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Thread: Gravitational Time Dilation

  1. #1 Gravitational Time Dilation 
    Forum Sophomore ChaosD.Ace's Avatar
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    Hi guys

    Is there a way of working out the distance you would have to be from a singularity, in order for 10 minutes to equal 2000 years outside the black holes time dilation field ( a point where the flow of time would be similar to deep earth's) taking into account entry and exit times.


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    Moderator Moderator Markus Hanke's Avatar
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    I am confused what exactly it is you are after - are you asking about gravitational time dilation at a given distance from a black hole relative to some observer at infinity ( outside the BH's gravitational influence ) ? If so, what does the Earth and entry/exit points have to do with it ?


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    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by ChaosD.Ace View Post
    Hi guys

    Is there a way of working out the distance you would have to be from a singularity, in order for 10 minutes to equal 2000 years outside the black holes time dilation field ( a point where the flow of time would be similar to deep earth's) taking into account entry and exit times.
    It sounds like you want to find the distance, , where in


    Gravitational time dilation - Wikipedia, the free encyclopedia

    Note that the distance depends on the mass of the black hole (it is expressed as the ratio to the event horizon radius.
    ei incumbit probatio qui dicit, non qui negat
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  5. #4  
    Forum Sophomore ChaosD.Ace's Avatar
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    Okay, for example let's say I wanna create my own planet, so I trigger the planet forming mechanism, however I can't just sit there and wait for millenia until it forms, so I would travel close to a black hole and use it's time dilation.

    Let's say at a distance d from the singularity time passes so that every 5 minutes (at d) equals 1000 years at the area of space in wihich my planet is forming (I understand the formation of a planet in itself will establish a new strong gravitational field in that area of space, thus also dilating time but not near as a black hole)

    How does one acquire a value for d in order to spend 1 year near that black hole but for 1 million years to have passed in relatively normal time flow. If parameters such as the black holes mass (m) are known ( if any other paramters need to be known I would love to know?)

    I do A2 physics at A-Level so I am familiar with the general equations for gravitation, it's the relativity I am having trouble with.

    Hope that clarifies.
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    Forum Sophomore ChaosD.Ace's Avatar
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    Oh thanks strange, I was already writing the above post before you posted, I'll have a look at what you mentioned.
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  7. #6  
    Forum Sophomore ChaosD.Ace's Avatar
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    This is in continuation from post #4

    What I mean by entry and exit points is that since grav fields expand ou infinitly there will be a point (let's call it the threshold) in every black hole where dilation becomes significant long before I reach That calculated distance. So spending a year at d, means more than 1 million years will pass at a point of "relatively normal time flow" because of the gradual increase in time dilation from the treshold to point d, and I want to spend exactly 1 year in that severe time dilation field so I would need to take into acount:

    Going from the treshold to point d (the entry into that significant portion of the black holes gravitational field)
    and
    Going from point d back to the treshold (the exit out of that significant portion of the black hole's gravitational field)

    Hopefully that makes sense
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    Brassica oleracea Strange's Avatar
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    A quick back-of-the-envelope calculation suggest that for any significant time dilation you would have to be pretty mcu at the event horizon. You can't hover there, you may not even be able to get away from there with an feasible amount of fuel.

    If you are going to travel to a black hole which is probably hundreds, if not thousands, of light years away you will want to do that at a significant fraction of the speed of light. As such, most of your time dilation will come from the speed of your journey, not the black hole. In which case, you might as well forget the black hole and choose a more scenic route.
    ei incumbit probatio qui dicit, non qui negat
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    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by ChaosD.Ace View Post
    Going from the treshold to point d (the entry into that significant portion of the black holes gravitational field)
    and
    Going from point d back to the treshold (the exit out of that significant portion of the black hole's gravitational field)
    This sounds like you are trying to take into the account what happens to the clock when you decelerate into the field, and accelerate out of it in the end. Treating this correctly using the full metric isn't really all that trivial, because it takes a finite proper time to get in and out of the field, and it will also depend on the exact trajectory the ship takes. I would suggest you disregard this bit, since there is no easy and straightforward relation for this.
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    Forum Sophomore ChaosD.Ace's Avatar
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    Thanks a lot, so I guess I should pick a less ambitious time dilation factor. I guess it all depends on how long it takes to make a planet (slightly bigger than earth) , do you happen to know?
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by ChaosD.Ace View Post
    Going from the treshold to point d (the entry into that significant portion of the black holes gravitational field)
    and
    Going from point d back to the treshold (the exit out of that significant portion of the black hole's gravitational field)
    This sounds like you are trying to take into the account what happens to the clock when you decelerate into the field, and accelerate out of it in the end. Treating this correctly using the full metric isn't really all that trivial, because it takes a finite proper time to get in and out of the field, and it will also depend on the exact trajectory the ship takes. I would suggest you disregard this bit, since there is no easy and straightforward relation for this.
    Yes, you are absolutely right. Assuming radial motion only we can start with the simplified metric:



    For two observers, situated at radial values and the above gives the ratios of proper times:

    , i=1,2i

    i.e.



    where v is the radial speed and is the Schwarschild radius.

