The Equivalence and/or the Effacing principle in $ f\left(R\right) $
  theories of gravity
  The Einstein-Hilbert action of general theory of relativity (GR) is the
integral of the scalar curvature $R$. It is a theory that is drawn from the
Equivalence principle, and has predictions that come out as a consequence of
the principle, in observables. Testing such observables to find
confirmation/infirmation of the principle have formed a significant chunk of
tests of GR itself. It is expected that quantum corrections to GR may add
additional higher powers of $R$ to the Einstein-Hilbert action, or more
generally, modifying the action into a generic class of functions of the Ricci
scalar. Testing the fate of the prized equivalence principle, in such modified
theories of gravity, hence become important in order to obtain a more generic
theory of gravitation, and consequently, of gravitating objects. In this study,
it is shown that a Post-Newtonian (PN) expansion of a class of $
f\left(R\right) $ theories lead to a sequence of solutions to the two-body
problem, which follows the equivalence principle (EP) at the Newtonian order,
and generalizes to the 'effacing principle' at a higher PN order.
