Gauge-invariant approach to the parametrized post-Newtonian formalism

TL;DR

This paper introduces a gauge-invariant method for the parametrized post-Newtonian formalism, simplifying calculations by focusing on physical quantities and avoiding gauge fixing, demonstrated through scalar-tensor theories.

Contribution

It develops a gauge-invariant approach to PPN formalism using higher order perturbation theory, applicable in metric and tetrad formulations.

Findings

Simplifies PPN calculations by using gauge-invariant quantities.

Eliminates the need for gauge fixing before solving field equations.

Successfully applied to scalar-tensor theories to compute PPN parameters.

Abstract

We present an approach to the parametrized post-Newtonian (PPN) formalism which is based on gauge-invariant higher order perturbation theory. This approach divides the components of the metric perturbations into gauge-invariant quantities, which carry information about the physical system under consideration, and pure gauge quantities, which describe the choice of the coordinate system. This separation generally leads to a simplification of the PPN procedure, since only the gauge-invariant quantities appear in the field equations and must be determined by solving them. Another simplification arises from the fact that the gauge-invariant approach supersedes the necessity to first choose a gauge for solving the gravitational field equations and later transforming the obtained solution into the standard PPN gauge, as it is conventionally done in the PPN formalism, whose standard PPN gauge is determined only after the full solution is known. In addition to the usual metric formulation, we also present a tetrad formulation of the gauge-invariant PPN formalism. To illustrate their practical application, we demonstrate the calculation of the PPN parameters of a well-known scalar-tensor class of theories.