    This should answer Chaos' question.
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  12. #11  
    Forum Sophomore ChaosD.Ace's Avatar
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    Thanks a lot for the equations, but I gotta ask one more thing, I can assume that black hole are spherically perfectly symmetrical right?

    Also where did you guys learn all this, is it undergraduate stuff?
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    Quote Originally Posted by ChaosD.Ace View Post
    Thanks a lot for the equations, but I gotta ask one more thing, I can assume that black hole are spherically perfectly symmetrical right?
    Yes, the solution I used is for the spherically symmetric, non-rotating, non-charged case (Schwarzschild). I could derive a (more complicated) solution for the more complicated case(s) for you.

    Also where did you guys learn all this, is it undergraduate stuff?
    No, grad stuff.
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    Forum Sophomore ChaosD.Ace's Avatar
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    Quote Originally Posted by xyzt View Post

    Also where did you guys learn all this, is it undergraduate stuff?
    No, grad stuff.
    I guess I'll be ahead then.

    Quote Originally Posted by xyzt View Post
    Yes, the solution I used is for the spherically symmetric, non-rotating, non-charged case (Schwarzschild). I could derive a (more complicated) solution for the more complicated case(s) for you.
    No it's okay I can work with this for now. Thanks a lot.
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    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by xyzt View Post
    No, grad stuff.
    Really ? I never studied physics at university level, so I wouldn't know...but I would have expected the Schwarzschild metric to be an undergrad thing, as it is the most basic solution to the GR field equations.
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    Wouldn't it be easier and use less energy, rather that risking proximity to a black hole, to just stay put and spin around close to the speed of light? The closer you are to the speed of light the slower your clock is relative to the planet you are creating.

    I think the equation is

    change_in_time_planet = change_in_time_spacecraft / sqrt( 1 - (v_spacecraft)2/(speed_of_light)2)
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  17. #16  
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    Quote Originally Posted by uptonryan View Post
    just stay put and spin around close to the speed of light
    What do you mean by "spin around" ?
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  18. #17  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by uptonryan View Post
    just stay put and spin around close to the speed of light
    What do you mean by "spin around" ?
    It is just the speed that is relevant not the displacement. You can travel is a big circle or just tiny circles. You may even be able to spin. Although in spinning the forces involved would be massive.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    No, grad stuff.
    Really ? I never studied physics at university level, so I wouldn't know...
    Based on your posts, I would have never guessed, you are doing a fantastic job.


    but I would have expected the Schwarzschild metric to be an undergrad thing, as it is the most basic solution to the GR field equations.
    I studied SR in undergrad and GR in grad school. GR is a lot more than the Schwarzshild solution.
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    Quote Originally Posted by uptonryan View Post
    Wouldn't it be easier and use less energy, rather that risking proximity to a black hole, to just stay put and spin around close to the speed of light?
    Yes, this are called "circular orbits" in GR. These orbits can be calculated from the metrics.



