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 $λ$ 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.