Today, I came across an article which says that the Universe began with the collapse of a 4-dimensional [spatial] Universe. Well, I don't know if there's any way to confirm these like it is with all other theories which deal with before the Big Bang.
The strange thing was that the article mentioned about 2-dimensional event horizons. Quoting from it :
In our three-dimensional [spatial] universe, black holes have two-dimensional event horizons — that is, they are surrounded by a two-dimensional boundary that marks the "point of no return." In the case of a four-dimensional [spatial] universe, a black hole would have a three-dimensional event horizon.
Why does the article say that black holes in 3 [spatial] dimensions have 2-dimensional event horizon. I will reach the "point of no return" no matter from what direction I approach, right? Is something missing here?
Best Answer
They are just saying that in our universe of 3 spatial dimensions the event horizon is a 2-sphere.
Ignoring time, our universe is a 3 dimensional manifold because it takes 3 numbers to specify a point within it. Likewise, an event horison is a 2 dimensional manifold because it takes 2 numbers to specify a point within it.
Judging by the comments there is some confusion with the fact that by the phrase "2D surface" we often mean a plane. A plane is a flat 2D surface and we can have curved 2D surfaces as well, and the event horizon is an example of a curved 2D surface. It also has a global topology that differs from the plane.
If you zoom in to a point on a sphere then it does indeed look like a plane. After all, I'm typing this while sitting on a 2D surface (the surface of the Earth) and from here my lawn looks pretty flat. Actually this is an important principle in GR generally. No matter what the spacetime, locally it always looks flat.