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If I travelled near a black hole, my time would progress slower relative to someone on Earth. This is clear enough. However, what if we sent a probe with a camera to a black hole? When we watch the screen, would we see time through the camera's perspective — that is, would the Universe appear to progress faster as the probe got closer and closer to the black hole?

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If I travelled near a black hole, my time would progress slower relative to someone on Earth. This is clear enough.

Yes, no problem with the gravitational time dilation.

However, what if we sent a probe with a camera to a black hole? When we watch the screen, would we see time through the camera's perspective — that is, would the Universe appear to progress faster as the probe got closer and closer to the black hole?

No. We'd see the universe progressing normally, because we aren't subject to that gravitational time dilation. (I presume we're at a safe distance). Let's suppose it was a TV camera that took a picture 25 times a second and sent it back to us, adequately catering for redshift. The camera starts off taking 25 pictures a second as measured by us. But after a while we notice we're only getting 24 pictures a second, then 23, and so on. We see events in the wider universe progressing at their normal rate, but eventually the movie starts getting jerky as the frame-rate reduces. In the end the frame-rate reduces to zero, and that's the end of the show.

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    $\begingroup$ @Nico : thanks. I'm not sure the quality is all that great myself, but nevermind. If it delivers a correct answer in a succinct clear simple fashion, it'll do. Because there's this saying attributed to Einstein "if you cannot explain it to your grandmother, you do not understand it yourself", IMHO it's important to be able to explain something, it helps your own understanding. Provided it's the correct explanation of course! $\endgroup$ – John Duffield Dec 30 '15 at 10:48
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    $\begingroup$ @JohnDuffield Of course it wouldn't reach the event horizon. But the answer would have been far less interesting if we were speaking about things that can actually happen :p $\endgroup$ – Nico Dec 31 '15 at 11:52
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    $\begingroup$ @Nico : actually, I think it's more interesting to talk about why that camera doesn't make it to the event horizon. See stuff like this. It's a black hole "firewall" proposed in 2001 by Friedwardt Winterberg. See an old version of the Wikipedia firewall article. It isn't in the new version, there's some kind of priority dispute going on. $\endgroup$ – John Duffield Dec 31 '15 at 12:22
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    $\begingroup$ @JohnDuffield this is quite complex for the French non-physicist I am. My assumption about throwing a camera in a black hole is that the gravity variations would just destroy the camera. I remember reading about "spaghetification"... $\endgroup$ – Nico Dec 31 '15 at 12:26
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    $\begingroup$ @Nico : I don't think it's complex at all. Not when you understand it. Why don't you ask a question about it? And I'll see if I can explain it to my grandmother. The question could refer to this one and say If I dropped a TV camera into a black hole, will it be destroyed before it reaches the event horizon, and if so, why? $\endgroup$ – John Duffield Dec 31 '15 at 12:33
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For simplicity, let's say that the black hole is isolated and non-rotating (and uncharged), so that the situation is described by the comparatively simple Schwarzschild spacetime. Let's also suppose that the camera free-falls radially into the black hole.

What is the camera looking at? Suppose it is looking at some stationary object that does something with a known frequency. Your question is basically how at what frequency it will be observed on the video feed emitted by the camera.

Without loss of generality, we can suppose that the camera is looking at us, and that we're shining a laser beam at it: the 'doing something at a known frequency' would be the oscillations in the electromagnetic wave of the laser beam. We can do this because time dilation affects every physical process, so we might as well pick one that is more convenient to think about.

At this point, it is straightforward why the camera feed will not show any time dilation: being equivalent to a reflected laser beam, the gravitational blueshift when going inward will be cancelled by the gravitational redshift going outward.

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