热力学几何中的外曲率和内曲率
Extrinsic and intrinsic curvatures in thermodynamic geometry
摘要：
我们研究了物理系统的热力学几何中某些超曲面的内禀曲率和外禀曲率，并表明它们包含有用的热力学信息。对于反Reissner-Nordström-（A）de Sitter黑洞（Phantom），常数$Q$超曲面的外曲率与相变点附近的热容具有相同的符号.对于Kerr-Newmann-AdS（KN-AdS）黑洞，$Q \to 0$超曲面（Kerr黑洞）或$J \to 0$超曲面（RN黑洞）的外曲率与相变点附近的热容同号.非本征曲率在相变点处也发散。超曲面的内禀曲率在临界点处发散，但没有关于热容符号的信息。我们的研究解释了KN-AdS黑洞与RN黑洞和Kerr黑洞\cite{ref1}的热力学几何之间的一致关系。这种方法可以很容易地推广到一个任意的热力学系统。
英文摘要：
We investigate the intrinsic and extrinsic curvatures of certain hypersurfaces in the thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner-Nordström-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant $Q$ hypersurface has the same sign as the heat capacity around the phase transition points. For a Kerr-Newmann-AdS (KN-AdS) black hole, the extrinsic curvature of $Q \to 0$ hypersurface (Kerr black hole) or $J \to 0$ hypersurface (RN black black hole) has the same sign as the heat capacity around the phase transition points. The extrinsic curvature also diverges at the phase transition points. The intrinsic curvature of the hypersurfaces diverges at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN and Kerr ones \cite{ref1}. This approach can be easily generalized to an arbitrary thermodynamic system.
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