Nonexistence of quasinormal modes in the extremal BTZ black hole

TL;DR

This paper demonstrates that quasinormal modes do not exist in the extremal BTZ black hole due to the impossibility of ingoing flux at the degenerate horizon, aligning with the absence of propagating dynamics in its near-horizon geometry.

Contribution

It provides a proof that quasinormal modes cannot occur in the extremal BTZ black hole, clarifying the nature of perturbations in this spacetime.

Findings

Quasinormal modes cannot exist in the extremal BTZ black hole.

Ingoing flux into the degenerate horizon is impossible.

No propagating dynamics in the near-horizon limit of the extremal BTZ.

Abstract

We show that quasinormal modes cannot exist in the extremal BTZ black hole. For this purpose, we consider propagations of a minimally coupled scalar and a single massive graviton obtained from the cosmological topologically massive gravity on the extremal BTZ black hole. The would-be quasinormal modes for a scalar and graviton could not exist because it is impossible to make an ingoing flux into the extremal (degenerate) horizon. This is consistent with the argument that there is no propagating dynamics in the self-dual orbifold of AdS(3) which is just the near-horizon limit of the extremal BTZ black hole.