TY - JOUR

T1 - The equivalence and/or the effacing principle in f(R) theories of gravity

AU - Bhattacharyya, Soham

N1 - Funding Information: The author would like to thank Bruce Allen and Badri Krishnan for a significant number of ideas and clarifications throughout the project. The author thanks Pierre Mourier for important comments on earlier drafts. The author would like to thank Yousuke Itoh, and the CBC group of MPI for Gravitational Physics, especially Andrey Shoom, for important comments and questions. The author would like to thank Chowhan Tanmay Tushar and Amanda Fajardo Garcia for some key inputs to the calculations of the Landau–Lifshitz formalism of GR. The technical computing system Mathematica, and some of the symbolic tensor manipulation packages supported by it, namely xAct [51] was used for most of the calculations in the study.

PY - 2022/7/13

Y1 - 2022/7/13

N2 - The Einstein-Hilbert action of the 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 has 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 (R) 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.

AB - The Einstein-Hilbert action of the 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 has 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 (R) 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.

UR - http://www.scopus.com/inward/record.url?scp=85134622062&partnerID=8YFLogxK

U2 - 10.1140/epjc/s10052-022-10574-9

DO - 10.1140/epjc/s10052-022-10574-9

M3 - Article

VL - 82

JO - European Physical Journal C

JF - European Physical Journal C

SN - 1434-6044

IS - 7

M1 - 611

ER -