Hope I got that right.
This is the radius at which a given mass becomes a black hole.
I'm writing this from memory so my figures may be wrong.
For the earth to become a black hole it's mass will have to be compessed to 1km radius. For the sun 10 km.
This won't happen because there is not enough gravity in iether the earth or the sun.
The measurement was then turned on the entire universe and the radius was much bigger than the entire universe.
Which means that the universe could be one big black hole.
In a sense if you were out side the universe(if it were possible) you would not see it no light or anything would escape. in fact would the universe appear like a tiny singularity to a outside observer or would it be vast?
Any thoughts

The Schwarzschild radius is the radius of the event horizon of a black hole. This is the distance from a black hole at which nothing can escape, not even light. Within the Schwarzschild radius, the escape velocity from the black hole is greater than the speed of light.
The size of the Schwarzschild radius may be proportional to the mass of the black hole. For a typical black hole with a mass 10 times that of the Sun, the Schwarzschild radius would be roughly 18.6 miles (30 km). The Schwarzschild radius is named for the German astronomer Karl Schwarzschild, who predicted the existence of collapsed stellar bodies that cannot emit radiation, in 1916

It equals; the square root of (GM/(C squared))


Sun's RS = 3km
Earth's RS= 9mm




But i don't see how the universe can be a black - the density is far too small and not even made of degenerate matter - also what do you use for the universe's radius and mass??
And how can the universe be black hole if its expanding??
Surely it the inverse of one ... no?

Sorry it's taken me so long to reply inca, iv'e been working.
Thanks for filling in the gaps in my mental musings.
I read about the possibility of the a universe wide swarzchild radius from and old 1970's asimov book, it was'nt one of his fine contributions to fiction but more of an attempt to work out the fate of the human race,long term.
Obviously he had no idea of the size of the universe, we still don't know. It was a kind of" what if ," possibility.
As you kindly wrote down the schwarz child radius is the point at which a given mass becomes a black hole.
The sun 3km.
A star 10 times the mass of the sun 30km.
This progression is arithmetical, meaning if you muliplied the mass by billions and billions the distance would go out billions and billions.
The point made in the book was. If the schwarzchild radius for the entire universe is bigger than the universe in size. That means in effect we could be inside a singularity and when the expansion of the universe reaches the limit (event horizon) what happens then?
Bear in mind he was also taking dark matter into account.

The Schwarzschild radius for the universe would be considerably less than the radius of the universe (if it is finite).

Quite apart from that fact, the universe cannot be a black hole, because funny things happen inside black holes which do not happen in our universe in general. For example, anything passing within the Schwarzschild radius of a black hole inevitably must hit the singularity at the centre of the hole. Space and time directions get swapped, so that forwards in time becomes towards the singularity. We do not observe such a swapping in our regular universe, so we cannot be inside an event horizon.