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So is a black hole 3 dimensional? Is it a sphere? Or does it only work in certain directions? Does everything "fall" the same direction? I ask because even in

So is a black hole 3 dimensional? Is it a sphere? Or does it only work in certain directions? Does everything "fall" the same direction? I ask because even in a brief history of time, the diagrams are very "single plane of space-time, pulled infinitely deep by the black hole"

PeanutNore 8y ago
A black hole itself (the singularity) is 1 dimensional - a single infinitesimal point. The event horizon around it is roughly a sphere. The diagrams that you are talking about are a visual metaphor that represent 3D space as a 2D plane and the 3rd dimension standing in for the influence of gravity. IRL, spacetime has 3 spatial dimensions, not 2, and gravity is not a dimension but a force. It's hard to visually represent gravitational distortion of 3 dimensional space without a 4th spatial dimension to do it with, so textbook diagrams use a 2D plane.
- pflats 8y ago
  I think you've got a typo here: points should be 0-dimensional.
  - curlypaul924 8y ago
    Are you sure it's a typo? https://physics.stackexchange.com/a/194947 https://physics.stackexchange.com/a/194947 (I'm not a physicist.)
    - checkyoursudo 8y ago
      I believe the previous poster is referring to a typo following from this: >A black hole itself (the singularity) is 1 dimensional - a single infinitesimal point. In Euclidean geometry, A cube is 3 dimensions. A plane is 2 dimensions. A line is 1 dimension. A point is ...
    - codethief 8y ago
      Not sure why you're getting downvoted, this is a legitimate question. However, in this particular case, I think the final sentence of the accepted answer on Physics.SE, namely that > In this diagram the singularity is a line in spacetime i.e. a one dimensional object in spacetime. is wrong or at least very misleading – the answer does (correctly) say that asking for the "dimensionality of a singularity […] is a meaningless question because the spacetime geometry is undefined at a singularity".
  - cuspycode 8y ago
    A point is 0-dimensional, but in a space-time diagram the time dimension is added, which makes it 1-dimensional. Penrose diagrams for black holes assume spherical symmetry, so all of space is represented by a single radial coordinate, which makes it possible to display such diagrams in 1+1=2 dimensions.
    - codethief 8y ago
      A singularity doesn't have a dimension. It is a portion of spacetime that is missing, not a point or set of points. We can't define its dimensionality, either.(×) What we can say is that the singularity in Schwarzschild black holes is spacelike. ×) Counterexample: Consider the manifold M := R³\B, where B is the closed unit ball, equipped with the standard Euclidean metric. This manifold is certainly not Cauchy-complete and we can reach the singularity at r=1 in finite time. Now, if we had to define the dimension of the singularity, what dimension n should it have? n=2 (a sphere)? Maybe. At least we could extend M by the unit sphere to make it complete. But could the singularity also be a point (i.e. n=1)? Yes, certainly. By diffeomorphism invariance, we could simply find new coordinates and map R³\B to R³\{0}, so the singularity would suddenly become a point. So, as you can see, interpreting the singularity as a point or set of points that have a topological dimension doesn't work.
- antidesitter 8y ago
  > A black hole itself (the singularity) is 1 dimensional - a single infinitesimal point. A point is 0-dimensional. A line is 1-dimensional. The singularity is 1-dimensional (more precisely, a ring) if the black hole is rotating. [1] [1] https://en.wikipedia.org/wiki/Ring_singularity https://en.wikipedia.org/wiki/Ring_singularity
- pavelrub 8y ago
  The singularity is likely a mathematical artifact of the fact that GR is insufficient to describe black holes. In reality (quantum gravity) they probably do not exist.
  - lostmsu 8y ago
    I would not be so sure. Its presence might simply indicate, that black hole's inner volume is infinite.
    - codethief 8y ago
