Static post-Newtonian equivalence of GR and gravity with a dynamical preferred frame

TL;DR

This paper demonstrates that a covariant extension of general relativity with a dynamical preferred frame matches GR's predictions in the weak field limit, showing equivalence in key post-Newtonian parameters.

Contribution

It establishes the static post-Newtonian equivalence of a covariant gravity theory with a dynamical preferred frame to general relativity.

Findings

Post-Newtonian parameters match GR in the weak field limit

Equivalence holds except for specific Lagrangian coefficient values

Supports viability of preferred frame theories in weak gravity regimes

Abstract

A generally covariant extension of general relativity (GR) in which a dynamical unit timelike vector field is coupled to the metric is studied in the asymptotic weak field limit of spherically symmetric static solutions. The two post-Newtonian parameters known as the Eddington-Robertson-Schiff parameters are found to be identical to those in the case of pure GR, except for some non-generic values of the coefficients in the Lagrangian.