Thermal Stability and QNMs of a Hairy Black Hole in the Presence of a Monopole Field

We study the stability of a generalization of the GHS-GM black hole in the presence of a dilaton and a monopole field. We find that the thermal behaviour of system depends on the scalar charge of the dilaton field and as this parameter is decreasing the system becomes more thermally stable. We also find that, as the charge of the black hole is increasing, both the real and the imaginary parts of the quasi-normal frequencies decrease in absolute value. The overtone modes die out faster than the fundamental modes and no positive imaginary parts appear, indicating the stabilty of the system