Parameterized second post-Newtonian framework with conservation Laws

TL;DR

This paper develops a parameterized second post-Newtonian framework for fluid systems in harmonic gauge, identifying key parameters that ensure conservation laws are satisfied.

Contribution

It introduces a minimal set of three independent 2PN parameters that uphold fundamental conservation laws in gravitational fluid systems.

Findings

Identifies three independent 2PN parameters ($$, $$, $_2$) for the metric.

Ensures conservation of energy, momentum, angular momentum, and center-of-mass motion.

Provides a framework for consistent 2PN gravitational modeling.

Abstract

We parameterize the second post-Newtonian (2PN) metric for a gravitating system of fluids in the generalized harmonic gauge, and find that there are only three independent 2PN parameters (i.e. $\omega$, $\delta$ and $\delta_2$) for satisfying some conservation laws including the conservations of energy, momentum, angular-momentum and the uniform motion of the center-of-mass.