      Could you elaborate on your definition of volume here (are you talking about spatial volume or spacetime volume?) and how the curvature going to infinity at the singularity should imply its infiniteness? My thought process here is the following: The inside of an (eternal) black hole carries four (Schwarzschild) coordinates t, r, theta, phi – r now being timelike and confined to the interval (0, 2M) and t now being spacelike and being any real number. That is, depending on when (at what time t) you cross the event horizon, you end up at a different point in space. The singularity at r=0 is then a point in your future which, like your own death, you cannot actually see but which you will nevertheless hit in finite proper time. So in this sense I'd say the volume is very finite (if we disregard the (trivially unbounded) spacelike coordinate t which, as mentioned before, simply corresponds to the time of entering the BH).
      - codethief 8y ago
        I should add: 1. In the interior of the BH, the determinant of the metric is bounded since the Schwarzschild factors in the metric cancel out. So the volume measure doesn't do anything crazy as one gets closer to the singularity and boundedness of coordinates implies boundedness of the volume. Again, I'm disregarding the spacelike t coordinate because to me the relevant fact is that all matter reaches the singularity in finite proper time, so while we could theoretically stack lots of (actually, an infinite amount of) (massless) cubes inside a black hole, they would soon all get crushed. 2. Of course the situation is slightly different if we're talking about a growing black hole whose mass (and, therefore, radius) increases as we throw matter into it.
SpeakMouthWords 8y ago
1. Yes 2. Basically 3. No 4. No
deleted 8y ago
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oppositelock 8y ago
1. Yes, but it's also up for debate, since it's also known that the information content of a black hole is proportional to its surface area, so 2D. 2. The event horizon is spherical. Mathematically we treat it as a point. Nobody knows. 3. It's a gravity well, so everything falls towards it like it does towards the earth. Since it's the center of a galaxy, and galaxies form a 2D spin plane, most matter will be circling it, like our solar system circling the sun, so most matter will come from that planar distribution. We will never see anything fall into a black hole, as in our space-time, this would happen at infinite time. As things get closer, they red shift from our frame of reference due to time dilation, until the light frequencies are so low that we can no longer detect them
- deleted 8y ago
  [deleted]
rtkwe 8y ago
The stretchy sheet of space time illustration is just a simplified visualization space is 3 dimensional so the warping is 3D. The stretchy sheet visual is used a lot because showing a warped 3D grid to be more accurate is a lot harder and a lot less clear and illustrative. Trying to show a 3D grid doesn't even fully capture the situation because it doesn't show how the passage of time gets distorted as well.
JimBrimble35 8y ago
Let's start a movement similar to flat Earth, but instead it's Spherical Black Hole. I refuse to believe that a black hole is anything but a sphere no matter what evidence I'm shown.
beat 8y ago
Is an image of a sphere printed on paper three dimensional? Think about that for a moment, and you'll see the problem. I am not a physicist, but from my lay understanding, a black hole (and all other forms of matter) exists in a four-dimensional space-time form that we can experience directly, plus a number of higher dimensions that we can only extrapolate, and observe indirectly via experiment (kind of how a picture of a sphere is not a sphere due to a missing dimension, but you can still tell it's a sphere based on other characteristics). The exact number of higher dimensions is the realm of string theory, and could be 10, 11, 26, or something else. The singularity of the black hole is one-dimensional, I think (I could be wrong, I'm often wrong). The event horizon is... funny. The outside of the event horizon is in four-dimensional space-time and is more or less "spherical". The inside is a land of theory and debate, because by definition we can't directly observe it from our space-time. Do space and time even exist inside the event horizon? I dunno, ask someone who knows what they're talking about. The best I can do is an analogy. Imagine it's the surface of the ocean. Above the surface, you're in air. Below the surface, you're in water.

