de Sitter-Schwarzschild正则黑洞的质量标量场扰动

Perturbations of the massive scalar field around de Sitter-Schwarzschild regular black hole

采用数值计算方法对de Sitter-Schwarzschild正则黑洞在质量标量场微扰下的稳定性问题进行了探讨,并计算它在扰动下的似正则模和分析了它的性质。首先讨论了de Sitter-Schwarzschild正则黑洞的构型:具有de Sitter时空的中心,外部平滑连接Schwarzschild时空,并验证它的时空无奇性。然后计算黑洞时空中的质量标量场扰动方程,分析有效势的特性。之后再利用3~6阶WKB近似计算扰动的似正则模,计算结果表明:de Sitter中心相关的参数r_(0)^(2)=3/Λ对质量标量场扰动下的似正则模影响很小;角量子数l对似正则模的作用与Schwarzschild黑洞相似;标量场的质量m^(2)变化对似正则模的影响与Schwarzschild黑洞的情况有显著的不同,这也成为区分该黑洞与Schwarzschild黑洞的关键因素。

The numerical method is used to discuss the stability of de Sitter-Swarzschild regular black hole(dSS BH)under the perturbation of the mass scalar field,and quasinormal modes under the perturbation is calculated and analyzed.First,the configuration of de Sitter-Schwarzschild regular black hole is discussed:it has the center of de Sitter spacetime and the outside smoothly connects Schwarzschild spacetime,and its singularity of spacetime is verified.According to the Klein-Gordon equation the perturbation of the massive scalar field around dSS BH is described,and the characteristics of the effective potential are analyzed.Then the quasinormal modes of perturbation is calculated by using the 3-6 order WKB approximation method.The results show that the parameters r_(0)^(2)=3/Λ have little effect on quasinormal modes;the influence of multipolar index l on quasinormal modes is similar to that of Schwarzschild black holes;but the mass m^(2) of the scalar field on the quasinormal modes is significantly different from that of the Schwarzschild black hole,which also becomes the key factor to distinguish the black hole from the Schwarzschild black hole.