Or the universe is not a black hole? If that's the case, why isn't it?
Applying that equation to the observable mass of the universe violates basically every single requirement needed to apply the equation.
But that density is not homogeneous. It's much denser in the middle. As you cross the event horizon you wouldn't notice anything happening (as long as the BH is big enough that the tidal forces were small so you didnt get spaghettified). But things would feel very weird as you got closer to the middle.
Probably. Nobody has proved any of this but it seems likely.
Is not a well-defined number. The number you are calculating assumes that the horizon is an ordinary 2-sphere enclosing an ordinary 3-ball [edited, see grandchild post] in Euclidean space, and divides the hole's mass by the calculated volume of that 3-ball. But the spacetime of a black hole doesn't work that way. The "space" inside the hole's horizon is not like any kind of ordinary space that your intuitions will work for.
Also, the interior of the hole is vacuum, so its mass is not something that's distributed throughout any kind of volume; it's just a geometric property of the spacetime.
If you are a free-falling observer, _nothing_ changes for you locally at the event horizon. You will cross it and reach the singularity within a finite (and quite short) time.
If I to guess, you'd see yourself outside an smaller event horizon (as nothing gets through one due to spacetime warping) and you's have a lot of mass very far behind you due again to space time warping so that yout local scape velocity is less than c.
An event horizon forming in front of you doesn't change anything locally. You'll just find out that however much you try, you'll be moving towards the singularity with greater and greater speed.
A point-like particle won't be able to tell that anything is strange until it hits the singularity. But an extended object will break apart due to tidal forces that become infinitely large.
This is for a non-rotating black hole. I can follow the math for it, but rotating black holes are just too math-heavy for me.
One cool thought expressed by Penrose is the possibility that all matter will eventually decay or annihilate and all that's left will be massless radiation such as photons. If this happens then the concept of space and time itself will cease since from within the reference frame of a photon space and time are undefined.
In this scenario the distinction between an infinitely expanded, cold, and dilute universe and an extremely small, hot, and dense universe becomes undifferentiable. Without any physical scale by which to distinguish the two, the far distant future of our universe where all matter has disappeared can be equivalently viewed as the big bang of a new universe.
This is what Penrose calls conformal cyclic cosmology [1]. There was a time when physicists debated whether the universe would continue expanding forever or whether gravity would eventually halt its expansion and cause it to collapse back in on itself in a Big Crunch, potentially giving rise to another Big Bang. Conformal cyclic cosmology allows for an endless repeating cycle of universes even in the case where the universe expands forever, by identifying the infinitely distant future of one universe with the Big Bang of the next.
This is highly speculative and almost certainly false, but it's at least grounded in actual physics and is kind of poetic.
[1] https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology
So all matter is pushed out (dark energy) eventually reaching its own event horizon in the dimension we call time, then continues as photons (Hawking radiation). And eventually after all the matter has done so, everything collapses and this universe ends? Sounds like we are in an aging BH to me.
Penrose also wrote a book proposing that the human brain is a quantum computer and its thought processes couldn't be simulated on a classical computer. I don't think that one has worked out.
Momentum-density is represented in the stress-energy tensor, and so is directly related to spacetime curvature. Light feels and generates gravity.
A sibling comment points out the hypothetical kugelblitz as an extreme example. In cosmology textbooks you can read about the "radiation-dominated era" of the first roughly 50000 years of the universe where the energy density working strongest against the expansion was dense photons (and neutrinos).
i didn't think about photons having momentum when i was 8, though.
To make a radiometer that runs on photon momentum, you’d need much lighter vanes, probably larger, a harder vacuum, mirrored surfaces, a stronger source of photons, like a laser, and probably most importantly, some way to reduce friction - like a torsion balance.
NASA does solar sail experiments along these lines, e.g. at the Space Power Facility at Plum Brook Station, Ohio - see e.g. https://www.sciencedirect.com/science/article/abs/pii/S00945...
Observations of distant galaxies and the cosmic microwave background do match the (expanding vacuum) Lemaître-Robertson-Walker metric with the distribution of matter-density described by the Friedmann equations. Distant galaxies fill the sky and are receding from us, from our perspective; they are not concentrating in any sort of middle.
There is insufficient evidence to conclude that a big crunch is in our future.
"Pure energy" is represented in the stress-energy tensor just fine. General relativity's Einstein Field Equations exactly relates the stress-energy tensor to the curvature of spacetime. It gravitates, your argument just falls down.
<https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor#/...>
What I haven't found is an accounting of our solar system's patterns in our galaxy.
We know about axial precession but we don't know the official cause and some suspect it's related to a pull from another galaxy or a swayish wobble from our solar system's rotation in the galaxy.
Same for a supposed magnetic flip in the earths core. They might be related but we seemingly only know of the precession measured as 1 degree per 72 years but the magnetic north pole doesn't align with any noted patterns nor cause.