# Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

## TL;DR

This paper investigates how noncommutative geometry influences fermionic quasinormal modes of the BTZ black hole, revealing modifications in horizon temperatures and supporting holography in a noncommutative context.

## Contribution

It introduces a duality between spinless and spinning BTZ black holes in noncommutative space and explores the effects on quasinormal modes and Hawking radiation.

## Key findings

- Noncommutative contributions alter horizon temperatures.
- Equivalence between quasinormal and non-quasinormal modes is established.
- Analysis of fermion emission and tunneling amplitudes in noncommutative geometry.

## Abstract

We analyze the fermionic quasinormal modes of the BTZ black hole in the presence of space-time noncommutativity. Our analysis exploits a duality between a spinless and spinning BTZ black hole, the spin being proportional to the noncommutative deformation parameter. Using the AdS/CFT correspondence we show that the horizon temperatures obtained from the dual CFT pick up noncommutative contributions. We demonstrate the equivalence between the quasinormal and non-quasinormal modes for the noncommutative fermionic probes, which provides further evidence of holography in the noncommutative setting. Finally we present an analysis of the emission of Dirac fermions and the corresponding tunneling amplitude within this noncommutative framework.