Study Of Geometrothermodynamics For(2+1)-dimensional Spinning Dilaton Black Hole

In this thesis, we first introduce the foundation of general relativity, which includes the metric, connection, Riemann tensor and Ricci tensor et. al.Then we introduce the basis of black hole physic:the produce of black hole, its evolvement and classification. We give a brief introduction of Schwarzschild black hole and Kerr-Newman black hole.At last, we mainly study the geometrothermodynamics of (2+1)-dimensional spinning dilaton black hole. We show that the Ruppeiner curvature vanishes, which implies that there exist no phase transitions and thermodynamic interactions. However, when the thermodynamics fluctuation is included, the geometry structure is reconsidered. The non-vanishing Ruppeiner curvature is obtained, which means the phase space is non-flat. We also study the phase transition and show that it can indeed take place at some points.