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

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