Extended Thermodynamic Study Of Black Holes In Phase Space

Since Michel and Laplace proposed the existence of objects from which light cannot escape,the possibility of the existence of black holes has been attracting scientists to study them.Modern astronomical observations suggest that black holes or objects with similar properties not only exist in our universe,but are likely to be distributed in large numbers throughout the universe.In view of this,the study of black holes is now driven not only by the fascinating theoretical unknowns possessed by these unique objects,but also to be able to better understand the universe around us.Since the emergence of the Bekenstein-Hawking entropy,it seems to be possible to look at black holes in a different way,for example,when considering them as a special thermodynamic system,black holes exhibit black hole thermodynamic properties that we can analogize to classical thermodynamic properties,especially in expanded phase space(AdS spacetime).We can well put it together with the Joule-Thomson expansion for an analogous study,this is a supplement to the thermodynamic system of black holes.In this paper,we study the Joule-Thomson expansion of the Lorentz violating massive gravity AdS black hole.We obtain the equation of state and the inversion temperature of the Lorentz violating massive gravity AdS black hole in the extended phase space,and in addition to this,we also study the inversion curve and the isoenthalpy curve on the T-P diagram.We find that the intersection of the inversion and isoenthalpy curves is exactly the inversion point,which can distinguish the cooling and heating regions.In addition,we find that the ratio of the minimum inversion temperature to the critical temperature is greater than 0.5 when for the case of parameter > 2.Our calculations show that for Lorentz violating massive gravity AdS black holes,their thermodynamic properties are sensitive to the parameter .In addition,we also studied the Joule-Thomson expansion of the exquisite RNAdS black hole with a string cloud,talked about the thermodynamic quantities and the equation of state of this black hole in the expanded phase space,analyzed the significance of the isoenthalpy curve and the inversion curve on the T-P diagram,and we can use the slope of the inversion curve or the isoenthalpy curve to distinguish whether the black hole is cooling or heating at this time,because the inversion curve is monotonically increasing,so this black hole is different from the When we calculate the ratio of the minimum reversal temperature to the critical temperature,we find that the ratio of the black hole,unlike other black holes,changes with the charge of the black hole,similar to the RN-AdS black hole at low charges,and changes abruptly at high charges,which is related to the characteristic of the black hole itself with a string cloud and being a delicate black hole.