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Should a black hole be considered two-dimensional or three-dimensional?

It means that a black hole doesn't occupy space, but interacts with it. Or it actually occupies space, and still interacts with it?

Qmechanic
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PlanetGazer8360
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  • If by black hole you mean the event horizon then it is a 2d surface embedded in 3D space. Can you clarify what you are asking in your second paragraph as it isn't clear at the moment? – John Rennie Jul 24 '17 at 14:58
  • "Also, what would happen when a black hole has absorbed, or done something that we just don't have any idea about, to all the matter that it has on its reach, would its size go decreasing steadily? If not, what would happen?" How do you expect anyone to answer that? – JMac Jul 24 '17 at 14:58
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    Possible duplicate of about the 1D singularity of black hole –  Jul 24 '17 at 17:36

2 Answers2

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The event horizon is a three-dimensional surface. It's obtained by restricting the Schwarzschild $r$ coordinate to to a single value, which takes four-dimensional spacetime and reduces its dimensionality by one. For the same reasons the surface of a basketball is a three-dimensional surface. In the case of the basketball's surface, there are two spacelike dimensions, and the basketball also has extent in time, so that makes a total of three dimensions.

The dimensionality of the singularity is not well defined. GR doesn't describe a singularity as a point or set of points. It describes it as something that is simply missing from spacetime. The missing part doesn't have a well-defined geometry or topology, so we can't define how many dimensions there are. There have been attempts to construct such a definition. These attempts are referred to as "boundary constructions." So far, nobody has come up with a satisfactory boundary construction that everybody agrees is correct in all cases.

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If you consider the even horizon of the black hole as where the black hole ends, then it is certainly a three-dimensional object.

If you consider just the singularity at its center you may get away with thinking of it as a zero-dimentional object, since you would think of it as a point. Of course, the story gets more complicated by the fact that you cannot visit this point and then go back, since once you are inside of the event horizon, you will keep moving towards the black hole singularity. In that sense the singularity is not at a point in space but rather a point in time. No matter what direction your travel, you will always end up there.....

You also mention "two-dimensional" in the question as well. I guess you are thinking of the holographic principle as the fast that the entropy of the black hole only grows as the area of the black hole and note the volume of the black hole. In that sense calling a black hole two-dimensional is the most accurate, since the information contained in the black hole scales as a two-dimensional object.

Finally: The black hole will eventually evaporate due to Hawking radiation.

Kenneth Kho
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Mikael Fremling
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  • I think you pretty much got it :) – Robert Poenaru Jul 24 '17 at 15:25
  • The shape of the black hole depends on the characteristics of the black hole. Schwarzschild black holes have a spacelike singularity that would be interpretable as a "line". If the hole has charge, the black hole singularity goes timelike, and you could imagine it as a point. Finally, if it is spinning, it would be a ring. – Zo the Relativist Jul 24 '17 at 15:28