cosmology - Are we inside a black hole?

I was surprised to only recently notice that

An object of any density can be large enough to fall within its own Schwarzschild radius.

Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's. Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards. Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light. Or Mt. Everest packed into one nanometer.

Reading on about this gravitational radius, it increases proportionally with total mass.

Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.

Question: For an object the mass of the observable universe, what would have to be its diameter for it to qualify as a black hole (from an external point of view)?

Would this not imply by definition that:

• The Earth, Solar system and Milky Way are conceivably inside this black hole?



• Black holes can be nested/be contained within larger ones?


• Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside?

Answer

No. The large scale geometry of the universe is described by the Friedmann-Lemaitre-Robertson-Walker metric.

The geometry of the spacetime of a black hole (in its simplest form) is described by the Schwarzschild metric.

These are totally different solutions of the Einstein Field Equations. For example, in the Schwarzschild metric, the spacelike part of the spacetime is curved, in the FLRW metric it is planar.