Quantum tunneling of Park black hole in IR modified Ho $$\check{\mathrm{r}}$$ava gravity with cosmological constant.

In this paper, we study the quantum tunneling of non-asymptotically flat Park black hole in IR modified Hořava gravity, as well as its thermodynamical stability. In order to calculate the quantum tunneling more comprehensively, Kraus-Parikh-Wilczek method and Hamilton-Jacoby method are used together. The results show that two methods give us the same logarithmic modified entropy, namely $$S = (\alpha - \Lambda _W) A/4\alpha + \pi /\alpha \ln A/4$$. This kind of logarithmic entropy is explained well by the effect of self-gravitation in quantum tunneling picture. At tow that the thermodynamics is stable for small case ( $$r_+ < r_3$$) and unstable for large case ( $$r_+ > r_3$$) where $$r_3$$ is the critical position of Park solution, which is concordant with asymptotically flat case shown by Kehagias-Sfetsos (Phys. Lett. B 678:127, ). [ABSTRACT FROM AUTHOR]