Near Horizon Geometry of Warped Black Holes in Generalized Minimal Massive Gravity

Abstract: We consider spacelike warped AdS$_{3}$ black hole metric in Boyer-Lindquist coordinate system. We present a coordinates transformation so that it maps metric in Boyer-Lindquist coordinates to the one in Gaussian null coordinates. Then we introduce new fall-off conditions near the horizon of non-extremal warped black holes. We study the near horizon symmetry algebra of such solutions in the context of Generalized minimal massive gravity. Similar to the black flower solutions, also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the warped black flower solutions. We show that the vacuum state and all descendants of the vacuum have the same energy. Thus these zero energy excitations on the horizon appear as soft hairs on the warped black hole.