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Dr. Christopher S. Baird

Is a black hole a 2D or a 3D object?

Category: Space      Published: July 20, 2022

black hole
Artistic rendering of a black hole. Public Domain Image, source: Christopher S. Baird

A black hole is actually a four-dimensional object. A black hole extends across all four physical dimensions of the universe. The four dimensions that form the background framework of the universe consist of three spatial dimensions and one time dimension. These four dimensions are inseparably connected into one unified framework called spacetime. While it may sound exotic to say that a black hole is a four-dimensional object, the mundane truth is that all physical objects are four-dimensional objects*. For instance, a desk extends a few feet in the x direction (we call this its width), extends a few feet in the y direction (we call this its length), extends a few feet in the z direction (we call this its height), and extends a few years in the t direction (we call this its lifetime). A desk is therefore spread out across many points in each of the three spatial dimensions and across many points in time. The size of the desk in the time dimension extends from the moment that it was built to the present moment and will continue to extend through time until the moment it is destroyed. In this way, the desk is a physical four-dimensional object that fills a four-dimensional volume. The same is true of chairs, apples, kites, asteroids, stars, and all other physical objects.

Calling the time dimension the fourth dimension is more than just a clever use of words. There are profound physical effects that force us to consider time as a dimension attached to the three spatial dimensions. An object that in one reference frame is observed to have a large extent in the length dimension and a small extent in the time dimension will, in another reference frame, be observed to have a small extent in the length dimension and a large extent in the time dimension. In other words, because of relativistic effects such as length contraction and time dilation, how an object fills out its four-dimensional volume depends on the reference frame. Therefore, the time component of spacetime cannot be ignored.

While a black hole is similar to a chair or a tree in that it exists extended across the four physical dimensions of the universe, a black hole is uniquely different for another reason. A black hole consists of spacetime that is so warped that nothing can escape, not even light. In fact, the spacetime of a black hole is so warped that, to a distant observer, spacetime itself is observed to cease to exist at the black hole's event horizon (which can roughly be thought of as the surface of the black hole). To a distant observer, a black hole is literally a hole in the spacetime framework; there is no "inside" of a black hole. All of the black hole's mass and trapped light is observed from far away (if it could be observed) to exist at its event horizon. To a distant observer, nothing exists inside a black hole, not even space or time. If this concept does not sit right with you, then you can think of it as an apparent effect arising from being in a reference frame that is observing the black hole from far away. To an observer very close to the event horizon of a black hole or even inside the event horizon, spacetime does not end at the event horizon and there is indeed an inside to a black hole. The views of both observers are correct, without there being a contradiction, because of the relativistic nature of spacetime.

If a black hole is a four-dimensional object, then what is its shape? A black hole that is not rotating is spherical in shape (i.e., its event horizon is spherical) and extends linearly through the time dimension. You can roughly think of a black hole as a star that traps all of its light, and therefore it seems natural that a black hole is spherical. Furthermore, a black hole that is rotating is very close to being spherical in shape but is slightly flattened along its rotational axis. This shape is called an oblate spheroid. A rotating black hole also extends linearly though the time dimension. Interestingly, all real black holes are rotating because they form from giant rotating clouds of matter. However, black holes that are rotating very slowly can be approximated to be not rotating. Note that if a black hole is changing (e.g., matter is falling non-uniformly into the black hole), then things get more complicated and its shape is not exactly spherical, but these basic ideas still apply to a good approximation.

In summary, a black hole is a four-dimensional object with a spherical or nearly spherical shape that extends linearly through time.

*Note that fundamental particles such as electrons act in certain ways like point particles, meaning that they act like they have exactly zero width, zero length, zero height, and extend across many points in time. You could therefore argue that fundamental particles are physical one-dimensional objects. However, fundamental particles are quantum particles and therefore simple concepts such as size and volume do not have direct, literal, physical meaning. An electron (when acting perfectly as a particle) indeed does not have a fixed, definite, non-zero physical radius. In fact, in many experiments, an electron acts externally as if it had a radius of exactly zero. However, an electron also has a finite mass and does not have an infinite mass density, which implies that it cannot have a fixed radius of exactly zero. Furthermore, if all the mass of an electron were truly packed into an infinitely small volume, it would become a black hole, which it does not. This apparent contradiction is resolved by the fact that fundamental quantum particles simply do not have a definite radius at all. Quantum particles are not definite, hard, fixed balls of matter and/or energy. Rather, quantum particles are fluctuating, ambiguous, smeared-out probability clouds of matter and/or energy. Fundamental particles do not have zero radius in a fixed, definite, classical sense and therefore are ultimately four-dimensional objects.

Topics: astronomy, black hole, dimension, energy, gravity, mass, relativity, spacetime