Quasibound states of massive charged scalars around dilaton black holes in $2+1$ dimensions: Exact frequencies

TL;DR

This paper analytically solves for quasibound states of charged massive scalars around 3D dilaton black holes, revealing how these frequencies depend on physical parameters and highlighting the model's relevance for black hole physics and analog gravity experiments.

Contribution

It provides exact solutions for quasibound state frequencies in a 2+1D dilaton black hole background, a novel analytical approach in this context.

Findings

Exact quasibound state frequencies derived analytically.

Dependence of frequencies on scalar and black hole parameters analyzed.

Highlights the role of the cosmological constant in perturbation behavior.

Abstract

In this work, we investigate massive charged scalar perturbations in the background of three-dimensional dilaton black holes with a cosmological constant. We demonstrate that the wave equations governing the dynamics of these perturbations are exactly solvable, with the radial part expressible in terms of confluent Heun functions. The quasibound state frequencies are computed analytically, and we examine their dependence on the scalar field's mass and charge, as well as on the black hole's mass and electric charge. Our analysis also underscores the crucial role played by the cosmological constant in shaping the behavior of these perturbations. This specific black hole metric arises as a solution to the low-energy effective action of string theory in $2+1$ dimensions, and it holds potential for experimental realization in analog gravity systems due to the similarity between its surface gravity and that of acoustic analogs. Moreover, the analytic tractability of this system offers a valuable testing ground for exploring aspects of black hole spectroscopy, stability, and quantum field theory in curved spacetime. The exact solvability facilitates deeper insights into the interplay between geometry and matter fields in lower-dimensional gravity, where quantum gravitational effects can be more pronounced. Such studies not only enrich our understanding of dilaton gravity and its string-theoretic implications but also pave the way for potential applications in simulating black hole phenomena in laboratory settings using analog models.