# Post-Newtonian approximation for binary gravitating system

I have been studying gravitation waves radiated by a binary source. I have linearised Einstein's field equation and approximated the source to a Quadrupole moment to get the power radiated by the source. Now what is post-Newtonian approximation? I have read in Wikipedia that weak field limit doesn't work for binary stars. So, one has to stick on to Post-Newtonian approximation. What is post Newtonian approximation and why do we need to study for the strong fields? Please explain.

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– Void
Jan 27 '15 at 9:28

The usual description of the post-Newtonian expansion will tell you that it is an expansion of this force in orders of $v/c$. Thus, it would seem the approximation will be valid even in strong fields - but it is not. The expansion starts with completely Newtonian equations and finds the appropriate corrections by successive iterations which find the next order correction in terms of $v/c$ - but this does not insure the rate of convergence of such iterations or convergence at all. Especially in very strong gravitational fields, e.g. for objects at a distance of few of their Schwarzschild radii, the iteration procedure will fail to give any reasonable results.