On the gravitational Chern-Simons action as entropy functional for three-manifolds, and the demystification of the Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper explores the geometrical flow related to the gravitational Chern-Simons action in three-manifolds and clarifies issues in four-dimensional Hořava-Lifshitz gravity, which aims to be a quantum gravity candidate.

Contribution

It extends the understanding of the geometrical flow associated with the gravitational Chern-Simons action and addresses problems in the four-dimensional Hořava-Lifshitz gravity model.

Findings

Derived a more general geometrical flow for the Chern-Simons action.

Identified issues with the four-dimensional Hořava-Lifshitz gravity.

Revealed challenges in using Hořava-Lifshitz gravity as a UV completion of Einstein gravity.

Abstract

We determine the more general geometrical flow in the space of metrics corresponding to the steepest descent for the three-dimensional gravitational Chern-Simons action, extending the results previously considered in Class. Quantum Grav. 25 (2008) 165019, and reveling another trouble with the four dimensional Ho\v{r}ava-Lifshitz gravity introduced in Phys. Rev. D 79, 084008 (2009), and JHEP 0903, 020 (2009), which attempts to be a candidate for an UV completion of Einstein general relativity.