中文摘要：

研究了带电的有质量标量场微扰下Reissner-Nordstrosm anti-de Sitter黑洞的稳定性问题．在乌龟坐标下推导出了标量场所满足的径向运动方程，并给出有效势．采用有限差分法将标量场所满足的波方程进行离散化．通过数值计算研究了扰动场随时间的演化．研究结果表明，随着时间的演化，带电的标量场在晚期会出现暴涨．这就意味着在带电的标量场扰动下，Reissner-Nordstrosm anti-de Sitter黑洞会出现不稳定．随着标量场电荷的增加，扰动场在晚期出现暴涨的速度将加快．随着标量场质量的增加，扰动场暴涨的速度将减慢．

英文摘要：

The stability of Reissner-Nordstr?m anti-de Sitter black hole under charged massive scalar field perturbation is studied.In the tortoise coordinate, the radial equation of motion of the scalar field is derived, and the effective potential is obtained.Using the finite difference method, the wave equation of the the scalar field is discretized.From a numerical investigation, the time domain profiles of the perturbation field is studied.The re-sults show that with the evolution of the time, the charged scalar field increased greatly at late time.It means that the Reissner-Nordstr?m anti-de Sitter black hole is unstable under charged scalar field perturbation.With the in-crease of the charge of the scalar field, the growth of the perturbation at late time would speed up.With the in-crease of the mass of the scalar field, the growth of the perturbation would slow down.