渐近AdS时空中能流边界条件的普适性及其应用研究

Boundary conditions play an important role in studying interactions between black holes and fundamental fields. One may obtain different physical results from same equations of motion by imposing various boundary conditions. The previous study of the applicant shows that, in order to obtain quasinormal modes, superradiant instabilities and bound states of Maxwell fields in asymptotically AdS black hole spacetimes, one has to impose energy flux to be vanished at infinity (energy flux boundary conditions). In particular, energy flux boundary conditions may produce a new branch of modes. This project aims at studying the universality of these boundary conditions and their applications. Firstly, we are going to study if these boundary conditions could be applied to other high spin fields, such as Dirac fields, Rarita-Schwinger fields, gravitational fields, and etc.; secondly, we are going to study if these boundary conditions are applicable to other gravitational theories, such as modified gravity theories with Gauss-Bonnet corrections; We are then going to apply these boundary conditions to look for quasinormal modes for various spin fields as well as in different gravitational theories, in particular for those which have not been explored in the literature (a new branch of modes).

边界条件在研究黑洞与基本物质场的相互作用方面起着重要的作用。同样的运动方程在考虑不同的边界条件时可以得到不同的物理结果。项目申请人的前期研究结果表明，为得到电磁场在渐近AdS黑洞时空中的似正模、超辐射不稳定性及束缚态，我们应当选取无穷远处能流为零的边界条件(能流边界条件)。特别地，能流边界条件能给出一类未被研究过的新模式。本项目致力于能流边界条件的普适性及其应用研究。首先，我们将研究能流边界条件是否适用于狄拉克场、Rarita-Schwinger场、引力场等其它高自旋场；其次，我们将研究能流边界条件是否适用于其它引力理论，比如Gauss-Bonnet修正的引力理论；最后，我们将应用这些边界条件，具体计算出不同自旋场在不同引力理论中的似正模，并探讨是否存在未被研究过的新结果(新的一类模式)。

由于引力/规范对偶的存在，对于渐近AdS黑洞时空的研究成为近年来人们关注的热门研究课题，特别是对于物质场与AdS黑洞的相互作用的研究。另外，由于AdS边界的类时特性，使得渐近AdS黑洞存在不同于其它黑洞时空的边界条件，从而导致很多新现象。本项目专注于研究渐近AdS黑洞时空中的普适的能流边界条件，并着重探讨其对高自旋场似正模的影响。具体而言，我们探讨了中性及带电狄拉克场和电磁场的边界条件并计算了它们在能流边界条件下的似正模，分析了背景参量和场参量对似正模的影响，揭示了AdS黑洞时空中物质场的动力学新特性。