Motivated by recent works [1,2], the influences of self-gravitational interaction on the Hawking radiation are studied both for (3 + 1) and (4 + 1) dimensional black holes in z = 4 Hoȓava-Lifshitz gravity. It is found that the tunneling entropies S B(3+1) and S B(4+1) independent on particle's mass are consistent with the thermodynamical entropies S BH(3+1) and S BH(4+1) , respectively. There is a very visible degree of uniformity between thermodynamics and quantum tunneling in z = 4 Hoȓava-Lifshitz gravity. It suggests that the entropies contained corrected terms could be explained well by the self-gravitational interaction of Hawking radiation. The study of tunneling process may shed light on understanding the Hoȓava-Lifshitz gravity.

The apparent discovery of logarithmic entropies has a significant impact on IR deformed Hořava–Lifshitz (IRDHL) gravity in which the original infrared (IR) property is improved by introducing three-geometry's Ricci scalar term "μ4 R" in action. Here, we reevaluate the Hawking radiation in IRDHL by using recent new Hamilton–Jacobi method (NHJM). In particular, a thorough analysis is considered both in asymptotically flat Kehagias–Sfetsos and asymptotically non-flat Park models in IRDHL. We find the NHJM offers simplifications on the technical side. The modification in the entropy expression is given by the physical interpretation of self-gravitation of the Hawking radiation in this new Hamilton–Jacobi (HJ) perspectives.