Probing Post-Newtonian Formalism of Binary Black Holes in General Relativity and Beyond

Abstract

This project studies the analytical methods used to model the non-spinning compact binaries in general relativity (GR), scalar-tensor theories, and f(R) theories of gravity. We have studied the post-Newtonian (PN) approximation methods and effective-one-body (EOB) formalism to understand the inspiral phase of compact binary coalescence. We have successfully reproduced the post-Newtonian dynamics in GR, scalar-tensor theory, and f(R) gravity. Additionally, utilizing second-order PN results from GR, we have recovered the 2PN conservative dynamics in the EOB framework, which were initially developed by Alessandra Buannano and Thibault Damour. Using the Hamiltonian in the effective framework, we have described the Innermost stable circular orbit. We have also derived the post-Newtonian dynamics at second-order for the general f(R) gravity. These 2PN results are helpful in modelling compact binary dynamics in f(R) gravity. Additionally, we have performed the conformal mapping between scalar-tensor and f(R) gravity.