# Could we live in a black hole?

## Is the Universe a Black Hole?

My question: do we live in a black hole? That sounds bizarre at first, but the following rough estimate does not make it seem impossible: The manageable universe has around 100 billion galaxies with an average of 100 billion stars (solar masses). Since the diameter of a black hole (SL) is proportional to its mass, the diameter of a corresponding SL would be around 1023 Kilometers or ten billion light years (possibly even more with dark matter and energy). But that is roughly the size of the known universe! So: are we living in a black hole?
(Herbert Haupt)

In the book "Modern Physics" by Gehrke and Koberle on p. 27 there is the equation for the temporal development of the scale factor ("world radius"). If one assumes a flat universe and one puts the necessary density in the equation, then one easily arrives at the fact that the expansion speed of the universe is equal to the escape speed from the expanding universe. Does that have any meaningful physical meaning?
(Günter nephew)

Over the years, more than half a dozen thoughtful readers have noticed that the mass of a (spatially) flat universe that is within its Hubble radius is equal to the mass of a black hole with that radius as the Schwarzschild radius. The Hubble radius is the distance D.at which the expansion rate ν according to the famous formula ν = H0D. formally reached the speed of light, whereby H0 is the Hubble constant measured today. If the Hubble radius is viewed as the radius of the universe, then this equality suggests that the universe could be viewed as a black hole.

First the short calculation that leads to the above-mentioned finding. The mass density ϱcr of a spatially flat universe results from the Hubble constant according to the general theory of relativity H0 and the Newtonian gravitational constant G to
\$\$ {\ varrho} _ {cr} = \ frac {3 \ space {{H} _ {0}} ^ {2}} {8 \ space \ pi \ space G}. \$\$
A sphere with the Hubble radius R.Hubble = c/H0 therefore closes the crowd
\$\$ M = \ frac {4 \ space \ pi} {3} \ left (\ frac {c} {{H} _ {0}} \ right) ^ {3} {\ varrho} _ {cr} = \ frac {c ^ {3}} {2 \ space G \ space {H} _ {0}} \$\$
a. Their Schwarzschild radius rS. is
\$\$ {r} _ {S} = \ frac {2 \ space G \ space M} {c ^ {2}} = \ frac {c} {{H} _ {0}} = {R} _ {\ text {Hubble}}, (1) \$\$
so just equal to the Hubble radius. Can it be a coincidence? Is the Universe a Black Hole? The answer to both questions is a resounding no, for the following reasons: 