# Schwarzschild radius of observable universe + escape from black hole

https://en.wikipedia.org/wiki/Observable_universe
Mass (ordinary matter) 10^53 kg
Ordinary (baryonic) matter (4.9%)
Diameter 8.8×10^26 m

OU=observable universe

Mass including dark matter/energy = 10^53 kg / 4.9% = 2E54 kg

SR = 2*G*m/c^2 = 3E27 m = 7 times the radius of the OU.

Anything wrong so far? I want to write that in wikipedia. Any unaccounted effect of matter expanding thus gravity at a distance not reflecting the position of where matter is now or so? I read the SR of the OU is equal to the radius of the OU, making the OU "flat".

Normally I would call a mass in a sphere 1/7 of it's SR a black hole. But here I'm assuming that the universe is filled with matter fairly evenly (despite irregularities like galaxies, supermassive black holes, stars or voids on a small scale :), so gravity generally cancels and everything is free to go wherever it wants and cross Schwarzschild radii which are everywhere depending on where you pick the center of the OU.

Now, would it be possible to get stuff out of a black hole if it's gravity was cancelled by nearby matter similar to the OU? Maybe a black hole cluster with overlapping event horizons. Would singularities remain (naked?) singularities and stuff could escape the singularities it was originally bound to? Could stuff eventually escape the black hole cluster, perhaps if there were also non singularities like neutron stars and normal stars in the cluster?

Because the universe is expanding faster than light. This allows it to escape its own Schwarzschild radius. Dark energy also helps but that is not strictly necessary. Also, the "observable universe" could be much smaller than the entire universe.

But wait, how is faster-than-light allowed!?

Special relativity ensures two particles can't exceed the speed of light relative to each other when they are close to each other. Expansion doesn't break this rule because the velocity-difference of nearby co-moving points is tiny.

General relativity with realistic matter/energy and boundary conditions ensures that there can be no time travel. This also rules out warp drives. A pair of faster-than-light travel tubes, for example, can be used to make a time-machine: moving faster-than-light in one reference frame is traveling back-in-time in some other frame. A stationary tube and a (slower-than-light) moving tube, if set up properly, can be used to travel back in time. But again, there is no way to do this using the expansion of the universe.

Apart from the universe itself, there is no way to create a non-blackhole that is smaller than its Schwarzschild radius. An object that is expanding faster than light cannot have an outside. A stationary particle outside the expanding object would either collide with or be pushed away from it faster than light, which would violate one of the two rules above.

• But even if the OU were not expanding stuff could get out. Imagine a static universe filled with iron at 300 K. Every point is the center of a mass large enough to be within a SR, but since gravity cancels there is no force on particles and they can travel anywhere, even across Schwarzschild spheres, which are not event horizons in this case. Aug 20 '16 at 8:47
• @darsie no it would collapse. Each atom would see all the other atoms going toward them. See the en.wikipedia.org/wiki/Friedmann_equations. Aug 20 '16 at 12:14
• the OP says that the expected radius of the universe is strictly lower than its Schwarzschild radius. Meaning we are in a super BH.
– user46925
Aug 20 '16 at 15:18
• @kevin You mean it would collapse similar as it's expanding now? Ok, but still there would be no one way event horizons. Thermal electrons could go both ways. Aug 20 '16 at 16:17