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#### The Equivalence and/or the Effacing principle in f (R) theories of gravity

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2103.04627.pdf

(Preprint), 308KB

Bhattacharyya2022_Article_TheEquivalenceAndOrTheEffacing.pdf

(Publisher version), 472KB

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##### Citation

Bhattacharyya, S. (2022). The Equivalence and/or the Effacing principle in f (R) theories
of gravity.* The European Physical Journal C,* *82*(7):
611. doi:10.1140/epjc/s10052-022-10574-9.

Cite as: https://hdl.handle.net/21.11116/0000-0008-2CBA-6

##### 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.

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.