# How does space time differ within a galaxy?

Not the same question but is similar to other marked duplicate. How much time dilation does the center of a galaxy can exist and sustain human life from our point of view? What would a day equal to each others point of view looking at each other?

I'm not asking about moving celestial bodies moving from each other but the difference in the gravity wells from the center of our galaxy being generally denser then the edge of a galaxy. This is another way of asking if I wasn't clear above the line. Not to invalidate any answers.

Point 1 being near the center of the galaxy and point 2 at the the most edge the galaxy. How much would the differences in the galaxies gravity well point 1 being deeper in the center compared to the point 2 the edge effect time? • Your question does not make much sense. What does the doppler shift due to a galaxy's rotation have to do with time dilation? Why would that affect the evolution of life? How would that affect the length of a day? – Phiteros Feb 19 '18 at 4:16
• @Muze - you're not incorrect but the difference is absolutely tiny - so small it could never be measured. – Fattie Feb 23 '18 at 19:00
• @Phiteros - it makes absolutely perfect sense, what do you mean? When you're near some gravity (say, on the surface of the Earth), there is a tiny time dilation. OP is just asking how big it is. The galaxy is astoundingly heavy so you can really see where it's a good popular science question. Great question. – Fattie Feb 23 '18 at 19:02
• @Fattie That's because he edited the question. The first question was asking about red and blue shifts, then talked about time dilation. – Phiteros Feb 23 '18 at 22:06
• @Phiteros - fair enough; sorry about that. Is question-editing annoying or what?! – Fattie Feb 24 '18 at 15:36

The gravitational redshift factor and also the factor by which time dilation occurs in a gravitational field is approximately $GM/Rc^2$. Here, $R$ would be the radius from which light was emitted and $M$ is the amount of mass within radius $R$ (making the crude assumption of spherical symmetry).

Thus, for an external observer, light emitted from a radius of 10 kpc, might have $M \sim 10^{11} M_{\odot}$ in the galaxy shown. The redshift/time dilation factor is only $5\times 10^{-7}$ and is basically negligible.

This could perhaps gets an order of magnitude bigger as one approaches the denser central bulge, but is still very small.

The only appreciable redshift and time dilation effects will come in the immediate surroundings of any supermassive black hole. By immediate, I mean within about a hundred Schwarzschild radii, where $R_s = 2GM/c^2$. In our Galaxy that would mean within a billion kilometres.

• So unless your world exist in orbit exclusively around the black whole( in the center of the galaxy: Sagittarius A) there would be no significant time dilation? That distance would be likely inside the acceleration disk orbit and completely inhabitable on any level? – Muze Feb 19 '18 at 18:09
• @Muze - that's totally correct. (I think you meant to spell "accretion" disk, by the way.) – Fattie Feb 23 '18 at 19:01
• Just BTW, there seems to be many black holes in our galaxy - as well as the big one in the middle. If you are very close to any of those BHs, you'd experience such effects. – Fattie Feb 23 '18 at 19:04

Quite simply,

in both cases the effect is absolutely tiny.

Here is your basic confusion, on both this and the other similar question:

1. very heavy objects cause time dilation
2. a galaxy is just totally badass heavy
3. you naturally assumed then that galaxies cause time dilation
4. Very surprisingly, this is simply not correct.

The reason? Galaxies are very big. That is to say very thin. They have incredibly low density. Because of this there is simply no dilation at all.

(Well, only a minuscule amount - but that is true of simply, say, standing on Earth.)

That's the story!