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چكيده انگليسي :

Thermodynamic Geometry of BTZ Black Hole with Cosmological Constant as a Thermodynamic variable Zahra Khaksari z khaksari@ph iut ac ir Date of Submission 10 04 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Behrouz Mirza b Mirza@cc iut ac ir AbstractIt has been recognized from a semi classical analysis that black holes are thermodynamic objects with aBekenstein Hawking entropy and a Hawking temperature However it has been established that thethermodynamic properties of black holes depend crucially on the choice of statistical ensemble in contrastto conventional thermodynamic system The fact that different ensembles lead to different heat capacitiesimplies that the phase transition structure depends on the statistical model under consideration It isgenerally thought that the local stability of a black hole is mainly determined by its heat capacity Negative heat capacity usually gives a thermodynamically unstable system and the positive one implies astable one The points where the heat capacity diverges are usually consistent with the points where thesecond order phase transition takes place The properties of a thermodynamic system can also be studiedwith the ideas of geometry An important question is how to construct a metric in this space Weinholdfirstly introduced the geometrical concept into the thermodynamics Few years later Ruppeinerintroduced another metric In particular it was found that the Ruppeiner geometry carries the informationof phase structure of a thermodynamic system In general its curvature is singular at the points where thephase transition takes place However for the rotating BTZ and Reissner Nordstrom RN black holes the cases are quite different The Ruppeiner geometry lead to a zero curvature which means there exist nophase transition points However there is phase transition for BTZ and RN black holes For thiscontradiction many researches has been carried out to explain it Queved et al pointed out that the originof the contradiction is that the Ruppeiner metric are not Legendre invariant A Legendre invariant metricwas introduced by them which could reproduce correctly the behavior of the thermodynamic interactionsand phase transitions for the BTZ and RN black holes and other black hole Liu et al introduced a newthermodynamical metric and demonstrate with various black holes in ADS Background that thedivergence of the specific heat corresponds to the curvature singularity In this thesis we studythermodynamic of some type of black holes on the state space Firstly we obtained thermodynamiccurvature by using the Quevedo Metric for Kerr Newman and Kerr ADS black hole The thermodynamicstability is also studied Under the assumption of an invariable cosmological constant the integral massformulas in the case of rotating black holes in ADS and dS backgrounds can never be satisfied any more Thus we study phase structure of BTZ black hole by considering the cosmological constant as a variable We discussed the local thermodynamics stability of BTZ black hole through the heat capacity Also weexamine the correspondence between curvature singularities and phase transition point by Ruppeiner Quevedo and Liu metrics Finally we found that only the Quevedo metric failed to predict the behavior ofphase space completely It should be noted that this result is also valid for Kerr DS sitter Space time Keywords Thermodynamics Black Holes Geometry Phase Transition Heat Capacity

خاكساري، زهرا

هندسه ي ترموديناميك سياهچاله ي بي-تي-زد چرخان با ثابت كيهان شناسي به عنوان متغير ترموديناميكي

هندسه , گذار فاز , ظرفيت گرمايي