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Abstract:
We discuss in detail the development of the Newtonian and post-Newtonian approximations to general relativity. By using an initial-value approach, we are able to show that the post-Newtonian hierarchy through gravitational-radiation-reaction order is an asymptotic approximation to general relativity, thereby verifying the validity of the quadrupole formula for radiation reaction. We also show with equal rigor that the radiation from nearly-Newtonian systems obeys the far-field quadrupole formula (Landau-Lifshitz formula).There are no divergent terms in these approximations at any order, although logarithmic terms in the expansion parameter do appear at high order. We discuss the relationships of observables to post-Newtonian quantities by the method of osculating Newtonian orbits. Finally we discuss the role exact solutions may play in shedding light on some of these questions.
