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There is not much difference. The relativistic factor is 1.030107, that is a ~3% change.

EDIT:

My amateur physics say that the gravitational well adds 9.7% to that.

I tried the same calculation for earth and it gave a sensible result: a change of 6.95 * 10^-10.

Here is an answer from physics exchange which gets the same result: http://physics.stackexchange.com/questions/10089/gravitation...

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That's about 11 days per year, or 43 minutes per day.

The quoted example admits that it ignores strong fields and non-relativistic matter, which we have already established to be dealing with. The angular momentum of an element of volume in the neutron star likely contains enough kinetic energy to affect the Einstein field equations in a significant way. General relativity can't be ignored, but the Newtonian approximations has this habit of being nearly right more often than not.

I know that for rotating black holes the Kerr solution to the Einstein equations offers the best way to test these metric-based questions but I'm not sure if that's what you'd use for a Neutron Star.

12.7% over 16km sounds like quite a lot to me. Especially since we're talking about time.

Keep in mind that differences in gravity will also affect time dilation.

And this correction goes in the other way.

No, time in a gravitational well runs more slowly relative to someone outside, just as your experience time slower if you are traveling very fast.

You are right. I was confused because the satellites in orbit need a different speed at different height, and in that case the when the special relativity effect increase the general relativity effect decrees. http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_P...

I think the point was that time in the center of the star is more affected by gravity than at the surface. Whereas someone on the surface (if that were possible) would experience greater time dilation relative to the center due to his high relative velocity. So for those two points (surface vs center), the two time dilation effects are working opposite each other.

Edit: I may have been reading too much into it. The effects you see will depend on which positions you're comparing, and people in this thread haven't really specified.

I think you mixed up some things. There is no gravity or time dilation in the center of a massive spherical object.

If you're in a small empty room in the middle of a neutron star, you will be floating weightless, but you're still at the bottom of a gravity well. Since it's the well, not the acceleration that affects time, time will tick slower for you.

(Don't try this at home.) (And if you do, don't touch the walls.)

Spacetime in the center of a perfect spherical object is the same as a point in empty space, you can't tell them apart. Of course that only counts for the exact point in the center. So the time will not tick slower there as to someone far from any objects.

What? The lowest potential in a uniform sphere is at the centre not the surface (http://en.wikipedia.org/wiki/File:GravityPotential.jpg). Also graviational time dilation depends on the potential not the force (curvature) so it is irrelevant if the point at the centre is shifted in spacetime

Time will still tick slower though regardless of the first part of what you say being right

Your link doesn't even relate to time dilation and is also about a hollow sphere, not a uniformly dense solid sphere. Moreover in a hollow sphere, time dilation still occurs because it depends on the absolute (or rather, relative to an outside distant observer) potential, not the gravitational field (which is the only thing that is necessarily zero as a result of the flat spacetime in the sphere). See for example this http://physics.stackexchange.com/questions/69821/a-hollow-bl...

It's like you didn't read your link

Being unable to tell is not an argument for time not ticking slower; the whole point of time ticking slower is that everything is consistent for your point of reference and you can't tell, but your point of reference has different time than other points.

Just as if you were inertially moving at 0.9c relative to me, the time frame would be different despite both me and you being 'the same as a point in empty space'.

My two comments above are wrong. Very counterintuitive. How can you have a difference with two points stationary relative to each other.

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