Propagation of a scalar field with non-minimal coupling in three dimensions: Hawking radiation and Quasinormal modes

In this paper we investigate an exact spectrum of quasi normal modes (QNMs) for perturbations of a scalar field coupled non-minimally with the Einstein tensor of an uncharged, non-rotating Banados, Teitelboim, and Zanelli (BTZ) black hole in three-dimensional spacetime. Due to the geometry around the black hole, the scalar field encounters an effective potential barrier. We study this potential numerically and derive exact numerical results for the greybody factors (GFs) and discuss their profiles in terms of the coupling constant and black hole parameters. We then proceed to derive the Hawking radiation spectrum for BTZ black hole.