Research On P-V Phase Transition Of AdS Black Hole In Modified Gravity

This paper studies the P-V phase transition of an asymptotic AdS black hole under modified gravity theory.The discovery of the four laws of black hole thermodynamics reveals the profound relationship between gravity and thermodynamics.Under this framework,black holes exhibit many properties similar to general thermodynamic systems,including P-V phase transitions and critical phenomena of Van der Waals-like systems.This article first briefly introduces the P-V critical phenomenon in the extended phase space of the RN-AdS black hole under Einstein's gravity.It has the same first-order phase transition and critical point as the P-V critical phenomenon in Van der Waals.The key point is the definition of the black hole thermodynamic pressure.In general AdS black holes,the pressure is defined as P=-?/8? related to the cosmological constant A.Under this definition,the critical phenomenon and critical exponent of RN-AdS black holes can be obtained.The above discussion in Einstein's theory can also be extended to the modified gravitational theory.The focus of this paper is on the P-V critical phenomenon in Horndeski's modified gravitational theory,which contains a scalar field.We discussed this issue and found that the pressure definition is no longer applicable in the asymptotic AdS black hole solution of Horndeski's modified gravitational theory,and is replaced by an effective cosmological constant related to asymptotic behavior P=-?eff/8?.Under this definition,the critical P-V phenomenon of the asymptotic AdS black hole solution under Horndeski's gravity was found.Different from the general asymptotic AdS black hole critical phenomenon,this critical phenomenon occurs not only when the cosmological constant is negative,but also when it is positive and zero.This means that P=-?/8? does not apply to all pressure definitions in asymptotic AdS gravity,which may imply that the definition of pressure P=?/8? is not the only pressure candidate for black hole at the microscopic level.In addition,the critical exponent of Horndeski's gravitational P-V critical phenomenon is calculated.The results are consistent with the mean field theory.