# Universal horizons and Hawking radiation in nonprojectable 2d Ho\v{r}ava gravity coupled with a non-relativistic scalar field

## TL;DR

This paper explores 2D Hořava gravity coupled with a scalar field, revealing the Hamiltonian structure, exact black hole solutions with universal horizons, and Hawking radiation with temperature related to surface gravity, extending understanding of quantum effects in modified gravity.

## Contribution

It provides the first detailed analysis of non-projectable 2D Hořava gravity with a scalar field, including Hamiltonian structure, exact solutions, and thermodynamic properties of universal horizons.

## Key findings

- Existence of black hole solutions with universal horizons.
- Hawking radiation at these horizons is thermal and related to surface gravity.
- The Hamiltonian analysis shows one local degree of freedom due to the scalar field.

## Abstract

In this paper, we study the non-projectable 2d Ho\v{r}ava gravity coupled with a non-relativistic scalar field, where the coupling is in general non-minimal and of the form $f(\phi)R$, where $f(\phi)$ is an arbitrary function of the scalar field $\phi$, and $R$ denotes the 2d Ricci scalar. In particular, we first investigate the Hamiltonian structure, and show that there are two-first and two-second class constraints, similar to the pure gravity case, but now the local degree of freedom is one, due to the presence of the scalar field. Then, we present various exact stationary solutions of this coupled system, and find that some of them represent black holes but now with universal horizons as their boundaries. At these horizons, the Hawking radiations are thermal with temperatures proportional to their surface gravities, which normally depend on the non-linear dispersion relations of the particles radiated, similar to the (3+1)-dimensional case.