In this article, we demonstrate how black hole quasi-normal modes can emerge
from a Dirichlet brickwall model normal modes. We consider a probe scalar field
in a BTZ-geometry with a Dirichlet brickwall and demonstrate that as the wall
approaches the event horizon, the corresponding poles in the retarded
correlator become dense and yield an effective branch-cut. The associated
discontinuity of the correlator carries the information of the black hole
quasi-normal modes. We further demonstrate that a non-vanishing angular
momentum non-perturbatively enhances the pole-condensing. We hypothesize that
it is also related to quantum chaotic features of the corresponding spectral
form factor, which has been observed earlier. Finally we discuss the underlying
algebraic justification of this approximate thermalization in terms of the
trace of the algebra.
In this article, we have explored how black hole quasi-normal modes can emerge from a Dirichlet brickwall model normal modes. Our study focuses on a probe scalar field in a BTZ-geometry with a Dirichlet brickwall, and we have demonstrated that as the wall gets closer to the event horizon, the poles in the retarded correlator become dense, resulting in an effective branch-cut. The presence of this branch-cut signifies the existence of black hole quasi-normal modes.
One significant finding of our research is that a non-vanishing angular momentum plays a crucial role in enhancing the condensing of poles. This enhancement may also be linked to quantum chaotic features observed in the spectral form factor. These findings provide important insights into the relationship between quantum chaos and black hole properties.
Going forward, there are several potential challenges and opportunities for further exploration in this field. Firstly, it would be valuable to investigate the behavior of other fields, such as electromagnetic or gravitational fields, in the context of a brickwall model. This could shed light on the universality of our findings and provide a more comprehensive understanding of black hole quasi-normal modes.
Additionally, studying the effect of different geometries and boundary conditions on the emergence of quasi-normal modes could yield interesting results. It would be particularly intriguing to explore how deviations from the BTZ-geometry impact the density of poles and the associated branch-cut.
Furthermore, our hypothesis regarding the connection between pole-condensing and quantum chaotic features in the spectral form factor warrants further investigation. Exploring this relationship in more detail could offer valuable insights into the underlying mechanisms of quantum chaos and its manifestation in black hole physics.
Lastly, it would be worthwhile to delve deeper into the algebraic justification of the approximate thermalization observed in terms of the trace of the algebra. Understanding the algebraic aspects of thermalization could provide a more rigorous foundation for our findings and potentially open up new avenues for research.
In conclusion, our study has revealed the emergence of black hole quasi-normal modes from a Dirichlet brickwall model. The role of angular momentum and its connection to quantum chaos have been highlighted. Future research should focus on exploring other fields, geometries, and boundary conditions, investigating the relationship between pole-condensing and quantum chaos, and further exploring the algebraic justification of thermalization.