# Why didn't the Normandy crew experience time dilation?

In the Suicide Mission in Mass Effect 2, Commander Shepard and the Normandy crew travel to the galactic core to destroy the Collector Base.

The Collector Base is located on the accretion disc of a black hole, indeed from certain angles in the cutscenes you can see the black hole.

Unless I'm not mistaken shouldn't they experience gravitational time dilation from being so close to a black hole? If so, was it just an oversight by the writers?

• How do you know they didn't? Time dilation is relative, of course. They would only experience time contraction relative to the rest of the universe - with which they didn't really have much of a contact (IIRC they're using communication relays - they probably didn't have any in range). Not to mention that it's a universe where FTL travel and signalling is possible - it's quite likely relativity doesn't hold in that universe, unlike ours, which might imply no dilation ever. Commented Jun 17, 2015 at 13:26
• Agreed, they make FTL jumps constantly but never seem to be out of sync time-wise with people staying on planets, etc. It's safe to say that relative time is simply not part of the game. Commented Jun 17, 2015 at 14:41

Let's figure out how much time dilation they might have experienced.

To begin with, we need the mass of the black hole. Generously assuming it's Sagittarius A* and not some other (most likely smaller) black hole, we have about 4 million solar masses to play with.

That gives us a Schwarzschild radius of about 10 million kilometers. This is the radius of the black hole's event horizon. Surprisingly, that's actually not all that much; it's less than the radius of the Earth's orbit (1 AU) by about an order of magnitude.

Precise orbital distance is hard to gauge. We can use solid angles to approximate it. It looks like the black hole takes up about a tenth of a steradian, or maybe a little more of sky area. Since we know its diameter, we can use this to calculate orbital distance. Unfortunately, we need the area of the spherical cap, which is rather hard to calculuate since the sphere's radius is unknown (it's the same value we're trying to calculate, actually). We can still take upper and lower bounds: the orbital distance must be greater than 66 million kilometers (underestimating the spherical cap as the cross-sectional area of the black hole) and less than 90 million kilometers (overestimating the cap as half the surface area), but I'm now running into a bug: Wolfram|Alpha isn't canceling the steradian unit properly, so I had to multiply by a factor of sqrt(1 steradian), which is just 1 since steradians are dimensionless.

90 million kilometers is really close, for something as dangerous as a black hole. It will be throwing out hard X-rays and lots of other nasty radiation, for example. I'm going to round up to 1 AU because that's ever so slightly less ridiculous.

We need the acceleration due to gravity at that distance.

Finally, we need the duration of the mission. I think it probably took at most two hours of in-universe time, and that's really generous.

So let's tie it all up. Plugging all of these values into Wolfram|Alpha, we get a total duration of 122.4 minutes. Note that two hours is 120 minutes. So time dilation added 2.4 minutes to the total duration. That's probably why Bioware didn't bother to mention it.

Just for kicks, I redid the calculations with our lower bound for the orbital distance, and came up with about 5.8 extra minutes instead. So this really isn't even close.

• So in one sentence, being in a 1 AU orbit around the biggest black hole in our galaxy still only gives a next-to-negligible time dilation in the 10-20% range? I'd have expected much more severe effects... thanks for doing the math! Commented Jun 17, 2015 at 8:10
• I expected a bigger effect too. Though in Interstellar the time dilation was so extreme (as a major plot point) because Kip Thorne made a scenario with particularly extreme conditions. Planet Miller was extremely close to Gargantua but survived because of its orientation and the nature of the black hole. Commented Jun 17, 2015 at 9:57
• Fantastic answer. Seems almost wasted to type all that for 2 mins time dilation ! Commented Jun 17, 2015 at 11:35
• @DevSolar Nope - 1-2% range. You miscalculated the magnitude. Interstellar was indeed rather silly :D Commented Jun 17, 2015 at 13:28
• Great post. Felt like I was reading an XKCD What If. Commented Jun 18, 2015 at 0:09

It's mentioned several times throughout Mass Effect 2 that the "safe zone" around the Collector Base is very narrow, hence the need for the Reaper IFF. Any ship jumping there without it would be destroyed, as the thousands of nearby wrecks attest.

As far as I remember, the nature of this "safe zone" is never explored, but there's clearly some kind of active protection going on. A force barrier, some kind of energy field, etc. At the very least, something is keeping all that wreckage from filling up the space immediately around the base.

It's never stated onscreen, but it's a reasonable assumption that whatever process protects the Collector Base from the locally destructive forces and nearby debris, would also make the location more habitable. Given that gravity-manipulation tech is commonplace in the ME universe, countering the gravitational effects of a distant black hole doesn't seem too difficult for the servants of the super-advanced Reapers.