Static post-Newtonian limits in non-projectable Ho\v{r}ava-Lifshitz gravity with an extra U(1) symmetry

TL;DR

This paper investigates the static post-Newtonian limits of non-projectable Hořava-Lifshitz gravity with an extra U(1) symmetry, showing consistency with solar system tests without requiring gauge field and Newtonian prepotential as part of the metric.

Contribution

It derives static spherical solutions in the infrared and relates Eddington-Robertson-Schiff parameters to the theory's coupling constants, demonstrating observational consistency.

Findings

Parameters align with solar system observations for viable couplings

Consistency achieved without including gauge field and Newtonian prepotential in the metric

Provides static solutions in the infrared regime

Abstract

In this paper, we study static post-Newtonian limits in non-projectable Ho\v{r}ava-Lifshitz gravity with an extra U(1) symmetry. After obtaining all static spherical solutions in the infrared, we apply them to the solar system tests, and obtain the Eddington-Robertson-Schiff parameters in terms of the coupling constants of the theory. These parameters are well consistent with observations for the physically viable coupling constants. In contrast to the projectable case, this consistence is achieved without taking the gauge field and Newtonian prepotential as part of the metric.