A two-dimensional event horizon?

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?

• The surface of a ball (a sphere) is a two-dimensional object Commented Aug 8, 2014 at 17:46
• But doesn't the event horizon refer to the sphere as a whole? Commented Aug 8, 2014 at 17:47
• $\uparrow$ Yes, the sphere $S^2=\partial B^3$. Commented Aug 8, 2014 at 17:57
• @Qmechanic The way the article is written, it seems to say that the event horizon exists in one plane only. Commented Aug 8, 2014 at 18:02
• The articles is from the Perimeter Institute. I followed a link to this thread via google. perimeterinstitute.ca/news/black-hole-birth-universe
– user56916
Commented Aug 8, 2014 at 18:31

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.

• Wonderful, simple answer! Commented Jan 17, 2018 at 17:56

I'm not sure why they suggest that it would take a 4d universe to create our universe that would exist inside of a 3d black hole. The reality is that even though our black hole's event horizon is 2d (x and y coordinates) the black hole itself would indeed be 3d as objects would fall toward the center (z coordinate). [think basketball sphere as something was placed inside the air hole] If our universe was indeed inside of a black hole you could simply look at this image of the expanding universe and instead invision us falling or being drawn inward toward infinity on the z coordinate which represents the passing of time and x and y representing the current location within space time. As Eistien states gravity is formed by the mass of an object which then warps space/time resulting in acceleration. If the bottom on this picture was a supermassive object infinitely falling toward a bottomless z coordinate in space and we are simply matter falling toward it along that z coordinate then things start to make a little more sense. Scientists seem to make the same mistakes over and over based on observation. We are at the center of the solar system/galaxy/universe. Its expanding, we are shrinking, etc. Dark matter, Dark energy, etc. I don't know how many times we will all go back to Einstien and realize everything is relative. It's really what made that man great. Realitive to us the universe appears to be expanding as we fall faster and faster relative to each other but observe red-shifts in light while not really understanding why our super nova surface area light test show constant luminocity between galaxies. While i could be wrong and we "may not be in a black hole".... I do believe we fall vicitim to looking at things from the wrong perspective more often than not. One could look at the picture generated from the radio telescopes looking to the center of the galaxy to see the very familar shape we see all throughout nature. We now understand that all galaxies are orbiting black holes and we will soon understand that the event horizon of a black hole is no more than space/time warped into a spiral due to massive amounts of pressure placed on the fabrik by an explosion beyond our minds comprehension. Let look at a few things here.

1) birth of black holes usually being with a big bang. 2) We are pretty sure the universe started with a big bang. 3) We've done calculations stating the expansion of the universe was faster than light 4) The initial growth of a black hole exceeds the speed of light. 5) The universe expands rapidly at first and slows over time. 6) Black holes expand rapidly at first and slow over time. 7) The universe has background radation that we cannot see beyond no matter the vantage point taken within the universe either we've reached the end or we've somehow exceeded the speed of light relative to everyting else. 8) Black holes have a event horizon which you can't see beyond because relative to us the gravitational force is greater than the speed of light.

There is a posilbity based on the physics and math.... we could be beyond an event horizon falling into a black hole while still observing light from objects outside of the horizon falling at a much slower rate and may be mistaking that for expansion...