Abstract
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.
Highlights
INTRODUCTIONHawking and Page [1] discovered that there is a first order phase transition from the thermal Anti-de Sitter (AdS) space to the large AdS black hole at a certain critical temperature nearly forty years ago
We study Hawking radiation and P − v criticality of charged dynamical (Vaidya) black hole in Anti-de Sitter (AdS) space
By using the result of Hawking temperature derived from Damour-Ruffini method, we are able to calculate variety of the thermodynamic properties that will reveal the P − v criticality of charged dynamical (Vaidya) AdS black hole and its analogy with the van der Waals liquid-gas system, including the equation of state, the P −v diagram, critical point, heat capacities, and critical exponents near the critical point, et al Especially, it is shown that, when the rate of change of the black hole horizon exceeds a critical value, the ”P-v” criticality of the charged dynamical (Vaidya) AdS black hole will disappear
Summary
Hawking and Page [1] discovered that there is a first order phase transition from the thermal AdS space to the large AdS black hole at a certain critical temperature nearly forty years ago. By using the result of Hawking temperature derived from Damour-Ruffini method, we are able to calculate variety of the thermodynamic properties that will reveal the P − v criticality of charged dynamical (Vaidya) AdS black hole and its analogy with the van der Waals liquid-gas system, including the equation of state, the P −v diagram, critical point, heat capacities, and critical exponents near the critical point, et al Especially, it is shown that, when the rate of change of the black hole horizon exceeds a critical value, the ”P-v” criticality of the charged dynamical (Vaidya) AdS black hole will disappear This could be due to the dynamical effect caused by the accreting matters surrounding the black hole. We will take rH as a parameter and consider the dynamical effect on the ”P-v” criticality
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