Analytical studies of Hawking radiation and quasinormal modes in rotating linear dilatonic black hole

TL;DR

This paper analytically investigates Hawking radiation and quasinormal modes of rotating linear dilatonic black holes, revealing their unique temperature properties and stability characteristics through scalar wave analysis.

Contribution

It provides the first analytical solutions for scalar wave equations, reflection coefficients, greybody factors, and quasinormal modes in this specific black hole background.

Findings

Hawking temperature depends only on the background parameter and differs from surface gravity temperature.

The black hole exhibits instability for certain scalar perturbation modes.

Analytical expressions for reflection coefficient and greybody factor are derived.

Abstract

The rotating linear dilatonic black hole is an asymptotically non-flat solution to Einstein-Maxwell-Dilaton-Axion gravity theory due to the existence of non-trivial matter fields. We have analytically studied the wave equation of scalar field in this background and shown that the radial wave equation can be solved in terms of hypergeometric function. By determining the ingoing and the outgoing fluxes at the asymptotic infinity, we have found the analytical expressions for reflection coefficient and greybody factor for certain scalar modes. In the high frequency regime, we obtain the Hawking temperature by comparing the blackbody spectrum with the radiation spectrum resulting from reflection coefficient. It is shown that the Hawking temperature, which depends only on the linear dilatonic background parameter, does not agree with the temperature calculated from surface gravity. At last, the quasinormal modes of scalar field perturbation are presented, which shows that the rotating linear dilationic black hole is unstable for certain modes apart from the superradiant modes.