含NUT荷时空和加速黑洞的热力学及其超引力解的推广

Hawking和Mann等著名专家证明含NUT荷欧氏时空的引力熵不等于其视界面积的1/4，它还包含来自Misner弦的贡献。另一方面，对加速黑洞热力学性质到目前为止很少给出过正确的分析。本项目致力于对广义相对论(GR)中此两类4维时空的热力学做出崭新研究，推导出自洽的热力学第一定律和Smarr质量公式，并将它们推广到4维STU规范超引力中，构造出含NUT荷和加速参数的最一般非极端转动带电AdS严格解，并深入研究其热力学性质。..主要研究内容为：(1)借助于引入新的热力学变量，推导出GR中含NUT荷时空的自洽的热力学第一定律和Smarr质量公式；(2)把前述工作推广到含宇宙学常数的转动带电情形和高维(带电)情形；(3)研究GR中加速黑洞的热力学性质，给出热力学第一定律和Smarr公式；(4)构造STU规范超引力含NUT荷和加速参数的最一般非极端转动AdS4精确解，并研究其热力学性质。

Hawking, Mann and others showed that gravitational entropies of NUT-charged Euclidean spacetimes are not equal to one quarter of areas of their event horizons (bolts), rather they still contain the contribution from the Misner string. On the other hand, thermodynamic properties of accelerating black holes have almost never been correctly analyzed. Already known results in the existing literature indicate that these two kinds of spacetimes might become counterexamples to General Relativity (GR) in the aspect of thermodynamics. This program will be devoted to undertaking novel studies on the thermodynamics of these two kinds of D=4 spacetimes and higher dimensional NUT-charged spacetimes in GR, as well as their extensions to D=4 STU gauged supergravity theory. What is more, we shall construct the most general rotating charged AdS4 solutions containing a nonzero NUT charge and an acceleration parameter in D=4 STU gauged supergravity, and further investigate deeply their thermodynamic properties...The main subject will be: (1)Aided by introducing new thermodynamic quantities, we will study thermodynamics of D=4 NUT-charged spacetimes in GR and derive consistently the first law and Smarr’s formula; (2)The above work will be extended to the cases of the Kerr-Newman-NUT-AdS4 spacetime and higher dimensional charged AdS spacetimes with (single or multiple) NUT charge parameters in GR; (3)We will investigate thermodynamic properties of D=4 accelerating black holes in GR and derive the first law and Smarr's formula; (4)Our final aim is to construct the most general nonextremal rotating charged AdS4 solutions with a nonzero NUT charge and an acceleration parameter, four independent electric charge and four independent magnetic charge parameters in STU gauged supergravity theory, and to investigate their thermodynamics in more detail.