Spherically symmetric solutions, Newton's Law and IR limit λ->1, in Covariant Horava Lifshitz Gravity

Abstract

In this note we examine whether spherically symmetric solutions in Covariant Horava Lifshitz Gravity can reproduce Newton's Law in the IR limit λ->1. We adopt the position that the auxiliary field A is independent of the space-time metric [10,11], and we assume, as in [4], that $\lambda$ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ->1, unless λdoes not run, and has the fixed value λ=1. Finally, we comment on the Horava and Melby Thompson approach [4] in which A is assumed as a part of the space-time metric in the IR.

Withdrawn because of a crucial sign error in eq.(15)

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• Solar system tests and interpretation of gauge field and Newtonian prepotential in general covariant Hořava-Lifshitz gravity
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• Vaidya Solutions in General Covariant Hořava-Lifshitz Gravity without Projectability: Infrared Limit
• Shear-free Dust Solution in General Covariant Hořava-Lifshitz Gravity