Timeline for Intuitively, why do attempts to delay hitting a black hole singularity cause you to reach it faster?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2018 at 2:24 | comment | added | safesphere | @tparker May be I'll post an answer later with more details, but in a nutshell, the radial direction $r$ is the coordinate time. If you move only radially, then you move only in time. There is only one way to do this and it is to be stationary in space along the $t$ coordinate. Also, moving inside in space along $t$ does not imply the angular momentum. Keep in mind that the geometry inside is not a sphere with a singularity in the center. There is no center and no singularity either before or "after" you hit it. The time when you hit it is defined only by the metric and your geodesic. | |
| Sep 3, 2018 at 0:53 | comment | added | tparker | @safesphere The nature of the singularity is important for understanding why the naive argument that you can't extend your proper time by firing rockets is wrong. It does not directly give the correct argument. I have no idea what you mean that "a free falling observer is ... not along the radius"; the paper only considers purely radial motion with no angular momentum. | |
| Sep 2, 2018 at 22:44 | comment | added | safesphere | @tparker How does it relate to this question what the singularity is? You spend your lifetime inside while moving through the spacetime clearly defined by the metric. The metric is clear that the longest proper time is straight along the radius and that the proper time of a free falling observer is shorter and thus is not along the radius, unless the fall starts from hovering at the horizon. (I see the moderators have deleted my original time dilation comment.) | |
| Sep 2, 2018 at 18:21 | comment | added | tparker | @knzhou FWIW, Ben Crowell's great answer here makes it clear that the singularity is definitely not a hypersurface, and while there are certain senses in which it's "like" a hypersurface, there are other senses in which it isn't. | |
| Sep 2, 2018 at 6:23 | comment | added | knzhou | @tparker Well, I don’t know any of those mathematical niceties, but I don’t see how the answer to this concrete computational question would change if we replaced “the singularity” with “the surface $r = \epsilon$”, since the change in the lifetime would then be arbitrarily small. Then there are no mathematical issues. | |
| Sep 2, 2018 at 4:45 | comment | added | tparker | @knzhou Could you elaborate on your claim that the singularity is "an entire hypersurface"? As discussed here and here, a singularity isn't a submanifold of spacetime, so you need to be very careful in defining its topology, dimensionality, and causal structure. | |
| Sep 1, 2018 at 22:48 | comment | added | Dale | @J. Murray you are correct that the singularity is more like a moment in time, that is why you cannot avoid it. Firing rocket engines will not move you away from Thursday, but it can change your proper time. | |
| Sep 1, 2018 at 22:24 | comment | added | J. Murray | @knzhou Thanks! That - along with the paper linked by Dale - provides a very clear clarification. | |
| Sep 1, 2018 at 22:17 | comment | added | tparker | This is certainly true, but I was looking for a more precise picture of what happens when you fire your jetpack. | |
| Sep 1, 2018 at 20:37 | comment | added | knzhou | That’s not quite right, because the singularity is not a point in spacetime. It’s an entire hypersurface, and you can extend your life by adjusting where you hit this hypersurface. | |
| Sep 1, 2018 at 19:00 | history | answered | J. Murray | CC BY-SA 4.0 |