  We study Hawking radiation and $P-v$ criticality of charged dynamical
(Vaidya) black hole in Anti-de Sitter (AdS) space. By investigating the near
horizon properties of scalar field, we derive Hawking temperature of dynamical
charged (Vaidya) AdS black hole. Based on this result, by regarding the
cosmological constant as the thermodynamic pressure, we investigate the analogy
between the charged dynamical (Vaidya) AdS black holes in the ensemble with the
fixed charge and van der Waals liquid-gas system in detail, including equation
of state, $P-v$ diagram, critical point, heat capacities and critical exponents
near the critical point. It is shown that the relationship among the critical
pressure, critical volume, and critical temperature gets modified while the
critical exponents are not affected by the dynamical nature of the black hole.
We also find that, when the rate of change of the black hole horizon exceeds
the critical value, the $P-v$ criticality of the charged dynamical (Vaidya) AdS
black hole will disappear.

General Relativity and Quantum Cosmology