Study of the Superradiance Phenomenon in the $\alpha$--attractor Potential using the Log Derivative Method

TL;DR

This paper investigates superradiance in the $\alpha$--attractor potential by solving the Klein-Gordon equation with the Log derivative method, confirming superradiance presence and validating the approach against analytical solutions.

Contribution

It applies the Log derivative method to the $\alpha$--attractor potential, demonstrating superradiance and validating results with analytical solutions.

Findings

Superradiance phenomenon confirmed in the $\alpha$--attractor potential.

The Log derivative method accurately computes reflection and transmission coefficients.

Results agree with analytical solutions for the hyperbolic tangent potential.

Abstract

In this article, we solved the time--independent one--dimensional Klein--Gordon equation in the presence of $\alpha$--attractor potential using the Log derivative method. We calculated the reflection coefficient $\mathcal{R}$ and the transmission coefficient $\mathcal{T}$, showing that the superradiance phenomenon is present. In order to demonstrate the accuracy of our method, we performed a comparison with the analytical solution for the hyperbolic tangent potential.