PeanutNore 8y ago

A black hole itself (the singularity) is 1 dimensional - a single infinitesimal point. The event horizon around it is roughly a sphere. The diagrams that you are talking about are a visual metaphor that represent 3D space as a 2D plane and the 3rd dimension standing in for the influence of gravity. IRL, spacetime has 3 spatial dimensions, not 2, and gravity is not a dimension but a force. It's hard to visually represent gravitational distortion of 3 dimensional space without a 4th spatial dimension to do it with, so textbook diagrams use a 2D plane.

pflats 8y ago
I think you've got a typo here: points should be 0-dimensional.
- curlypaul924 8y ago
  Are you sure it's a typo? https://physics.stackexchange.com/a/194947 https://physics.stackexchange.com/a/194947 (I'm not a physicist.)
  - checkyoursudo 8y ago
    I believe the previous poster is referring to a typo following from this: >A black hole itself (the singularity) is 1 dimensional - a single infinitesimal point. In Euclidean geometry, A cube is 3 dimensions. A plane is 2 dimensions. A line is 1 dimension. A point is ...
  - codethief 8y ago
    Not sure why you're getting downvoted, this is a legitimate question. However, in this particular case, I think the final sentence of the accepted answer on Physics.SE, namely that > In this diagram the singularity is a line in spacetime i.e. a one dimensional object in spacetime. is wrong or at least very misleading – the answer does (correctly) say that asking for the "dimensionality of a singularity […] is a meaningless question because the spacetime geometry is undefined at a singularity".
- cuspycode 8y ago
  A point is 0-dimensional, but in a space-time diagram the time dimension is added, which makes it 1-dimensional. Penrose diagrams for black holes assume spherical symmetry, so all of space is represented by a single radial coordinate, which makes it possible to display such diagrams in 1+1=2 dimensions.
  - codethief 8y ago
    A singularity doesn't have a dimension. It is a portion of spacetime that is missing, not a point or set of points. We can't define its dimensionality, either.(×) What we can say is that the singularity in Schwarzschild black holes is spacelike. ×) Counterexample: Consider the manifold M := R³\B, where B is the closed unit ball, equipped with the standard Euclidean metric. This manifold is certainly not Cauchy-complete and we can reach the singularity at r=1 in finite time. Now, if we had to define the dimension of the singularity, what dimension n should it have? n=2 (a sphere)? Maybe. At least we could extend M by the unit sphere to make it complete. But could the singularity also be a point (i.e. n=1)? Yes, certainly. By diffeomorphism invariance, we could simply find new coordinates and map R³\B to R³\{0}, so the singularity would suddenly become a point. So, as you can see, interpreting the singularity as a point or set of points that have a topological dimension doesn't work.
antidesitter 8y ago
> A black hole itself (the singularity) is 1 dimensional - a single infinitesimal point. A point is 0-dimensional. A line is 1-dimensional. The singularity is 1-dimensional (more precisely, a ring) if the black hole is rotating. [1] [1] https://en.wikipedia.org/wiki/Ring_singularity https://en.wikipedia.org/wiki/Ring_singularity
pavelrub 8y ago
The singularity is likely a mathematical artifact of the fact that GR is insufficient to describe black holes. In reality (quantum gravity) they probably do not exist.
- lostmsu 8y ago
  I would not be so sure. Its presence might simply indicate, that black hole's inner volume is infinite.
  - codethief 8y ago
    Could you elaborate on your definition of volume here (are you talking about spatial volume or spacetime volume?) and how the curvature going to infinity at the singularity should imply its infiniteness? My thought process here is the following: The inside of an (eternal) black hole carries four (Schwarzschild) coordinates t, r, theta, phi – r now being timelike and confined to the interval (0, 2M) and t now being spacelike and being any real number. That is, depending on when (at what time t) you cross the event horizon, you end up at a different point in space. The singularity at r=0 is then a point in your future which, like your own death, you cannot actually see but which you will nevertheless hit in finite proper time. So in this sense I'd say the volume is very finite (if we disregard the (trivially unbounded) spacelike coordinate t which, as mentioned before, simply corresponds to the time of entering the BH).
    - codethief 8y ago
      I should add: 1. In the interior of the BH, the determinant of the metric is bounded since the Schwarzschild factors in the metric cancel out. So the volume measure doesn't do anything crazy as one gets closer to the singularity and boundedness of coordinates implies boundedness of the volume. Again, I'm disregarding the spacelike t coordinate because to me the relevant fact is that all matter reaches the singularity in finite proper time, so while we could theoretically stack lots of (actually, an infinite amount of) (massless) cubes inside a black hole, they would soon all get crushed. 2. Of course the situation is slightly different if we're talking about a growing black hole whose mass (and, therefore, radius) increases as we throw matter into it.

SpeakMouthWords 8y ago

1. Yes 2. Basically 3. No 4. No

deleted 8y ago

[deleted]

oppositelock 8y ago

1. Yes, but it's also up for debate, since it's also known that the information content of a black hole is proportional to its surface area, so 2D. 2. The event horizon is spherical. Mathematically we treat it as a point. Nobody knows. 3. It's a gravity well, so everything falls towards it like it does towards the earth. Since it's the center of a galaxy, and galaxies form a 2D spin plane, most matter will be circling it, like our solar system circling the sun, so most matter will come from that planar distribution. We will never see anything fall into a black hole, as in our space-time, this would happen at infinite time. As things get closer, they red shift from our frame of reference due to time dilation, until the light frequencies are so low that we can no longer detect them

deleted 8y ago
[deleted]

rtkwe 8y ago

The stretchy sheet of space time illustration is just a simplified visualization space is 3 dimensional so the warping is 3D. The stretchy sheet visual is used a lot because showing a warped 3D grid to be more accurate is a lot harder and a lot less clear and illustrative. Trying to show a 3D grid doesn't even fully capture the situation because it doesn't show how the passage of time gets distorted as well.

JimBrimble35 8y ago

Let's start a movement similar to flat Earth, but instead it's Spherical Black Hole. I refuse to believe that a black hole is anything but a sphere no matter what evidence I'm shown.

beat 8y ago

Is an image of a sphere printed on paper three dimensional? Think about that for a moment, and you'll see the problem. I am not a physicist, but from my lay understanding, a black hole (and all other forms of matter) exists in a four-dimensional space-time form that we can experience directly, plus a number of higher dimensions that we can only extrapolate, and observe indirectly via experiment (kind of how a picture of a sphere is not a sphere due to a missing dimension, but you can still tell it's a sphere based on other characteristics). The exact number of higher dimensions is the realm of string theory, and could be 10, 11, 26, or something else. The singularity of the black hole is one-dimensional, I think (I could be wrong, I'm often wrong). The event horizon is... funny. The outside of the event horizon is in four-dimensional space-time and is more or less "spherical". The inside is a land of theory and debate, because by definition we can't directly observe it from our space-time. Do space and time even exist inside the event horizon? I dunno, ask someone who knows what they're talking about. The best I can do is an analogy. Imagine it's the surface of the ocean. Above the surface, you're in air. Below the surface, you're in water.