How do black holes move if they are just regions in spacetime?

If black holes are just regions of spacetime, how can black holes even move? When matter moves through spacetime, it bends the spacetime around it, but if black holes are just regions of spacetime, how can a region in spacetime bend other regions of spacetime? If a black hole has no mass, how can it bend the spacetime around it, so it can remain a black hole, if there is no matter to continuously bend it?

• Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. Commented May 29 at 16:57

Black holes are not just regions of space time. There was once a star there. According to the law of conservation of mass and energy, the star is still there. The star has spin and angular momentum. According to the law of conservation of angular momentum, the star inside the black hole and the black hole still have that angular momentum. If you crush a paper ball smaller, it still has the same mass. If you crush a paper ball infinitely small, it will still have the same mass. Any object falling into the black hole will increase the black hole's mass and alter it's speed and direction it is moving. When the black hole pulls a star closer to it, the black hole moves closer to that star. The ratio of how much the black hole moves toward the other star to how much the other star moves towards the black hole can be calculated using the mass of the black hole and the mass of the other star. When calculating the orbital path of a black hole, think of it as a very massive star. You will often hear black holes as described in terms of their mass. This is how that mass is calculated.

• Such a shame that this answer is not voted much higher yet. If black holes are just regions of spacetime in OP is clearly wrong. Black holes generally have mass, charge and angular momentum (not to speak of the information conundrum which I'm not qualified to talk about), and from sufficiently far away behave just like any other star of similar mass, charge and momentum. This is the fact that should be explained to OP (as this answer does), but all higher-voted questions seem to run with OP's statement and explain things in more or less complicated ways...
– AnoE
Commented May 28 at 14:02
• Agreed. In fact there’s research to suggest that not all (or even no) black holes are “just” a vacuum solution to the EFE, and that singularities can’t exist at all. The matter continues to exist even after it collapses into its final state, and retains momentum/velocity/mass/charge/angular speed/etc. Commented May 28 at 17:39
• OP : "the slope of spacetime is infinite at it's center" - citation needed. Just because you need light to see something doesn't mean it's not there. Commented May 29 at 8:11

Remember, we are talking about spacetime, not just space. In space by itself, the black hole is a ball-shaped region. But it extends far into the past and future, so it's more like a kind of tube.

So imagine a black hole, with the mass of a star, that's orbiting the center of our galaxy. If you pretend the galaxy is just a two-dimensional spiral, and ignore the third spatial dimension, then you can imagine a 3-dimensional spacetime, with time as the 3rd dimension. Then the black hole is a corkscrew-shaped region of spacetime spiraling around the center of the galaxy.

Everything in spacetime is a kind of tube, or bundle of lines, going from the past to the future. Relative motion is just one line being tilted relative to another. In the past, thing A was to the left of thing B, and, in the future, it's on the right.

• I think the weird implication is that if black holes move, then other regions of space must also move. Are there a bunch of empty regions of space also orbiting the center of the galaxy? Movement is usually imagined as something you do in space, not what the space itself does. Commented May 28 at 11:59
• You could also think of it as the singularity is moving through spacetime. Empty space doesn't move but the mass of the blackhole moves. Commented May 28 at 13:40
• @DanielDarabos - Remember, the black whole is a region of spacetime with special properties. If you like, you can think of the high curvature as moving through space kind of like (and this is only an analogy) a wrinkle that you can move around in a piece of fabric but can't quite get flat. Commented May 28 at 17:00
• That doesn't really answer the question. It just rephrases it in different language. Because I now I can simply ask about the shape of this region: why it changes from time slice to slice? Btw this reasoning implies that everything moves, because everything is a region in 4d. But that's clearly false, I can just pick straight line in 4d parallel to time axis. The difference is that the black hole is not just a region of spacetime. Commented May 29 at 7:28

Adding a picture to illustrate what some other answers here already have said. Suppose you throw a ball straight up into the air, and then it falls back down. You've probably seen a picture like this, representing the flight of the ball:

That picture is a spacetime diagram. It's a simplified spacetime, because it's only two-dimensional, and it only depicts one dimension of space, but it is a spacetime diagram. It represents both space and time as different axes in a mathematical space.

Mark Foskey said

Remember, we are talking about spacetime, not just space. In space by itself, the black hole is a ball-shaped region. But it extends far into the past and future, so it's more like a kind of tube.

In my diagram, the downward facing parabola is the ball. It's not the ball in some particular instant, it's the ball in every moment during the whole experiment. In a full, 4D spacetime, that parabola would be the "tube" that Mark talked about

S.G. said,

It might sound strange but nothing really moves in spacetime.

