# Can you escape a black hole by going into another (4th) dimension? [closed]

I imagine if there was a 2D black hole on a piece of paper, and something was inside the black hole had access to the 3rd dimension, they could just go "upwards" out of the black hole. Could it be possible, that if there were something, perhaps a particle that was inside a blackhole, escape it by going into the 4th dimension and back into the 3rd dimension elsewhere in space?

• Welcome on the Astronomy SE! Note, we are real humans, not some search engine or so. Please honor us by using capital letters and sentences. – peterh Feb 13 at 20:08
• FYI: currently there is nothing, not even a minuscule experimental estimation, for the existence of any 4th space dimension. Most of the current physics formulas could work in any number of dimensions, and general relativity would look much better if our 3d world would be embedded into a higher d one. Side note: the formulas of the General Relativity somehow do not require it. – peterh Feb 13 at 20:11
• I see. I guess i was just wondering how things might work assuming that there does exist a 4th (or higher) dimension. I didn't think that gravity from a black hole (or any object) could reach those higher dimensions as well. – user289602 Feb 13 at 20:19
• Gravity decreases quadratically by the distance. This makes likely that it works only in 3D. In a 4d sphere ("4-sphere"), the surface area increases with the third power of the radius, so gravity would likely decrease cubically with the distance. It would have interesting side-effects, for example there would be no stable planetary orbits. – peterh Feb 13 at 21:17
• While it's not a good question for this site, I like your flatland approach to this. In Flatland, it's impossible for a 2d object to see, much less move into the 3rd dimension. If we take that approach, then a 3d object couldn't escape a black hole that way, and this is all theoretical. Could a 4 dimensional being reach inside a black hole and pick something out of it . . . That's getting into the theoretical and hypothetical quite a bit. Fun idea, but no real answer. – userLTK Feb 13 at 23:27

That all depends on how gravity works in your hypothetical universe. Let's imagine a Flatland black hole.

In flatland (a two dimensional world embedded in a three dimensional one) a two dimensional star collapses and forms a black hole. What happens next? Well it is at least possible to imagine that in flat land, gravity does not pass out of the 2-d universe into the 3d one. This means that particle in the 3d world could pass through the disc of the 2d black hole. It would only be "in" the black hole for an instant.

It is equally plausible that gravity causes a curvature of the spacetime not only in the the 2-d flatland world, but in the 3d world which contains it. Then the black hole would appear as a sphere, and a particle in the 3d world could not pass through the disc.

There are string theories with more than 3 dimensions. But in these theories, we are not like a flatland universe, because the other dimensions are curlled up tighter than a proton. (You can use the metaphor of a long thin straw: It looks one dimensional, but the surface of the straw is in fact 2d. It is flat in one direction but highly curved in another) In such universes the black hole does pass through all dimensions (as does everything else) and you can't escape it by "going up a dimension".

Even if there was a large flat 4th dimension, that was not affected by gravity, getting into it would be at least as hard as escaping a black hole. Just as a flatlander can't get into the 3d world except with help from that world.

Multidimensional black holes are actually studied, mostly because of theories where there are extra (usually very small) dimensions or our world is a lower-dimensional brane inside a bulk space. In these cases gravity propagates in the extra dimensions and one cannot escape the black hole by moving at right angles to normal reality.

There are a lot of black hole-like solutions in higher dimensions, with very different properties. However, if you have a d-dimensional black hole with some metric $$ds^2=g^{ij} dx_i dx_j$$ ($$0\leq i,j\leq d$$) you can always add an extra flat dimension $$x_{d+1}$$ that just extends the black hole horizon $$\Sigma$$ to $$\Sigma \times \mathbb{R}$$, commonly called a black string. In this case jumping along $$x_{d+1}$$ will not save you. Generally higher-dimensional black holes also have trapped surfaces, and are hence inescapable.