Black Hole Phase Transition And Thermodynamic Geometry

What is the microscopic structure of black hole?Perhaps we could never get the final result before the correct quantum gravity is built.But perhaps we could get clues for it from the consideration of black hole thermodynamics and phase transition.As is the studies of thermodynamics in the 19~thh century,which lead to the understanding of microscopic structure of matter and the building of quantum theory and standard model.This thesis investigates the thermodynamics of Grumiller black hole and BTZ black hole.This thesis presents a geometric derivation of the integral formula of the first law for Grumiller black hole,which is an exact example the the mass of the whole space-time is infinite,but the mass of the black hole is finite.The results show that the Rindler acceleration should be considered as a new thermodynamic variable.Having the first law,this thesis investigates Ruppeiner geometry and Quevedo geometry for Grumiller black hole.The Ruppeiner geometries for Rindler acceleration fixed ensemble and pressure fixed ensemble are curved.To uncover possible microscopic interactions,we plot the graphs for curvature scalar of Ruppeiner geometries and study its behavior.For pressure fixed ensemble,we find,by comparing with heat capacity,the vanishing point of curvature scalar indicating the change of stability.While,the Quevedo geometry shows there exists a second order phase transition for Grumiller black hole.This thesis also investigates the thermodynamics and Ruppeiner geometry for BTZ black hole.The Ruppeiner geometry for angular momentum fixed ensemble is curved,but the Ruppeiner geometry for pressure fixed ensemble is flat.This thesis presents a review for the interpretation of Ruppeiner geometry,but with no definite result.The results of Ruppeiner geometries for BTZ black hole further support that the curvature scalar of Ruppeiner geometry sometimes indeed encode information about the system's stability.