Unitarity issue in BTZ black holes

TL;DR

This paper investigates unitarity in various three-dimensional AdS black hole spacetimes by analyzing wave equations, revealing non-unitary behavior in non-rotating BTZ black holes and potential unitarity in extremal cases.

Contribution

It provides an exact frequency condition analysis for wave modes in different BTZ black hole spacetimes, highlighting unitarity issues and potential unitary candidates.

Findings

Non-rotating BTZ black hole exhibits quasinormal modes indicating non-unitarity.

Pure AdS spacetime shows real, discrete modes confirming unitarity.

Extremal BTZ black holes have real, continuous modes suggesting unitarity.

Abstract

We study the wave equation for a massive scalar in three-dimensional AdS-black hole spacetimes to understand the unitarity issues in a semiclassical way. Here we introduce four interesting spacetimes: the non-rotating BTZ black hole (NBTZ), pure AdS spacetime (PADS), massless BTZ black hole (MBTZ), and extremal BTZ black hole (EBTZ). Our method is based on the potential analysis and solving the wave equation to find the condition for the frequency $\omega$ exactly. In the NBTZ case, one finds the quasinormal (complex and discrete) modes which signals for a non-unitary evolution. Real and discrete modes are found for the PADS case, which means that it is unitary obviously. On the other hand, we find real and continuous modes for the two extremal black holes of MBTZ and EBTZ. It suggests that these could be candidates for the unitary system.