关于de Sitter相对论及黑洞问题的研究

This project, along the route of the domestic original work of de Sitter (dS) special relativity, aims at the study on dS general relativity and black hole. In the 1970s, Lu et al generalize the principle of relativity, and establish new special relativity in dS/Anti-dS space-time with Beltrami metric(BdS). After the discovery of cosmic acceleration, dS relativity attracted wide interest. However, the distinction of dS and Einstein's relativity could only be observed in cosmoscopic scale, hence cosmology and dS general relativity, which has not been studied enough, are needed to explore. This project will mainly study dS general relativity, describe dS gravity, and get new exact solutions of the Einstein field equations. Using the metric obtained and following the Hamiltonian formalism, Unruh effect will be explored, to distinguish dS and Einstein's relativity. Hawking radiation will be studied: the temperature will be calculated with Hawking's and Unruh's methods; the entropy will be calculated with the brick wall model and quantum tunneling method. By comparing Unruh effect and Hawking radiation, this project will find out advantage of inertial BdS frames, and seek some suitable effects to check whether dS group is the real space-time symmetry.

本项目沿着国内原创性工作de Sitter(dS)狭义相对论的路线，进一步研究dS广义相对论及黑洞问题。70年代陆启铿等把相对性原理推广，在Beltrami度规的非零常曲率dS(BdS)/Anti-dS时空建立狭义相对论。宇宙加速膨胀发现后，dS相对论引起广泛兴趣。但只有宇观尺度时dS和爱因斯坦相对论才可观测区分，故需深入探索尚未得到充分研究的dS广义相对论和宇宙学。本项目主要研究dS广义相对论，描述dS引力，求解引力场方程的新严格解。利用求得的度规，基于先前研究的哈密顿形式量子化，探讨dS相对论的Unruh效应，从物理效应本质上把渐近BdS和Minkowski的相对论区分开。用霍金的和Unruh的方法，计算黑洞辐射的温度，用砖墙模型和量子隧穿方法计算熵。本项目通过对比研究Unruh效应、霍金辐射，找出局域BdS惯性系的优势，寻求效应和方案检验时空对称性是dS群还是Poincaré群。

本项目沿着国内原创性工作de Sitter(dS)狭义相对论的路线，进一步研究了dS广义相对论。70年代国内学者在dS时空用Beltrami度规(BdS)建立狭义相对论。随着宇宙加速膨胀发现，dS相对论引发研究热忱。本项目推进此原始创新研究dS广义相对论，描述dS引力，求解爱因斯坦引力场方程的渐近BdS的新形式的解。成功得到Kerr-Newman-BdS(KN-BdS)等一系列解。讨论了这些解的性质和物理意义，从物理效应本质上把渐近BdS和Minkowski的相对论区分开。也在数学上重新探讨了严格描述BdS惯性系等问题。还得到基于Beltami惯性坐标做微扰论的办法，量子化将在延续工作更严格论证，从而完成Unruh效应、霍金辐射等问题的计算。