SL(2, R) symmetry and quasi-normal modes in the BTZ black hole

With the help of two new intrinsic tensor fields associated with the SL(2, R) quadratic Casimir of Killing fields, we uncover the SL(2, R) symmetry satisfied by the solutions to the equations of motion for various fields in the BTZ black hole in a uniform way by performing tensor and spinor analysis without resorting to any specific coordinate system. Then with the standard algebraic method developed recently, we determine the quasi-normal modes for various fields in the BTZ black hole. As a result, the quasi-normal modes are given by the infinite tower of descendants of the chiral highest weight mode, which is in good agreement with the previous analytic result obtained by exactly solving equations of motion instead.