Constraints on Flows in Horava-Lifshitz Gravity by Classical Solutions

TL;DR

This paper finds exact classical solutions in Horava-Lifshitz gravity to help constrain the theory's flow patterns, revealing effects like surplus angles and negative effective charges, and discusses implications for understanding gravity's behavior at different scales.

Contribution

It introduces a method to constrain flow patterns in Horava-Lifshitz gravity using classical solutions, highlighting effects of graviton speed and quartic derivatives near the UV fixed point.

Findings

Change in graviton speed causes surplus angles.

Quartic derivatives lead to negative effective electric charge.

Flow of constant graviton speed with variable Newton's coupling is favored near IR fixed point.

Abstract

We find exact static stringy solutions of Horava-Lifshitz gravity with the projectability condition but imposing the detailed balance condition near the UV fixed point, and propose a method on constraining the possible pattern of flows in Horava-Lifshitz gravity by using the obtained classical solutions. In the obtained vacuum solutions, the parameters related to the speed of the graviton and the coefficients of quartic spatial derivative terms lead to intriguing effects: the change of graviton speed yields a surplus angle and the quartic derivatives make the square of effective electric charge negative. The result of a few tests based on the geometries of a cone, an excess cone, a black string, and a charged (black) string seems suggestive. For example, the flow of constant graviton speed and variable Newton's coupling can be favored in the vicinity of IR fixed point, but the conclusion is indistinct and far from definite yet. Together with the numerous classical solutions, static or time-dependent, which have already been found, the accumulated data from various future tests will give some hints in constraining the flow patterns more deterministic.