# Ho\v{r}ava Gravity at a Lifshitz Point: A Progress Report

## TL;DR

This paper reviews recent progress in Hořava gravity, a Lorentz-violating quantum gravity theory, focusing on its different versions, experimental consistency, black hole thermodynamics, gauge/gravity duality, and quantization efforts.

## Contribution

It provides a comprehensive update on the development, experimental tests, and theoretical advancements of Hořava gravity since its inception in 2009.

## Key findings

- Analysis of four main versions of Hořava gravity for self-consistency.
- Assessment of experimental constraints including solar system and cosmology.
- Progress in understanding black holes, thermodynamics, and quantum aspects of the theory.

## Abstract

Ho\v{r}ava gravity at a Lifshitz point is a theory intended to quantize gravity by using techniques of traditional quantum field theories. To avoid Ostrogradsky's ghosts, a problem that has been plaguing quantization of general relativity since the middle of 1970's, Ho\v{r}ava chose to break the Lorentz invariance by a Lifshitz-type of anisotropic scaling between space and time at the ultra-high energy, while recovering (approximately) the invariance at low energies. With the stringent observational constraints and self-consistency, it turns out that this is not an easy task, and various modifications have been proposed, since the first incarnation of the theory in 2009. In this review, we shall provide a progress report on the recent developments of Ho\v{r}ava gravity. In particular, we first present four most-studied versions of Ho\v{r}ava gravity, by focusing first on their self-consistency and then their consistency with experiments, including the solar system tests and cosmological observations. Then, we provide a general review on the recent developments of the theory in three different but also related areas: (i) universal horizons, black holes and their thermodynamics; (ii) non-relativistic gauge/gravity duality; and (iii) quantization of the theory. The studies in these areas can be generalized to other gravitational theories with broken Lorentz invariance.