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We study Hawking radiation and $P-v$ criticality of charged dynamical(Vaidya) black hole in Anti-de Sitter (AdS) space. By investigating the nearhorizon properties of scalar field, we derive Hawking temperature of dynamicalcharged (Vaidya) AdS black hole. Based on this result, by regarding thecosmological constant as the thermodynamic pressure, we investigate the analogybetween the charged dynamical (Vaidya) AdS black holes in the ensemble with thefixed charge and van der Waals liquid-gas system in detail, including equationof state, $P-v$ diagram, critical point, heat capacities and critical exponentsnear the critical point. It is shown that the relationship among the criticalpressure, critical volume, and critical temperature gets modified while thecritical 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 exceedsthe critical value, the $P-v$ criticality of the charged dynamical (Vaidya) AdSblack hole will disappear.

Hawking Radiation and $P-v$ Criticality of Charged Dynamical (Vaidya) Black Hole in Anti-de Sitter Space