The Effacing Principle in the Post-Newtonian Celestial Mechanics

TL;DR

This paper investigates how internal structures of celestial bodies affect their motion in scalar-tensor gravity theories, revealing violations of the effacing principle at post-Newtonian orders, especially for neutron stars and black holes.

Contribution

It demonstrates the violation of the effacing principle in scalar-tensor theories at the first post-Newtonian level, highlighting the role of internal structure and non-linearity parameters.

Findings

Effacing principle is violated by terms related to rotational moments of inertia.

Violations depend on the non-linearity parameter eta; in GR, eta=1, leading to different effects.

Neutron stars and black holes contribute to orbital dynamics at higher PN orders.

Abstract

First post-Newtonian (PN) approximation of the scalar-tensor theory of gravity is used to discuss the effacing principle in N-body system, that is dependence of equations of motion of spherically-symmetric bodies comprising the system on their internal structure. We demonstrate that the effacing principle is violated by terms which are proportional to the second order rotational moment of inertia of each body coupled with \beta-1, where \beta is the measure of non-linearity of gravitational field. In case of general relativity, where \beta=1, the effacing principle is violated by terms being proportional to the rotational moment of inertia of the forth order. For systems made of neutron stars (NS) and/or black holes (BH) these terms contribute to the orbital equations of motion at the level of the third and fifth PN approximation respectively.