Quasinormal modes in the field of a dyon-like dilatonic black hole

TL;DR

This paper investigates quasinormal modes of a massless scalar field around a non-extremal dilatonic dyonic black hole, revealing how these modes depend on coupling parameters and confirming the Hod conjecture in certain regimes.

Contribution

It provides the first analysis of quasinormal modes in a dilatonic dyonic black hole background with two scalar fields and verifies thermodynamic relations.

Findings

Quasinormal modes depend on a parameter a, linking to Schwarzschild and Reissner-Nordström limits.

The Hod conjecture holds for 0 < a ≤ 1 across all parameters.

Thermodynamic laws and Smarr relation are confirmed for the black hole solution.

Abstract

Quasinormal modes of massless test scalar field in the background of gravitational field for a non-extremal dilatonic dyonic black hole are explored. The dyon-like black hole solution is considered in the gravitational $4d$ model involving two scalar fields and two 2-forms. It is governed by two 2-dimensional dilatonic coupling vectors $\vec{\lambda}_i$ obeying $\vec{\lambda}_i (\vec{\lambda}_1 + \vec{\lambda}_2) > 0$, $i =1,2$. The first law of black hole thermodynamics is given and the Smarr relation is verified. Quasinormal modes for a massless scalar (test) field in the eikonal approximation are obtained and analysed. These modes depend upon a dimensionless parameter $a$ ($0 < a \leq 2$) which is a function of $\vec{\lambda}_i$. For limiting strong ($a = +0$) and weak ($a = 2$) coupling cases, they coincide with the well-known results for the Schwarzschild and Reissner-Nordstr\"om solutions. It is shown that the Hod conjecture, connecting the damping rate and the Hawking temperature, is satisfied for $0 < a \leq 1$ and all allowed values of parameters.