Distance from Black Hole to experience Time Dilation

1. Mar 25, 2015

eiyaz

How close do you have to be from a black hole to experience noticeable time dilation. I always believed you will not experience noticeable dilation until you are at or in the event horizon is this correct?

Also does rotation/spin of mass such as a planet decrease it's inherent gravitational pull? I understand that at the surface an object will experience centrifugal force from spin, but what about object orbiting a mass? It should not have any effect, correct?

Interstellar the film suggested there could be habitable planet experiencing time dilation due to the distance from a black hole, logically I would assume any planet experiencing noticeable (such 1 to 5 hours) time dilation could not exist because it would eventually fall into the black hole is this correct?

2. Mar 25, 2015

Staff: Mentor

What's noticeable depends on how sensitive your instruments are. The GPS (Global Positioning System) has no difficulty at all noticing time dilation from the earth's gravity, although the effect is far weaker than you would find near the surface of the sun, which is in turn far weaker than the effect that you'd find near the surface of a neutron star or the event horizon of a black hole.

Google for "Kerr metric" and "frame dragging". The rotation makes for all sorts of strange effects, none of which can be predicted if you're thinking of the black hole as something with a Newtonian gravitational field except stronger.

I don't know about habitability, but the amount of gravitational time dilation is depends on how deep in the potential well the planet is relative to an observer at infinity. Thus, if the central mass is large enough (whether black hole or not) we can construct a stable orbit with any time dilation we please.

3. Mar 27, 2015

eiyaz

More specifically I was wondering if a planet with say a 1 to 20 time dilation ratio (1 to 20 hours) could exist outside of the event horizon of a black hole and be habitable, or does time dilation not occur until you enter the event horizon

4. Mar 27, 2015

Staff: Mentor

Not only does gravitational time dilation happen before you cross the event horizon, it happens even if you never cross the event horizon because you aren't in the gravitational field of a black hole so there's no event horizon to cross. Any gravitational field will cause time dilation - it doesn't matter whether the gravity is produced by a black hole or an ordinary object.

5. Mar 27, 2015

rootone

I'd reckon that anywhere close to a black hole is not a good place to be from the point of view of habitability, if by that you mean a planet on which a human being might stand a chance of surviving.
Many black holes have accretion disks consisting of matter which is so hot that it emits substantial amounts of x rays.
Additionally such a planet would experience enormous tidal effects, which if they didn't cause the planet to actually melt, would result in total chaos on the surface, literally tides of matter rolling around the place.

Last edited: Mar 27, 2015
6. Mar 27, 2015

phinds

and eiyaz, just to clarify something that I don't see mentioned in the other responses, you don't ever "experience" time dilation, what you experience is aging by a different amount (but not at a different rate) than people who are not in the same circumstances. Your clock always ticks at one second per second but it will tick a different number of times than those in different cicumstances, so that when you meet up again, you and your clock have aged by a different amount even though at the same rate. This is because you have taken a different path through space-time.

7. Mar 28, 2015

stevebd1

The equation for time dilation for an object hovering at a specific distance (r) from a static black hole is-
$$d\tau=dt\sqrt{1-\frac{2M}{r}}$$
where M=Gm/c2. For a rotating black hole, it's a little more complicated.

The following is the equation for gravity for a static black hole in geometric units (multiply the answer by c2 to get SI units)-
$$a_g=\frac{M}{r^2}\frac{1}{\sqrt{1-\frac{2M}{r}}}$$
where M=Gm/c2, source- http://www.mathpages.com/rr/s7-03/7-03.htm

The equations for gravity for a rotating black hole in geometric units can be found in post #12 of this thread, equations (2) & (3) (the equations for the various components can be found in this post and note that a=J/mc).

If you just use the equatorial equation, you can compare the two using excel to see what effects frame dragging and spin have on gravity.

On a side note, you might also find this interesting-
http://saturn.jpl.nasa.gov/faq/FAQSaturn/#q14 [Broken]

You might find this following thread of interest-
Equation for time dilation of body in orbit around Kerr black hole?
In brief, the faster the black hole spin, the closer to the event horizon the innermost stable orbit, the greater the time dilation.

Last edited by a moderator: May 7, 2017
8. Mar 28, 2015

Staff: Mentor

For a stellar mass black hole, yes, this would be true. But for a supermassive black hole, such as the holes at the centers of many galaxies (including our own), tidal gravity near the horizon is much smaller.

9. Mar 29, 2015

rootone

Yes, I thought that tidal mayhem could be less of a problem for SMBH, but not sure how much less.
However there is at least one other problem in this case.
Galaxy centers are usually pretty crowded with many objects interacting gravitationally,
It could be very difficult for a planet to remain in a stable orbit for any amount of time.
Being in a stable orbit somewhere near a star is certainly a factor in whether a planet can be habitable.

10. Dec 30, 2016

Phillip Sublett

If a black hole is just a collapsed star, then it would have no more gravity than the original star did. So the question should be, could there be a habitable planet orbiting a collapsing star, whose mass is so great that spending a few minutes on the planet would cause 20 years to pass on a space ship a few million miles away?

In terms of our Solar system, if you spent an hour on Mercury while your twin spent an hour on Pluto, how much time dilation would you notice between clocks on those two planets, due to the Sun's gravity? So how much more massive would the Sun have to be so that there would be a major time dilation between different planets (e.g., you age an hour on Mercury while your twin on Pluto ages 20 years)?

11. Dec 30, 2016

Staff: Mentor

You can calculate this for yourself: @stevebd1 posted the formula in post 7 above.

12. Dec 30, 2016

Jonathan Scott

It's theoretically possible to have orbiting objects with huge time dilation near a large enough black hole. However, to have tolerable tidal forces, this has to be a long way from a really huge black hole, and for a space probe or similar to be able to visit it at time dilation 1/n, the energy required to bring it to a halt (or for it to return) corresponds to a fraction (n-1)/n of its original rest mass, compared for example with less than one part in a billion to escape from Earth, so it would require some unknown method of propulsion which is more than a billion times better than the methods we currently use to get into space (and which would probably have to violate known laws of physics).

13. Dec 30, 2016

ZapperZ

Staff Emeritus
I just want to make sure you are AWARE of what has been said here, because it appears that you have missed it.

The GPS system that are in used currently have to correct for gravitational time dilation effects between your device on earth and the satellite orbiting the earth. In other words, we are already "experiencing" that effect!

And we are nowhere near a black hole!

Edit: Oh wait, I can top myself. I recall a while back reading a paper on a more sensitive clock. And it is so sensitive that it can detect a variation in the clock rate by going up just ONE RUNG of a ladder[1]!

http://www.nature.com/news/2010/100923/full/news.2010.487.html

So who needs a black hole?

Zz.

[1]C.W. Chou et al., Science v.329, p.1630 (2010).

Last edited: Dec 30, 2016
14. Dec 30, 2016

vanhees71

Take the Schwarzschild solution. Outside of the event horizon a black hole doesn't look different than any other spherically symmetric distribution of matter (like any kind of star) with the same mass. Indeed, as Zz says, you don't need a black hole to observe gravitational redshift (or equivalently time dilation).

15. Mar 28, 2017