The Equivalence and/or the Effacing principle in $ f\left(R\right) $ theories of gravity

TL;DR

This paper investigates $f(R)$ theories of gravity, demonstrating that they uphold the equivalence principle at Newtonian order and extend to the effacing principle at higher post-Newtonian orders, thus testing the robustness of gravitational principles beyond general relativity.

Contribution

It shows that a class of $f(R)$ theories of gravity preserve the equivalence principle at Newtonian order and generalize to the effacing principle at higher post-Newtonian orders.

Findings

$f(R)$ theories follow the equivalence principle at Newtonian order.

Higher PN order solutions support the effacing principle.

Results extend the understanding of gravitational principles in modified theories.

Abstract

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.