de Sitter时空黑洞熵和热力学相变性质

In de Sitter (dS) spacetime, both black hole horizon and cosmological horizon exist at the same time if the parameters of the spacetime are appropriately chosen. In general the radiation temperatures of the two horizons are not equal, so dS spacetime is not in thermodynamic equilibrium. The thermodynamic quantities corresponding to the two horizons meet the laws of black hole thermodynamics respectively, but they are not independent and the entropy entangles each other. We will investigate the modification of the entropy of the whole spacetime on the base of the black hole thermodynamics and entropy proposed by other scholars. Considering the results on the entropy, we will establish a thermodynamic equation for the quantities of state of the spacetme to build a modified thermodynamic theory of dS spacetime. Therefrom we will discuss the behaviors and properties about phase transition of dS spacetime. We will also investigate the effects of field parameters to entropy and phase transition behaviors of dS black holes when a external field exists. It will contribute to further understand the thermodynamic quantities of dS spacetime. Furthermore it is significant to analyze the evolution process of dS spacetime and perfect a self-consistent thermodynamic geometric theory of dS spacetime by investigating the modification of entropy of dS spacetime, analyzing its effects to the phase transition, and proposing a reasonable explanation for the phase transition of dS spacetime thermodynamic system.

当参数取适当的值时，de Sitter（dS）时空具有黑洞视界和宇宙视界，两视界对应的辐射温度一般不相等，因而dS时空处于热力学非稳态。两视界对应的热力学量分别满足黑洞热力学定律，但两视界对应的热力学量并非独立，推断两视界的熵存在“纠缠”。我们将在黑洞热力学和前人给出的dS时空黑洞的熵的基础上研究熵的修正。考虑熵的修正结论，建立时空态参量满足的热力学方程，得到修正的dS时空的热力学理论。由此研究dS时空黑洞的相变性质及其行为。讨论在外场的作用下，场参数对黑洞熵及其热力学相变的影响。探究不同dS时空中黑洞熵的修正，分析修正项对相变的影响，给出合理的dS时空热力学系统相变理论解释，这不仅有助于更进一步深入认识dS时空热力学量，而且对分析其演化过程和完善自洽的dS时空热力学几何理论有着极其重要的意义。

将dS时空黑洞视界和宇宙视界之间的区域看作一个热力学系统，考虑两视界之间的关联，我们做了以下工作：（1）我们推导了多种dS时空黑洞熵的修正项的表达式，总结得到一般表达式；（2）由dS黑洞熵的修正项得到两视界之间的熵力，讨论了熵力与宇宙膨胀之间的关联；（3）将dS时空两视界之间的熵力与微观粒子之间的相互作用力（分子力）相比较，得出它们相似的结论；（4）利用熵的修正项推导出多种dS时空系统的一系列等效热力学量，并利用等效热力学量分析了时空系统的热力学稳定性和相变问题；（5）在以上各个工作中分析了涉及到的场参量和维数的影响。我们的工作对研究dS时空的热力学问题提以及研究宇宙的加速膨胀供了一种基本思路和方法．