My picture represents the motion of the ball, but nothing in the picture itself moves. The picture just is what it is—a static representation of how the ball moved during the experiment.

The picture is a "spacetime." Nothing moves in the picture, and nothing moves in spacetime.

You said,

If black holes are just regions of spacetime...how can black holes even move?

YOU are just a region of spacetime. In spacetime, you are one of those "tubes" that Mark Foskey talked about. When you move about in space, that's represented by bends in your non-moving spacetime tube.

• But if I draw a flat line then the ball is stationary (at least in height dimension). In other words we now just rephrased the question, and are asking about changes between time slices. You've just used different language, which has different "movement" definition, no? Commented May 29 at 8:06
• @freakish, I'm sorry, but I do not understand what you are trying to say. If you are trying to say that it is possible to draw a spacetime diagram that represents an object whose velocity in the chosen coordinate system is zero, then yes. I agree. That is entirely possible. If you are trying to say that I have defined the word "movement" to mean something different from what most people mean, then please explain your position in more detail. I think that my idea of what "movement" means is entirely conventional. Commented May 29 at 14:20
• I'm saying that you didn't answer the "why black holes move" question. That's not true that "nothing moves in the spacetime picture". Movement is defined as change of spatial coordinates with respect to time. It doesn't matter that you switched view to 4d. The "not moving in 2d ball" analog is incorrect, because we indeed can draw stationary ball: the constant, flat line. Everything else moves. Including the ball on your picture. So the OP's question can be rephrased as: why black holes don't have constant flat drawing in 4d? Or at least that's how I see it. Commented May 29 at 15:00
• @freakish, I totally agree with you that, "Movement is defined as change of spatial coordinates with respect to time," but I think you don't quite get what "spacetime" means. I think you should stare at the diagram in my answer, which is a kind of spacetime picture, and I think you should keep watching it until you see the spatial coordinates of the parabolic curve change over time. When you see that happen, come back here and tell me about it, and we can use your observation to invigorate our discussion about whether or not things can "move in the spacetime picture." Commented May 29 at 15:29
• @freakish, Exactly! That's what people mean when they say, "Nothing moves in spacetime." That wouldn't even make sense. And, when they talk about a "region in spacetime," they are talking about something that does not move because, "nothing moves in spacetime." We use spacetime as a representation of motion, but nothing in that representation moves. Commented May 29 at 17:43

How do black holes move if they are just regions in spacetime?

It might sound strange but nothing really moves in spacetime. Say, for example, we have two black holes orbiting each other in the frame of reference of an observer far away from them. Then, if (hypothetically assuming) I can write the spacetime solution for such a configuration of black holes, then the solution will tell me about the entire behavior of this system, i.e., encompassing all of space and all of time. In such a sense, there is no scope for any motion. Motion only happens when we choose an observer who decomposes this spacetime into hyperslices of co-dimension 1.

That being said, w.r.t. to an external observer, the mass that forms the black hole only asymptotically reaches the black hole horizon but never crosses it. So, you can assume that it is this mass that is in motion.

If black holes are just regions in spacetime, how can it bend the spacetime around it

Black holes are regions in spacetime that are categorized according to the curvature they produce, i.e., if there is no curvature, then there is no black hole. Once matter disappears for the external observer, it leaves its mark on the region around it in the form of this curvature. It is this curvature that bends spacetime. Also, the whole idea that black holes are empty from within, is from classical general relativity. It is likely that this may not be true.

• Once matter disappears behind the event horizon” - This never happens for as long as the universe exists. Secondly, if this hypothetically happens, it would cause the black hole to disappear, because nothing inside can have any observable effect outside. In other words, the inside is in the future relative to the outside. Tomorrow’s earthquake cannot shake your house today. Commented May 27 at 7:20
• I mean, it disappears for the external observer, and only the curvature remains.
– S.G
Commented May 27 at 7:39

If black holes are just regions in spacetime, how can it bend the spacetime around it, so it can remain a black hole, if there is no matter to continuously bend it?

There is no matter, but there is gravity. The nonlinearities in Einstein equations imply that the presence of curvature leads to more curvature. Some people like to interpret this as thinking that the gravitational energy-momentum also bends spacetime.

If black holes are just regions of spacetime, where the slope of spacetime is infinite at it's center, how can black holes even move? When matter moves through spacetime, it bends the spacetime around it, but if black holes are just regions of spacetime, how can a region in spacetime bend other regions of spacetime?

As I said, curvature leads to curvature due to the nonlinear features of Einstein's equations. Furthermore, to understand how this can have motion, I think it is interesting to picture waves in water: the disturbances on the top of the water can move around, and similarly the disturbances in the curvature of spacetime can move around.

