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

Abstract

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.

JHEP style, 1+13 pages, version to appear in JHEP

References in corpus (4)

• Warped AdS_3 Black Holes
• Hidden Conformal Symmetry and Quasi-normal Modes
• Self-Dual Warped AdS${}_3$ Black Holes
• Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry

Cited by in corpus (2)

• $SL(2,R)\times U(1)$ symmetry and quasinormal modes in the self-dual warped AdS black hole
• $sl(2,\mathds{C})\times D$ symmetry and conformal primary basis for massless fields