Spherically symmetric solutions, Newton's Law and IR limit \lambda->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 \lambda->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 \lambda->1, unless \lambda does not run, and has the fixed value \lambda=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.