Quasibound states of charged dilatonic black holes

TL;DR

This paper analyzes quasibound states of massive scalar fields around charged dilatonic black holes using numerical and analytical methods, revealing charge effects and matching solutions for eigenfrequencies.

Contribution

It provides a detailed numerical and analytical study of quasibound states in charged dilatonic black holes, including charge effects on eigenfrequencies and solution matching techniques.

Findings

Numerical and analytical eigenfrequencies agree for large black hole charge.

Charge influences the real and imaginary parts of eigenfrequencies.

Analytical solutions match numerical results in high-charge regimes.

Abstract

Investigation of quasibound states of black holes is significant for expected ultra light particles, as well as black holes through gravitational waves. We first investigate quasibound states of a massive scalar field for dilatonic charged black holes via numerical analysis. We study the complex eigen frequencies of the massive scalar field in a wide range of gravitational fine structure constant $\mu M$ in detail, and show the effects of charge. Further, we study the eigen frequencies of the massive field through analytical approach by matching the near horizon solution and far field solution, and find its spectra for excited states by iteration method. We demonstrate the numerical solution and analytical solution perfectly agree with each other in the region where charge of the black hole is large, both for real and imaginary parts of the eigen frequencies.