Thermodynamics and quasinormal modes of the regular Dymnikova-Letelier black hole

Abstract: In this work, we investigate the thermodynamic properties and quasinormal modes of a regular Dymnikova-Letelier black hole. Starting from the Einstein field equations sourced by an effective anisotropic fluid, we analyze the resulting spacetime geometry and derive the associated thermodynamic quantities, including the Hawking temperature, heat capacity, and Gibbs free energy. The thermodynamic analysis reveals the existence of phase transitions characterized by divergences in the heat capacity, whose location depends sensitively on the string fluid parameter. We then study the dynamical response of the system under scalar perturbations by computing the quasinormal mode spectrum using the sixth-order WKB approximation. Our results show that, for all considered values of the parameters, the imaginary part of the quasinormal frequencies remains negative, while the real part stays positive, indicating the stability of the black hole under scalar perturbations. Furthermore, the presence of the string fluid leads to systematic shifts in both the oscillation frequencies and damping rates. These results demonstrate that the string fluid significantly affects both the thermodynamic behavior and the dynamical stability of the Dymnikova-Letelier spacetime.