The Exact Relativistic Scalar Quasibound States of The Dyonic Kerr-Sen Black Hole: Quantized Energy, and Hawking Radiation

TL;DR

This paper derives exact solutions for scalar quasibound states around a Dyonic Kerr-Sen black hole, revealing quantized energies and decay rates, and investigates Hawking radiation using these solutions.

Contribution

It provides the first exact analytical solutions for scalar quasibound states in the Dyonic Kerr-Sen black hole background, including energy quantization and decay properties.

Findings

Exact energy levels for massive and massless scalars are obtained.

The decay rates of quasibound states are characterized by the imaginary parts of the energies.

Hawking radiation spectrum and temperature are derived from the scalar wave functions.

Abstract

We consider Klein-Gordon equation in the Dyonic Kerr-Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein-Maxwell-Dilaton-Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field's governing equation, i.e., the covariant Klein-Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states's decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr-Sen black hole's apparent horizon, via the Sigurd-Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are successfully obtained.