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

TL;DR

This paper investigates the near horizon geometry and symmetries of warped black holes in generalized minimal massive gravity, revealing a Heisenberg algebra structure and zero-energy soft hairs on the horizon.

Contribution

It introduces new fall-off conditions and identifies the near horizon symmetry algebra as a Heisenberg algebra in the context of warped black holes.

Findings

Heisenberg algebra as the near horizon symmetry

Vacuum and descendants have same energy

Soft hairs with zero energy on the horizon

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.