Horizon Structures and Effective Potential of Charged Black Holes Surrounded by Domain Walls

In our research, we investigate the horizon structure and effective potential of charged black holes immersed in domain walls within the two-component Kiselev spacetime framework. While superradiance and stability in Reissner-Nordström-de Sitter spacetimes are well-studied, the impact of negative-pressure domain walls, with a state parameter w=−2/3, remains less explored. These domain walls introduce unique curvature dynamics, modifying horizon structure, black hole stability, and conditions for superradiance.

Solving the Einstein equations, we reveal up to three distinct horizons—Cauchy, event, and cosmological—through an interplay of black hole mass M, charge Q, and curvature parameter K of the domain wall network. We constrain the parameter space using the dominant energy condition (DEC) and employ Mathematica and the implicit function theorem to identify metric roots and map configurations in 2D and 3D surfaces in parameter space. This analysis provides insight into how charge and curvature shape observable spacetime regions and influence superradiance phenomena.

Our next focus is on calculation quasinormal mode (QNM) frequencies, representing the characteristic oscillations of the perturbed black hole with this potential. Using analytical and numerical methods to compute these frequencies, we aim to uncover insights into black hole stability, gravitational wave signals, and how domain walls shape black hole evolution and observable characteristics.