# 1PN metric vs. Schwarzchild

I'm sure there is a simple answer to this question, but I have been looking at the first Post-Newtonian (1PN) metric (for my own research) and noticed that the time-time component of the GR metric is:

$$g_{00} = -1 + 2U - 2 U^2$$

where U is the Newtonian potential.

The time-time component of the Schwarzchild metric, however, is

$$g_{00} = -1 + 2M/r$$.

There is no quadratic in the Newtonian potential even though this metric is an exact solution of the field equations. Is this because it is in a different gauge?

bcrowell
Staff Emeritus
$$g_{00} = -1 + 2M/r - 2(M/r)^2$$