![Figure 2](methods.png)
Figure 2: Different analytical approximation schemes and numerical techniques to study black
hole binaries, depending on the mass ratio
and the post-Newtonian parameter
. Post-Newtonian theory and perturbative self-force analysis can be
compared in the post-Newtonian regime (
thus
) of an extreme mass ratio
(
) binary.
![q = m ∕m 1 2](article2141x.gif)
![2 2 2 2 𝜖 ∼ v ∕c ∼ Gm ∕(c r12)](article2142x.gif)
![𝜖 ≪ 1](article2143x.gif)
![2 r12 ≫ Gm ∕c](article2144x.gif)
![m1 ≪ m2](article2145x.gif)