• Are you sure there's no matter? Even the Schwarzschild metric has a delta function stress-energy tensor. Commented May 27 at 2:27
• Yes, matter does not disappear, otherwise where does the mass & energy come from when they evaporate? Commented May 27 at 3:01
• This answer is incorrect on multiple points. (1) “There is no matter” - In physically existing astrophysical black holes, energy is conserved. Thus all mass/energy of a collapsing star remains intact in the black hole. A vacuum solution requires a zero stress energy tensor. This simply means all energy must be kinetic, not zero. (2) The Schwarzschild solution is valid at an arbitrarily large radius where non-linearities are negligible. The curvature is due to the boundary conditions and would be there even in the linear gravity. Non-linearities have nothing to do with this. Commented May 27 at 7:07
• (3) “the gravitational energy-momentum also bends spacetime” - It doesn’t. The equation of a black hole is $R_{ab}=0$ - Nothing bends spacetime. It just follows the boundary conditions of spherical symmetry Commented May 27 at 7:08
• @safesphere I originally responded by saying the Schwarzschild metric having a delta function singularity is well-known, but I might be wrong on that. It's still a straightforward calculation: regulate the factors of $1/r$ in the Schwarzschild metric any way you choose (I like $\frac{1}{\sqrt{r^2 + \eta^2}}$) and calculate the stress-energy tensor of the regulated metric. The stress-energy tensor of the regulated metric ends up being proportional to a nascent delta function that becomes a delta function in the limit as $\eta$ to zero. Commented May 27 at 7:44

First of all, a point to note is that a black hole is not a "body" in of itself. Black holes are just solutions to point masses in general relativity, analogous to point masses in newtonian gravity. However in relativity, these point masses produce a boundary called the horizon, where the gravitational acceleration is so huge that not even light can't escape. This is for this reason, the point mass seems to create "black" region, that we call a black hole. Analogous to how point masses can move in Newton's theory of gravity, point masses (and hence black holes) can move in general relativity.

• Black holes are just solutions to point masses” - This doesn’t mean what you imply. The original Schwarzschild’s paper was titled “On the gravitational field of a mass point…”. However in this paper he describes the horizon as “the mass point”, because the spatial radius of the horizon is indeed zero for any black hole. What you imply by “the mass point” evidently is the singularity inside the horizon, which is wrong, because (1) the singularity is an infinitely long line, not a point, and (2) it has no mass. Commented May 27 at 7:35
• Frankly, I have not read about the actual paper written by Schwarchild. However, I have read many books about the his metric. What I learnt from all this is that it is true that there is a singularity at the horizon, but this singularity is just a coordinate artifact. It is because of the bad choice of coordinates. There is only one "real" singularity, which is at r = 0. Please read the comment after this comment too. Commented May 27 at 12:51
• I think what you mean by "the spatial radius of horizon is indeed zero" is that you are talking about a particular coordinate transformation, such as the kruskal seekers coordinates, in which the space-like coordinate, or the space-like "radius" is 0 at the horizon and it is imaginary beyond it. It is a very popular coordinate transformation to study black holes. However, the singularity is where the metric elements go to infinity. In kruskal szekers coordinates, it is at an imaginary point of the radius, which is dependent upon the Schwarz radius of the black hole. Commented May 27 at 12:55
• By spatial distance I mean the spacelike distance (the distance measured in meters, as opposed to a time period measured in seconds). By spatial radius I mean the spacelike radial distance from the horizon to the origin. It is defined in the Schwarzschild paper as $r\equiv\sqrt{x^2+y^2+z^2}$ - In the Schwarzschild coordinates this distance is zero. Once you get to the horizon, you are already at the place where the singularity will happen in the future. All you need to do is to wait. The radial interval between the horizon and the singularity is a period of time, not a distance in space. Commented May 27 at 17:23

The renowned John Archibald Wheeler (Princeton) once (the 1960's) said

"Matter tells space-time how to curve, space-time tells matter how to move"

This expresses the intimate, "nonlinear", relationship between matter and space-time curvature. Indeed, it merely repeats the relationship announced by Einstein in his 1917 Field Equations:

$$R_{ik} - \frac{1}{2} R g_{ik} = \kappa T_{ik}$$

or, in English

$$Geometry = Matter$$

This hopefully adds to a mental visualisation of what those equations are about, as opposed to how they work. This is, in a sense, an answer to the question posed by the OP, though admittedly not description of how the phenomenon works. A small digression into the Wheeler's world of Geometrodyanmics might help.

