Does an object in a stable orbit around a black hole experience time dilation relative to a region far away?

[Shermann]

This is a quantum physics question I've been wrestling with. An object which is accelerating into the black hole clearly would experience the time dilation. However, in orbit, the object would experience centripetal acceleration from the continual changes in direction which would cancel out exactly the accelerative pull into the black hole. So, while the object would be in an area of significantly curved spacetime, how can there be this time dilation with no net acceleration?

If the answer is no, then that whole Gargantua/Miller planet scene in Interstellar is bogus.

[Stardust Mirror]

1. I thought this was a question about Trump lawyers nt

[Shermann]

2. Yeah they definitely are looking for ways to slow down time!

[marble falls]

3. Planning a little intergalactic trip and want to make it seem longer or shorter?

[Salviati]

4. Yes.

Being in a stronger gravitational field does cause time dilation.

You're correct in that there is a centripetal acceleration that the object has, but it's a common misconception that this is some additional influence on an object that is moving in a circle. Instead, the centripetal force (switching terms slightly) is just the special name we give to the component of the net force that must be present for the object to move along a circular path (as needed by the constantly changing direction, as you've noted). This centripetal force does not cancel the pull from the black hole - it IS the pull from the black hole.

The centripetal force is a role that must be played in order for the object to move on it's circular path, and that role may be played by any force, or combination of forces. In this case, like in any planet's orbit around its star, it's played by the gravitational force. Swing a ball on a string around your head and the role of the centripetal force is played by tension.

[Shermann]

10. Right, but can the effects be canceled out?

Einstein established that gravity and acceleration not only feel the same, but they ARE the same.

Is it not the case that one can cancel out the other when it comes to time dilation?

What if there were two black holes of the same size and the object were positioned exactly between them?

[Salviati]

11. They aren't canceled

In the case of the orbiting object the acceleration is not zero. The object is undergoing a continuous change in its direction, which is an acceleration.

In the case of an object right in between two black holes, those two gravitational forces could cancel out, but if we look at the details of the time dilation between two different points it depends on the difference in gravitational potential, so while the force cancels out, the time dilations would actually combine to get bigger.

The way to visualize it is with the common rubber sheet analogy for thinking about spacetime curved by objects. The gravitational force is represented by the slope of the sheet. The steeper the slope, the stronger the force. If you're a distant observer very far away from an object, the sheet is flat and horizontal.

Time dilation depends on the height of the rubber sheet though, not the slope. The lower the height, the slower a distant observer will see a clock on that object running. At a point midway between two black holes, the sheet may be horizontal, but it will still be at a lower level than a distant observer.

[Shermann]

14. OK so gravitational field strength and gravitational potential are two separate things

The potential can be subtractive, but the field strength is always additive. The field strength affects time dilation, not the potential. I think I've got it!

So the movie is legit!

[Salviati]

16. Right, they're different - but related.

But it works the other way around mostly. The gravitational field can cancel out - because it had a direction to it, and two contributions can point in opposite direction.

The gravitational potential is just a number, and as far as we know so far it seems it must always be negative, so it's always going to combine to give a bigger negative value.

(Though if it could be positive, it would be interesting to see if that would make clocks run faster than compared to a distant observer...)

[Shermann]

22. Oh I got them reversed! Oh well.

So, there's one other issue with the Interstellar scene I'm skeptical of. Miller's planet would have to have been tidally locked. If it's tidally locked, there can't be tidal waves. There are technically tides, but they would be unchanging. Thus, no waves.

[Arne]

5. I feel that time changes when I stand up.

So I say yes.

[sanatanadharma]

6. Does an object ... experience time dilation?

Only if the object partakes of consciousness.

Nothing is conceivable in the absence of 'conscious-existence'. The word "being' has too much baggage and simply means 'existent' anyway.

[Shermann]

7. "Experience" means simply encounter or undergo in this context.

There's nothing metaphysical going on in this thread.

[Backseat Driver]

8. I "googled" this through Duck Duck Go: stable orbits around black holes and time dilution

There's some pretty complex answers at the links to check out to clear up your astrological confusion. Something about Newtonian versus Einstein's GR...Are you Mr. Peabody's boy, Shermann? If so, I would also ask Mr. Peabody concerning the workings of his WABAC (Wavelength Acceleration Bidirectional Asynchronous Controller) machine. If one reverses the mechanisms involved, there might definately be a created "memory hole" fast forward to a reassembed future instead of a WABAC, yes? And you don't want to ask Wiki about a "memory hole," LOL! or me - I barely passed algebra - it's no wonder so many including me have SMH syndrome.

[Shermann]

9. Just for funzies I posed the question to Microsoft Copilot

It sort of hallucinated and actually cited this thread as a reference!

Is there time dilation in a stable orbit around a black hole?

Yes, there is time dilation in a stable orbit around a black hole. According to the theory of general relativity, time slows down near a black hole due to the extremely strong gravitational field of the black hole. This phenomenon is due to the gravity of the black hole curving spacetime in a way that affects all measurements of time and space near the black hole 1.

In fact, the closer you get to a black hole, the stronger the gravitational pull becomes, and the more time slows down. This effect is known as gravitational time dilation 1.

While it is not possible to orbit just above the Schwarzschild radius of a black hole, if an object is in a stable orbit around a black hole, it would experience centripetal acceleration from the continual changes in direction which would cancel out exactly the accelerative pull into the black hole 2.

I hope this helps!

