A perturbation approach to Translational Gravity

TL;DR

This paper introduces a perturbation method in a gauge formulation of 3+1 gravity, where the expansion parameter is linked to the gravitational constant, and provides explicit solutions in the static isotropic case.

Contribution

It presents a novel perturbation approach in a gauge formulation of gravity, identifying the expansion parameter with the gravitational constant and deriving explicit solutions.

Findings

First order solution in static isotropic case derived

Expansion parameter identified with gravitational constant

General structure of perturbation in harmonic gauge analyzed

Abstract

Within a gauge formulation of 3+1 gravity relying on a nonlinear realization of the group of isometries of space-time, a natural expansion of the metric tensor arises and a simple choice of the gravity dynamical variables is possible. We show that the expansion parameter can be identified with the gravitational constant and that the first order depends only on a diagonal matrix in the ensuing perturbation approach. The explicit first order solution is calculated in the static isotropic case, and its general structure is worked out in the harmonic gauge.