Wheeler saw space-time and matter as inseparable and coined the name "Geometrodynamics" for this relationship. Wheeler went as far as to say "what is matter if not space-time geometry?" adding that one might wonder what matter is made from if not geometry! This thinking leads to Wheeler's list of what geometrodynamics might achieve:

1. gravitation without gravitation
2. electromagnetism without electromagnetism
3. charge without charge
4. mass without mass.

It is not clear that others would necessarily follow him as far as that, but it should be noted that the concept was rapidly generalised to "quantum geometrodynamics" by Bryce deWitt with what is called the "Wheeler-deWitt equation". This was Wheeler's route towards bringing together the classical force of gravity (ie. geometry!) and quantum mechanics!

There is a video on Youtube of a lecture "Geometrodynamics - The Nonlinear Dynamics of Curved Spacetime" given by Kip Thorne at the International Centre for Theoretical Physics in Trieste:

The lecture starts 7 minutes into the video and the few minutes thereafter describe Geometrodynamics in an intelligible way. Following that there is a fine explanation of the dynamics of black holes and gravitational waves which touches on some of the issues raised in other answers. It is a great talk by the person who is arguably one of the world's foremost experts on this!

Kip Thorne was a PhD student of John Wheeler and went on to win the Physics Nobel Prize for the discovery of gravitational waves using the LIGO detector. I might add in passing that another Nobel prize winner, Richard Feynman, was also a PhD student of John Wheeler. Wheeler was widely regarded as one of the "great teachers" of physics, possibly the greatest.

The textbook "Gravitation" written by Misner, Thorne and Wheeler could have been entitled "Geometrodyanmics". This is one of the great textbooks in science. I would describe the level as "advanced", but a must-read for all those who propose to work on GR.

The black hole is a region around a singularity. It's the singularity that creates the "gravity well" around it that we call a "black hole" and the singularity itself can move like any other object in space.

For example: two black holes can orbit (move around) each other in a binary system. They can also collide and merge, like possibly PKS 1302-102.

In very simple terms, you can replace a black-hole with a "star" of the same size and mass and how it behaves and affects its environment are not going to be that different from how a star would. It's just once you enter the black hole's event horizon (our star's surface) that physics starts becoming unusual.

Now as to how the movement of the singularity occurs in the extremely distorted space-time and gravity conditions it exists in, that's a moot question because the known laws of physics break in that scenario, which is why we call it a singularity to begin with. No one can currently answer that.

A black hole has all the properties of an object with mass. has gravitational influence on other objects, it responds to the gravitational field of other objects (e.g a bigger black hole) and accelerates towards them. it has linear and angular momentum and kinetic kinetic energy. There is no known experimental proof that a black hole is massless. There is not even a thought experiment that suggests a black hole has no mass. It is not clear why the elitist members feel so strongly that black hole is massless. Where does the mass that forms a black hole go? Suggestions that the mass is spewed out into another parallel universe where it looks like a white hole are bit fanciful at best.

In relativity mass and energy are interchangeable and it might well be that interior of the black hole is pure energy that has a mass equivalent. One uncomfortable result of GR is that all the mass is compressed to a point of infinite density at the centre. This indicates a possible limitation of GR and scientists have been trying to come up with an alternative quantum description of gravity that can cope with the extreme curvature inside a black hole.

how can black holes even move?

Imagine yourself in a powerful ship hovering outside a black hole (BH) event horizon. You start to accelerate in a particular direction then get to a constant velocity and based on observations safely conclude you are moving away from the black hole. But the point about relativity is that there are no privileged frames. That is, "you travelling away from the BH" is the same as "BH is travelling away from you". In this sense, black holes do move (note how the same is true that if you move towards one, it moves toward you).

There is no absolute frame (ignore CMBR argument for now) from which all motion in the universe is relative too, as your question suggests. Object "A" moving away (or toward) another object "B" is equivalent to object "B" moving away (or toward) object "A".

• "In this sense, black holes do move." I think this works for a single black hole in the Universe, but if you have at least two black holes they will move toward each other, and a mere change of reference can't get rid of this effect Commented May 27 at 0:37
• E pur si muove, as Galileo very well stated. Commented May 27 at 3:02
• @josephh I'm not sure I understand how your edit helps. Black holes can't move by your reference frame trick because more than one black hole exists. Not to mention the fact that presumably the black holes accelerate to start moving Commented May 28 at 17:10
• @RichardTingle If you can find a frame in which you are moving away, then the BH moves away. The key is that the first case is no different from the first because one inertial frame is no more privileged than another. Commented May 28 at 20:24
• Right, but how does that help if you have many black holes, all moving independently. There is no one reference frame in which none of the black holes are moving. So the change of reference frame doesn't help in general (even if you can find special cases where it might - they are coincidences) Commented May 28 at 21:31