Learn more

1 profoundphysics.com
2 democraticunderground.com

[Salviati]

12. Have to be careful about trusting AI

The last sentence is not true.

The centripetal acceleration and the acceleration due to the black holes gravity do not cancel in a stable circular orbit, they are the same thing. And I don't mean they are equal, I mean there is just one interaction - the acceleration caused by gravity, and it causes the acceleration we can determine from the motion of the object, which we call the centripetal acceleration.

[Shermann]

13. Yeah Copilot got part of that from the OP!

That's actually more fascinating than the black hole thing. It took a question asking if a statement supported a claim and presented it as if it did (after merging in the bit about the Schwarzschild radius). So, it didn't conceptualize that this was a question about a claim which included some conjecture.

I didn't realize generative AI could incorporate new data in such a timely fashion (albeit erroneously).

[Jeebo]

15. What about gravitational tides?

I just glossed quickly through this thread. It's way over my head, frankly, but have y'all ever read Robert L. Forward's novels Dragon's Egg and sequel Starquake? They had to do all kinds of weird things with superdense asteroids and complicated orbital trajectories within a locus of those asteroids with their spacecraft at the center of the locus to compensate for the intense gravitational tides before they could get close enough to that neutron star to study it. It looks to me like an object that close to a black hole would be ripped apart by the tides. Those two novels, incidentally, were as hard to put down as anything I've ever read.

-- Ron

[Salviati]

17. Some really weird stuff happens around black holes - even outside of the event horizon.

For an object orbiting a normal planet/star/other object, the orbiting object needs a net force inwards, to make the centripetal acceleration required to cause the velocity to change direction to follow the circular orbit instead of traveling in a straight line. That net force is provided by gravity, and the orbital speed is the speed at which the orbing object can travel so that the gravitational force provides exactly the right amount of centripetal acceleration for that speed and that orbital distance.

Very close to a black hole (but still outside the event horizon) space is so curved, that what is considered a straight line is now bent in a circle. The path that the orbiting object would want to take, if it had no net force on it, would be in a circle around the black hole. This happens at a radius of 1.5 times the radius of the black hole. Normally, the faster you move around in a circle, the more force you need to keep you on your circular path, but in this case, you don't need any force to keep you on the path. This is a problem, because a normally orbiting object uses the gravitational force to provide that force to keep it in circular motion, but in this case we still have the gravitational force, but we don't need it for the orbit. if you were in a rocket, you'd need to constantly fire your engines inwards, just to balance out the gravitational force, but then you could orbit at any speed without adjusting your engines.

Its even weirder inside this radius. Inside 1.5 times the radius of the black hole, what is considered a straight line is actually curved tighter than a circle. Now the centripetal acceleration actually points outwards instead of inwards. The faster you move around your orbit, the harder you need to fire the engines to keep yourself from curving inwards.

Of course if you were around a smallish black hole, the tidal forces would likely be pretty insane at that point, but around supermassive black holes, the area around the event horizon can be pretty uniform from what I understand.

[Jeebo]

18. Again, pardon my ignorance, but ...

... you mentioned the radius of a black hole twice. I've always understood the radius of a black hole to be ... zero! That's because it's a point source of intense gravity, which is why it's sometimes called a gravitational singularity. Another of the really weird things about black holes. Maybe you were talking about the radius of the black hole's event horizon? As I said, all this stuff is way over my head. I know a little about it just from the perspective of a fan of science fiction, and of science popularizers like Carl Sagan and Isaac Asimov. It sounds like you could be another Sagan or Asimov, if you want to explore your option. Thanks for trying to educate me.

-- Ron

[Salviati]

20. By radius here...

.. yes, I mean it's Schwartzchild radius, the radius of the event horizon. That's the point of no return, where once you're closer than that, you can't get back out of the black hole.

I teach physics, and have a masters in it, so I'm not an expert at black hole physics by any stretch, but definitely know more than the average person about it.

[Jeebo]

21. Could you help me find something?

Years and years ago, shucks, it might have been 40 years ago or even a little more, I read one of those books written by popularizers of science. It wasn't written by Sagan or Asimov, I don't think it was written by that fellow who wrote Red Giants and White Dwarfs, Jastrow as I recall was his name, I don't think it was written by Robert L. Forward, but it might have been because I didn't know who Forward was then. Anyway, it was about relativity, and even though I'm something of a dumbass when it comes to stuff like that, after reading that book, I actually UNDERSTOOD relativity. I actually UNDERSTOOD why the universe just doesn't make any sense without that cosmic speed limit. That understanding faded from my consciousness very quickly, though. I can't offer you any better description of the book than that, but if you have any idea of which book that might be, I would appreciate it if you could direct me to it. I would love to read it again. I want to stress, I really did understand why that cosmic speed limit exists. It actually made sense to me, for a while. That was probably the best explanation of science to the layman that I've ever read. Thanks, Salviati, if you can help me find it.

-- Ron

[Salviati]

23. That doesn't give a whole lot to go on, and it's not ringing any bells.

I'd suggest searching for relativity books written for a general audience published in the target timeframe, you can probably exclude ones you can tell aren't right from the summary, and then check out google books for samples until you find the right one.

[Chainfire]

19. The last time I orbited a black hole, time just stood still, just like it does on the church pew on Sunday morning.

My friend, who was sucked in said that time reversed and the last time I talked to him he was his 318th great grandfather and said that he was really developing an appetite for bananas.

Phisics and higher math escaped from me by the 11th grade in high school. I have a hard time wrapping my head around special relativity.