How do you explain the observed fact that “black hole” objects move?

As per Newton objects with mass attract each other, and per Einstein this is further explained by saying that mass warps space-time. So a massive object makes a "dent" into space-time, a gravity well. I have taken to visualizing this as placing a object on a rubber sheet and the resulting dent, being the gravity field. So obviously placing two objects on the sheet not to far from each other will make the dents overlap, and the object will roll towards each other. BUT for a BLACKHOLE, this is not a dent. It's a cut or rupture in the rubber sheet. Furthermore, space-time is constantly falling INTO the blackhole, and everything else that exists in space-time, including light. So a blackhole is not just a super-massive object, it's really a hole, and how can a hole move? How does it react to the gravity pull of a nearby object, when everything just falls thru it? Thanks!

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It can move because space-time can move. – Raskolnikov Jan 2 '11 at 21:31
i understand, that, for example amassive object like earth attracts space-dust, meteorites and ? and grows in mass every year by many tons. but tho earth gets heavier, it grows in diameter too. but a blackhole actually "attracts" space-time. for a lack of better words, it doesn't just dent, or ripple space-time but consumes it. not just light and meteorits and space-dust that follow a bent or flat space-time trajectory, but the ... "trajectory" itself? – freeside Jan 2 '11 at 22:02
The rubber sheet analogy pretty much breaks down when you talk about a blackhole. – Malabarba Jan 3 '11 at 0:31

2 Answers

Your mental picture is pretty correct except for the part "space-time is falling into the blackhole". This is completely wrong. Space-time is not falling anywhere. Consider Schwarzschild's solution. This one is static. So it's obvious that nothing happens with space-time at all, it just sits there.

In fact, you wouldn't be able to distinguish the black hole from an usual object of the same mass just by its gravitational effects on other distant objects alone. For objects that are far away from the BH the good old Newtonian limit will apply and it will attract them as described by Newton's gravitational law. In particular, it will attract another BH.

The picture you had in mind about the attraction of two objects as dents in rubber sheet that get closer is correct. This continues to hold even with black holes except that in this case it is not matter that bends the space-time but instead it's a self-sustaining space-time configuration. So a BH can in fact be thought as a special form of matter. Also, never mind that the sheet is ruptured at the singularity because on the outside of the horizon the space-time is perfectly regular and the inside of the horizon is causally disconnected from outside observers anyway (meaning that black hole is indeed black).

Einstein's equations will tell you how this curved space-time, which describes e.g. two (or more) black holes, will evolve into the future. Besides the usual Newtonian scattering you'll get relativistic corrections for their motion, you'll get gravitational waves flying away and other effects. E.g. the two black holes could join into one bigger hole.

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I think in the second paragraph you mean to say you wouldn't be able to tell it's distortion of space-time. Black Holes are distinguishable in other ways, of course. – PearsonArtPhoto Jan 2 '11 at 23:36
@pearson: correct. I'll edit that part to make it clearer. – Marek Jan 2 '11 at 23:39
There's nothing wrong with the mental picture of "space-time is falling into the blackhole". The Schwarzschild geometry has the Gullstrand-Painlevé chart, which has as a time coordinate the proper time of an observer freefalling from rest at infinity and completely Euclidean constant-time hyperslices. In the frame field of such observers, space is flowing into the singularity. The Kerr-Newman geometry has a corresponding form (the Doran chart). – Stan Liou Jan 18 '11 at 6:12
@Stan: space-time is static so by the very definition it's not only not falling anywhere but also not moving at all. Of course, it's possible to foliate it in different non-stationary ways but then you are talking just about space, not space-time ;-) – Marek Jan 18 '11 at 8:14
@Marek: the spacetime is sort-of static. It is "t" independent, but t stops being a timelike coordinate at the horizon, so the horizon is not static exactly, but null-static, while the interior is not static at all. The violation of static condition at the horizon allows for particle production. – Ron Maimon Aug 20 '11 at 6:24

How do you explain the observed fact that “blackhole” objects move?

$$G_{\mu\nu} = 8\pi T_{\mu\nu}$$

Einstein's equation allows for black holes to move when viewed from an external reference frame. That's all the explanation we need.

What I mean to say is that you're taking the rubber sheet analogy too far. It doesn't explain anything. All it's supposed to do is give you a sense of how coordinates can be distorted around a massive object or any gravity well, like a black hole. It doesn't really work when you want to figure out what's going on at the singularity, because rubber sheets in real life don't have singularities.

A black hole is not literally a "hole" in spacetime; it's just an infinitely deep gravity well. There's really no fundamental qualitative difference between the gravitational field of a black hole and that of a less dense object (they're both described by the Schwarzschild metric); it's just that the black hole happens to be of a high enough density that it prevents light from escaping within a certain surface. Probably a better (though still imperfect) way to relate it to the rubber sheet analogy is to say that a black hole is not a rupture in the sheet, it's just a dent that's deep enough and small enough so that the slope of the sheet exceeds some critical value. (General relativity predicts that whenever matter forms a black hole, it will all fall inward to a central point, creating a singularity, which could be represented in the rubber sheet analogy as a dent which is infinitely deep at a central point.)

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thank you for all the answers. so can i then further ask, if there could exist some sort of object that cannot move? it could have any size, shape, be made -up of any kind of matter, etc. but the only fixed thing is the fact that it cannot change position once created? – freeside Jan 3 '11 at 12:41
No, it's not possible to make an object that cannot move, because relative motion is the only thing that matters. You can't pick out a particular frame as the "real" stationary frame, and put your unmovable object in it. As long as any other object in the universe is capable of motion, your unmovable object will appear to be moving to an observer with the moving object, and will be completely described by the usual physical laws for ordinary moving objects. – Chad Orzel Jan 3 '11 at 13:30
Good answer. But to expand with a fairly reasonable alternative interpretation of the question of immovability, let's interpret it as something like this: is it possible to have a gravitating body that is not itself affected by gravity? In GTR, that's also not possible, because spacetime curvature determines the inertial behavior of matter, but things may be different in alternative theories. An example that's actually not ad hoc to this followup, having the field a rank-2 sym. tensor in flat spacetime gives an inconsistency if a particle is both a source of and respondee to gravity. – Stan Liou Jan 18 '11 at 9:32