  We review a recently proposed effective Tolman temperature and present its
applications to various gravitational systems. In the Unruh state for the
evaporating black holes, the free-fall energy density is found to be negative
divergent at the horizon, which is in contrast to the conventional calculations
performed in the Kruskal coordinates. We resolve this conflict by invoking that
the Kruskcal coordinates could be no longer proper coordinates at the horizon.
In the Hartle-Hawking-Israel state, despite the negative finite proper energy
density at the horizon, the Tolman temperature is divergent there due to the
infinite blueshift of the Hawking temperature. However, a consistent
Stefan-Boltzmann law with the Hawking radiation shows that the effective Tolman
temperature is eventually finite everywhere and the equivalence principle is
surprisingly restored at the horizon. Then, we also show that the firewall
necessarily emerges out of the Unruh vacuum, so that the Tolman temperature in
the evaporating black hole is naturally divergent due to the infinitely
blueshifted negative ingoing flux crossing the horizon, whereas the outgoing
Hawking radiation characterized by the effective Tolman temperature indeed
originates from the quantum atmosphere, not just at the horizon. So, the
firewall and the atmosphere for the Hawking radiation turn out to be
compatible, once we discard the fact that the Hawking radiation in the Unruh
state originates from the infinitely blueshifted outgoing excitations at the
horizon. Finally, as a cosmological application, the initial radiation energy
density in warm inflation scenarios has been assumed to be finite when
inflation starts. We successfully find the origin of the non-vanishing initial
radiation energy density in the warm inflation by using the effective Tolman
temperature.
