Hawking radiation, local temperatures, and nonequilibrium thermodynamics of the black holes with non-Killing horizon

Recently, a class of stationary black hole solutions with non-Killing horizon in the asymptotic AdS bulk space (i.e., nonequilibrium funnel) was constructed to describe far from equilibrium heat transport and particle between boundary holes via AdS/CFT correspondence. It is generally believed that temperature can not be properly defined by conventional methods used Killing horizon. In this study, we calculate spectrum Hawking radiation funnel using Damour-Ruffini method. Our results indicate temperatures as well chemical potentials do depend on one spatial coordinates. This different horizon, where are uniform. Therefore, overall steady state while viewed local corresponding regarded being funnel. By AdS/CFT, discuss some possible implications our for thermodynamics dual conformal field theory. We further funnel, first law formulated entropy production rate equal sum changes entropies system (black environments second given larger than or zero. found time arrow emerged dissipation. also how dissipation may influence evaporation process