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

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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.