环面黑洞的热力学几何及临界行为

Thermodynamic geometry and critical behavior of a toroidal black hole

将几何方法应用于研究环面黑洞的热力学性质,计算了该黑洞的温度和热容,并探讨了黑洞热力学几何度规与黑洞的临界行为及相变特征之间的联系.结果表明:环面黑洞热力学温度等于其Hawking温度;由于其标量曲率等于零,因而环面黑洞的Weinhold度规不能给出关于该黑洞热力学临界行为及相变的任何信息;而环面黑洞的Ruppeiner度规和Legendre协变度规却能很好地反映出黑洞的相结构信息.

In this paper,we study the thermodynamic properties of a toroidal black hole from a geometric viewpoint.After the temperature and heat capacity of the black hole have been calculated,we investigate the relationship between its thermodynamic geometry metric and critical behavior,as well as phase transition characteristics.The results show that the temperature of the toroidal black hole is equal to its Hawking temperature.Moreover,because its curvature scalar is zero,the Weinhold geometry fails to provide some information about the critical behavior and phase transition characteristics of the toroidal black hole.But the Ruppeiner geometry and the Legendre invariant metric can provide a good description of its phase structure.