# Spectroscopy of Rotating Linear Dilaton Black Holes From Boxed Quasinormal Modes

## TL;DR

This paper analytically derives the resonance spectra of confined scalar fields around rotating linear dilaton black holes and uses these results to explore their entropy and area quantization.

## Contribution

It provides an analytical calculation of boxed quasinormal modes for rotating linear dilaton black holes, linking these modes to entropy and area spectra.

## Key findings

- Derived boxed quasinormal mode frequencies analytically.
- Connected quasinormal modes to black hole entropy and area spectra.
- Validated the use of Maggiore's method for this black hole geometry.

## Abstract

Numerical studies of the coupled Einstein-Klein-Gordon system have recently revealed that confined scalar fields generically collapse to form caged black holes. In the light of this finding, we analytically study the characteristic resonance spectra of the confined scalar fields in rotating linear dilaton black hole geometry. Confining mirrors (cage) are assumed to be placed in the near-horizon region of a caged rotating linear dilaton black hole $\frac{r_{m}-r_{2}}{r_{2}}\ll 1$ ($r_{m}$ is the radius of the cage and $r_{2}$ represents the event horizon). The radial part of the Klein-Gordon equation is written as a Schr\"{o}dinger-like wave equation, which reduces to a Bessel differential equation around the event horizon. Using analytical tools and proper boundary conditions, we obtain the boxed-quasinormal mode frequencies of the caged rotating linear dilaton black hole. Finally, we employ Maggiore's method, which evaluates the transition frequency in the adiabatic invariant quantity from the highly damped quasinormal modes, in order to investigate the entropy/area spectra of the rotating linear dilaton black hole.