Gravitational Time Dilation Inside the Sun

How can time dilation, lets say 500000 km inside the sun be calculated ?

Using the appropriate spacetime metric, which i must admit I don't know. Try searching the Internet for it.

This would be the interior Schwarzschild metric:
https://en.m.wikipedia.org/wiki/Interior_Schwarzschild_metric

One of the assumptions is constant density, so that probably isn’t the best assumption, but it should be a reasonable approximation given the resulting simplification

Dale said:

One of the assumptions is constant density, so that probably isn’t the best assumption, but it should be a reasonable approximation given the resulting simplification

To do much better you'd need a density and pressure profile, and I would suspect you'd have to do it numerically. Especially if you stopped pretending it was a non-rotating sphere.

Ibix said:

To do much better you'd need a density and pressure profile, and I would suspect you'd have to do it numerically. Especially if you stopped pretending it was a non-rotating sphere.

Yes. I agree that anything more exact than this would probably have to be numerical.

Here is a "recipe" from MTW's Gravitation:

Is ##n## (23.28c and d) defined somewhere? Number density of particles?

Ibix said:

Is ##n## (23.28c and d) defined somewhere? Number density of particles?

Here:

Ibix said:

To do much better you'd need a density and pressure profile, and I would suspect you'd have to do it numerically. Especially if you stopped pretending it was a non-rotating sphere.

Dale said:

This would be the interior Schwarzschild metric:
https://en.m.wikipedia.org/wiki/Interior_Schwarzschild_metric

One of the assumptions is constant density, so that probably isn’t the best assumption, but it should be a reasonable approximation given the resulting simplification

Dale said:

Yes. I agree that anything more exact than this would probably have to be numerical.

The weak field approximation is going to be way more accurate than the interior Schwarzschild metric in this case. Input a solar model for the density and voila.

(I actually did this computation not too long ago for a cosmology course I took for undisclosed reasons. The teacher was somehow surprised when I used the standard solar model for the density profile )

Orodruin said:

The weak field approximation is going to be way more accurate than the interior Schwarzschild metric in this case. Input a solar model for the density and voila.

I have to admit that it didn’t even occur to me!