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

TL;DR

This paper investigates whether spherically symmetric solutions in Covariant Horava-Lifshitz Gravity can recover Newtonian gravity in the IR limit, finding that it generally fails unless bb=1, and discusses alternative assumptions about auxiliary fields.

Contribution

It demonstrates that under common assumptions, the IR limit does not reproduce Newtonian physics unless bb=1, highlighting a limitation in Covariant Horava-Lifshitz Gravity.

Findings

Standard solutions do not recover Newtonian gravity as bbd1.

Recovery of Newtonian physics requires bb=1.

Discussion of alternative assumptions about auxiliary field A.

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.