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چكيده انگليسي :

Generalization of Ehrenfest s Equations for Black Holes with Three Parameters and Phase Transition in Black Holes Mohammad Bagher Jahani Poshteh mb jahaniposhteh@ph iut ac ir 19 9 2012 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Dr Behrouz Mirza b mirza@cc iut ac ir Abstract The celebrated prediction of black hole entropy and Hawking radiation made black hole thermody namics an interesting field in cosmology and high energy physics Black hole as a solution to Einstein field equation behaves like a thermodynamic system One of such thermodynamic properties is the phase transition between locally stable and unstable black hole investigated by Davies for the first time in 1977 An important question about this phase transition is the order of transition The order of phase transition shows that whether entropy and volume of a system change continuously or discontinuously in the transition If these changes are discontinuous then the transition is of first order otherwise it is called a higher order or continuous transition This kind of classification which this thesis heavily relies on is named after Ehrenfest In this thesis we investigate thermodynamic phase transition for a large class of black holes In these black holes there was a possibility of second order phase transition caused by the discontinuity in specific heat which is proportional to second derivative of free energy In ordinary thermodynamics there are two Ehrenfest s equations which are supposed to be true at the point of second order phase transition We show that Ehrenfest s equations are satisfied at the point in which specific heat is discontinuous so there occurs a second order phase transition in canonical and for some black holes also in grand canonical ensemble We study some useful definitions in ensemble theory of black holes throughout this dissertation In canonical ensemble extensive parameters such as electrical charge or angular momentum are sup posed to be fixed at the boundary of black hole In grand canonical ensemble extensive parameters can be exchanged between black hole and its environment We also investigate Kerr Newman black hole which has three degrees of freedom In this case there are also two mixed ensembles which are defined by taking one extensive parameter and one intensive parameter to be fixed at the horizon while their conjugate quantities can be changed The discontinuity of specific heat reflects the possibility of the second order phase transition in canonical and two mixed ensembles However there are differences between the second order phase transition in black holes and ordinary thermodynamic systems for which the discontinuity of specific heat is not an infinite one Usual Ehrenfest s equations are written for systems with two degrees of freedom so they are helpless for Kerr Newman black hole with three degrees of freedom In this thesis we generalize Ehrenfest s equations We find seven new equations with six new parameters that diverge at the same point in which the heat capacity diverges We show that all generalized Ehrenfest s equations are satisfied at the divergent point of specific heat in canonical and two mixed ensembles So Kerr Newman black hole undergoes a second order phase transition in these ensembles

جهاني پشته، محمدباقر

تعميم معادلات اهرنفست براي سياه چاله هاي سه پارامترهاي و گذار فاز سياه چاله ها

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