We study the propagation of scalar fields in the background of \(2+1\)-dimensional Coulomb-like AdS black holes, and we show that such propagation is stable under Dirichlet boundary conditions. Then, we solve the Klein–Gordon equation by using the pseudospectral Chebyshev method and the Horowitz–Hubeny method, and we find the quasinormal frequencies. Mainly, we find that the quasinormal frequencies are purely imaginary for a null angular number and they are complex and purely imaginary for a non-null value of the angular number, which depend on the black hole charge, angular number and overtone number. On the other hand, the effect of the inclusion of a Coulomb-like field from nonlinear electrodynamics to general relativity for a vanishing angular number is the emergence of two branches of quasinormal frequencies in contrast with the static BTZ black hole.

我们研究了\(2+1\)背景下标量场的传播维库仑类 AdS 黑洞，我们表明这种传播在狄利克雷边界条件下是稳定的。然后，我们使用拟谱切比雪夫方法和 Horowitz-Hubeny 方法求解 Klein-Gordon 方程，并求出准正规频率。主要是，我们发现准正规频率对于零角数是纯虚数，对于角数的非零值，它们是复数和纯虚数，这取决于黑洞电荷、角数和泛音数。另一方面，从非线性电动力学到广义相对论的库仑类场对消失角数的影响是与静态 BTZ 黑洞形成对比的两个准法向频率分支的出现。