplier of the metric tensor. So it's the full relativistic metric doing the work but we absorb some of that into cosmological coordinates in the cosmological frame of reference, carving up the metric tensor into a set of vectors including an expansion vector identical at every point in spacetime.
The expansion vector can also be thought of in terms of pressure: in a collapsing cosmological frame, a pressure drives galaxies together into a denser configuration. The inverse of pressure is tension, so in an expanding cosmological frame, it's a tension that pulls galaxies apart into a sparser configuration. (The reason one uses pressure or its inverse is that the matter fields are idealized as a set of perfect fluids at rest in the cosmological frame; each such fluid has an associated density and internal pressure which evolve with the expansion or contraction of the cosmos, generally becoming less positive in the time-direction of expansion (i.e., in the future direction in a universe like ours). Another way of thinking about pressure is as a measure of isotropic inflow of energy-momentum into a point; increasing pressure at a point therefore increases the curvature at that point. Tension is an isotropic outflow, and so positive tension is repulsive as opposed to the attraction from positive pressure.)
> that explanation felt unsatisfactory to me
Hopefully the above helps a bit. Unfortunately there's only so much teaching one might do in a series of HN comments, and ultimately one probably is better served in developing some grounding in the full Einstein Field Equations / Friedmann-Lemaître equations before thinking in quasi-Newtonian ways. Going the other direction tends to lead to misunderstandings and developing false intuitions when running into situations where the quasi-Newtonian picture needs post-Newtonian correction terms.
It's cool that you have all sorts of questions. You could consider signing up for part time / non-business-hours courses in relativity at a nearby community college or the equivalent, depending on where you are, or maybe just bringing a hot lunch to a lecturer there in exchange for a quick informal tutorial. Anything like that is bound to get you to better answers than raising comments on HN threads about astrophysics in the broadest sense, as answers here are often somewhere between non-standard and unreliable.
That is a very interesting idea… the equation and its assumptions doesn’t seem to have any exceptions so it does strongly suggest our universe is a black hole, inside a black hole?