# Time Dilation question for a writing project

first time posting a question, so please forgive me if I break any protocols.

I'm working on a writing project and while the science is not the focus, I want to make sure I get it right. So my question is 2-fold:

1) If an object orbiting a black hole and affected by gravitational time dilation, is it possible to experience a relative dilation of 1 / 120 near it as compared to an outside observer. Basically, for 10 years to pass "outside" for every month "inside".

2) I'm crafting a narrative for what that exactly would look like. I imagine that the stars in the sky would be 120x brighter, and that colors below visible would be blue-shifted into the visible spectrum, making the starfield a brilliant display of colors that you wouldn't see otherwise. Also, looking toward the Event Horizon would show some of the light from the other side severely red-shifted and twisted around the singularity (so you wouldn't ever actually SEE the E.H.). I imagine it would look like a dark, vaguely red ocean as the tidal forces gave it an almost water-like appearance.

Can anyone weigh in on these 2 questions and tell me if my understanding and assumptions pass muster?

• I need to clarify on #1: I guess the mass of the black hole would play a factor here, so I guess there's an additional question of "What size B.H. would be required to hit that mark?" I know it's POSSIBLE to hit that mark, but the question is can I hit that mark and still be outside the ISCO? Extra credit if I can find out what the time dilation ration would be at the IBCO. Feb 7, 2017 at 22:42
• Just for clarification, what do you mean by outside and especially, " inside". Also, how could you " see" the event horizon, even in any situation? Thanks, and best of luck with your question
– user140606
Feb 8, 2017 at 2:06
• @Countto10 When I'm saying "outside" and "inside", I'm using bad vernacular to refer to being further from or closer to the IBCO. "Outside" in this case is a substantial enough distance away to be relatively unaffected by the gravitational time dilation, while "inside" is being very close to the IBCO. As for seeing the E.H., that I know is impossible. But the light from the other side is being bent around it, and would be heavily red-shifted so when you looked towards the E.H. you would see an unusual reflection of the star-field on the other side, hence my analogy. Does this help? Feb 8, 2017 at 15:02
• yep, thanks I kinda knew from ISCO in your comment, you did not mean inside the E.H., up to that, from the wording I wasn't sure, sorry :) maybe include the comment in your post, they get deleted a lot of the time.
– user140606
Feb 8, 2017 at 16:55

## 1 Answer

To answer number 1, there is an infinite number of possible ways to orchestrate a circular orbit around a black hole so that the inhabitants experience time 120 times slower than outside observers. This is because both the mass of the black hole and the radius/velocity of the orbit matters! A ship orbiting a small black hole very close and fast could experience more time dilation than a ship orbiting a more massive black hole slower and farther away. For the sake of your story (which, by the way, could you please link to? I'm very interested in reading it), I would suggest that you pick a larger black hole and an larger orbital radius so that the tidal forces would be smaller and impose less strain on the structure. If you can give me a mass that you want the black hole to be I can tell you how far away to set the orbit so that the time dilation factor is 1/120.

As for question 2, I'm not entirely sure how time dilation would affect light. There would be a lot of gravitational affects on light that close to a black hole, which means that stars would appear to be in vastly different locations than where they actually are. There probably would be significant Doppler shifting, but I think a lot of it would depend on the direction of your orbit. I.E. moving toward a star it would be blueshifted, moving away from it would be redshifted. However, I'm unsure about how time dilation would affect light coming in from outside stars. Perhaps the 1/120 time dilation would make the people on board think and observe things 1/120 as fast, making events coming in from outside seem 120 times faster? That could make light seem brighter as the effective photon density hitting your eyes would be proportionally higher. However, I defer to someone more experienced with how light behaves in areas of high time dilation for this one.

Hope you can use some of this!

• @g-smith Thank you very much for the reply. I am thinking most likely a larger mass black hole for the exact reasons you cited, but something that could be "realistically close" to Earth. I.e. would have to be inside the Milky Way, and hopefully closer than the SMBH at the center. If that is the only candidate then I can work with that. As for the light, the blue-shifting of light coming toward the B.H. I BELIEVE would cause deep IR light to be visible, and for all of it to be at least 120x brighter than normal. The light coming "up" from near the E.H. I might have to get creative with. Feb 9, 2017 at 0:38
• The blue shifting could even get to the point that the microwave background is visible, I really don't know. I think as far as the more extremely warped paths of light coming up from near the black hole, you might look at the black hole from interstellar. They modeled all of the light really well. However, I think you have some creative leeway here given just how complex the paths of rays near a black hole can be. Best of luck Feb 10, 2017 at 14:02