# B Do black holes have a world line?

#### tionis

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I'm referring to the black hole itself, not some object falling in it.Thanks.

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#### Orodruin

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I would not call it a world line. It is a region of space-time, not a single line.

#### tionis

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So the answer is no, then? Black holes do not have a world line?

#### martinbn

The question is misguided. A planet doesn't have a world line. It has a world tube. Same for a black hole, but you have to be careful what you call a black hole. If you refer to the whole space-time region, then the question is meaningless. If you refer to a space-like section, then it has a whole family of world lines.

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#### jedishrfu

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I think the point of the OP's question is the confusion of things dropping into a black hole where worldlines terminate as discussed at length in books and articles on the subject VERSUS the black hole moving through spacetime itself on its way to gobble up more matter or to shrink and evaporate away.

As an aside. sometimes spacetime diagrams with the appropriate coordinate system can help:

https://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates

#### Nugatory

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As an aside. sometimes spacetime diagrams with the appropriate coordinate system can help:
https://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates
Yep - looking at the diagram it is clear that the black hole is a region of spacetime that cannot be described as either a worldline or a worldtube. Those concepts are only useful for objects moving on timelike paths through spacetime, whereas the blac hole is a more complicated thing: event horizon is a lightlike surface, singularity is in the future of all infalling worldlines.

#### tionis

Gold Member
Hawking said horizons probably don't exist. If that is found to be the case, are astrophysical black holes going to be assigned a worldtube, a worldline, or neither?

#### PeterDonis

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looking at the diagram it is clear that the black hole is a region of spacetime that cannot be described as either a worldline or a worldtube.
Not if we insist on looking at the entire spacetime geometry, true. But for many purposes we can use an approximation, which works something like this: pick a "tube" of timelike worldlines that are all at some constant radial coordinate $r$ which is outside the hole's horizon. If we don't care about what happens to things that fall into the hole--we only care about how things look far away from the hole--then we can treat the hole as an ordinary object of the same mass that is confined within the "tube" we have picked out, and the "tube" itself is just the surface of the "world tube" of this ordinary object. For all events outside the tube, this works fine.

#### PeterDonis

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Hawking said horizons probably don't exist. If that is found to be the case, are astrophysical black holes going to be assigned a worldtube, a worldline, or neither?
In the models Hawking is talking about, where quantum effects prevent an actual event horizon from forming, then you can still use the "tube" approximation I described in my previous post. The difference is that, instead of an event horizon and singularity being inside the tube, there will be whatever quantum effects prevent them from forming. These quantum effects are still pretty counterintuitive, and it is possible that a spacetime description would not work everywhere inside the tube (that depends on what kind of quantum gravity theory ultimately turns out to work). So the answer to your question could still be "a worldtube" or "neither".

"Do black holes have a world line?"

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