II. International "Baskent" Congrees on Physcial, Social and Health Sciences, Ankara, Turkey, 25 - 26 September 2021, pp.148-153
We consider a test scalar field under the influence of external magnetic field in the near-horizon geometry of the BTZ black hole and analyse the effect of the magnetic field on the evolution of such a test field through solving the corresponding Klein-Gordon equation. We obtain an exact solution of the corresponding equation in terms of Whittaker function and accordingly arrive at a frequency spectrum. This frequency spectrum depends explicitly on the strength of the external magnetic field besides to the parameters of the geometric background. This fact allows us to analyse the effect of external magnetic field on the decay times for the considered test field and we discuss the effect of external magnetic field on the evolution of the test field. Our results imply that the presence of external magnetic field in the near horizon of the BTZ black hole may effect the time to be reached the thermal equilibrium of the BTZ black hole.