    I think the equation is

    change_in_time_planet = change_in_time_spacecraft / sqrt( 1 - (v_spacecraft)2/(speed_of_light)2)
    No, it is not, it is much more complicated than that. I wrote this for wiki, it contains the answer to your question. Why don't you wait until you start studying GR? Making up things is not the right thing to do.
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  21. #20  
    Forum Cosmic Wizard icewendigo's Avatar
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    Btw, why does time go slower on earth than at a higher altitude? Why/how does the G-force/mass slow down the clock?
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    Quote Originally Posted by icewendigo View Post
    Btw, why does time go slower on earth than at a higher altitude? Why/how does the G-force/mass slow down the clock?
    No one knows "how" and "why". We just have the GR predictions that is DOES and experiment confirms (see GPS) that it DOES.
    Last edited by Howard Roark; November 7th, 2013 at 11:16 AM.
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  23. #22  
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    Quote Originally Posted by xyzt View Post
    I studied SR in undergrad and GR in grad school. GR is a lot more than the Schwarzshild solution.
    Ha ha, trust me, I know that
    What I meant was that I encountered the Schwarzschild metric long before I knew anything about the field equations, or tensors, or any of the deeper and finer points...but perhaps it isn't done that way in undergrad courses.
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    Quote Originally Posted by icewendigo View Post
    Btw, why does time go slower on earth than at a higher altitude? Why/how does the G-force/mass slow down the clock?
    That's because the presence of mass-energy goes hand-in-hand with space-time curvature, and curvature in the time direction manifests itself as gravitational time dilation.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    I studied SR in undergrad and GR in grad school. GR is a lot more than the Schwarzshild solution.
    Ha ha, trust me, I know that
    What I meant was that I encountered the Schwarzschild metric long before I knew anything about the field equations, or tensors, or any of the deeper and finer points...but perhaps it isn't done that way in undergrad courses.
    Yes, many people did. Yet, the Schwarzschild solution needs to be learned AFTER the EFEs. This is why I think it ended up in my grad curriculum.
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    Quote Originally Posted by xyzt View Post
    Yet, the Schwarzschild solution needs to be learned AFTER the EFEs.
    Yeah, I can see your point here.
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  27. #26  
    KJW
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    Quote Originally Posted by icewendigo View Post
    Btw, why does time go slower on earth than at a higher altitude? Why/how does the G-force/mass slow down the clock?
    The basic answer to this is the equivalence principle, which basically says that standing on earth is the same as accelerating upward at g. It is the accelerated frame of reference that produces the time dilation with respect to distance.

    What this means as far as the OP is concerned is that to exploit time-dilation, one doesn't need a blackhole and that having one doesn't make it any easier, only more hazardous.
    uptonryan likes this.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  28. #27  
    Forum Sophomore ChaosD.Ace's Avatar
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    Yeah but which one makes me seem more Badass, Moving in circles (in some random place) really fast or spittin in the face of a black hole
    U gona do somethin do it in style.

    Which reminds me, what would the hawking radiation do to me?

    Also which one would be easier to achieve, making a ship move close to the speed of light (in circles) in deep space or escaping a black hole (in a straight trajectory)?
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    Quote Originally Posted by ChaosD.Ace View Post
    U gona do somethin do it in style.
    The black hole, then

    Which reminds me, what would the hawking radiation do to me?
    Depends how big/small the black hole is, and how close you are planning to get to it.

    Also which one would be easier to achieve, making a ship move close to the speed of light (in circles) in deep space or escaping a black hole (in a straight trajectory)?
    They would both be equally difficult, but the black hole is more badass
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  30. #29  
    Forum Sophomore ChaosD.Ace's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    how close you are planning to get to it.
    Depends on how long it takes for a planet to form, if around a 1000 years then travelling to the black hole alone would suffice, but if above 100s of thousands then I would have to run the equation.
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  31. #30  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by ChaosD.Ace View Post
    Which reminds me, what would the hawking radiation do to me?
    For a black hole large enough to provide significant time dilation without the tidal forces tearing you apart, the Hawking radiation would be immeasurably small.
    ei incumbit probatio qui dicit, non qui negat
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    I would be more scared of the jets at the top and bottom of the black hole that spit matter out at close the speed of light. As per the picture below.

    http://www.cv.nrao.edu/course/astr534/images/3C175.gif
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  33. #32  
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    Not to forget any accretion disc which might be present - matter infalling at relativistic speeds would emit large amounts of x-rays and gamma rays, so you might get fatally irradiated long before you get anywhere near the black hole.
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    KJW
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    Quote Originally Posted by Strange View Post
    the tidal forces tearing you apart
    Oh, I forgot the tidal forces with regards to my previous post. That would make the blackhole a little bit less comfortable compared to simple acceleration, for which there are no tidal forces. The equivalence principle is local and gravitation does distinguish itself from simple acceleration by the tidal effect which is a direct result of the spacetime curvature associated with gravitation (an accelerated frame of reference in flat spacetime is still flat spacetime).
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by Markus Hanke View Post
    Not to forget any accretion disc which might be present - matter infalling at relativistic speeds would emit large amounts of x-rays and gamma rays, so you might get fatally irradiated long before you get anywhere near the black hole.
    Assuming you can even get there. Wouldn't we need to invent interstellar travel first? That in of itself has its dangers. Space is not exactly empty and encountering an asteroid or worse at close to the speed of light would be fatal.

    Of course far better to rip a hole in space time and jump there if that is even possible. Probably best to send a robot.
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    I think they made a movie about this.

    The Black Hole (1979) - IMDb

    Lots of people die in the movie though.
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