How to use S-metric to periastron precession of binary stars

[Vincentius]

The Schwarzschild metric allows to calculate the precession of an elliptic orbit of a particle around a large central mass, provided the mass of the particle is much smaller than the central mass M. This condition is not met in the case of binary stars m1 and m2 revolving around each other.
There is mention of a possibility of still using the Schwarzschild metric, but then one must take the sum of the masses of the two stars for the central mass, i.e. M=m1+m2.
I can imagine this works, but don't know how. Could anyone supply a reference on this subject.
Thanks!

 

[Dale]

This is known as the two-body problem:
http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity

At this time there is no closed form solution.

 

[Vincentius]

Yes, I know there is no analytical solution, that's why I asked about the approximation using M=m1+m2. But I cannot find a derivation of this approximate solution. Can anyone help out? Thanks

 

[grav-universe]

Here is a Wiki link about the two body problem in GR.

 

[Mentz114]

Yes, I know there is no analytical solution, that's why I asked about the approximation using M=m1+m2. But I cannot find a derivation of this approximate solution. Can anyone help out? Thanks

This is the only paper on this subject I've got - arXiv:gr-qc/0502062v1 14 Feb 2005.